The following is the presentation I gave at GDC Austin '09.
In general, we tend to think of randomness in games as a bad thing.
Our sense of fiero or accomplishment at winning a game depends on the feeling that we have, in some sense, mastered it, and either that we out-played our opponents, or at least, in a soloplay game, overcame the challenges it posed by dint of hard work and skill. If, instead, we feel that we just got lucky -- or, worse, that someone else won even though we were obviously the smarter player, because they just got lucky -- we're likely to think less of the game.
But clearly many, many games have some random elements, and some are highly luck-dependent, and yet people continue to play them. What really is the role of randomness in games, and how can designers work to harness it to beneficial effect?
Magical Thinking
Randomness has been part of games since their earliest inception -- and when I say "earliest inception," I mean deep into the unwritten Neolithic past. Game scholars sometimes point to The Royal Game of Ur as the earliest known game, and in a sense it is -- but we also know of games from any number of Neolithic cultures that survived into the modern era, many of them documented by Stewart Cullin in a series of books for the Smithsonian, published in the early 20th century.
The simplest games, variations of which exist in innumerable cultures, are what Dave Parlett (in the Oxford History of Board Games) calls race games, and what others may think of as track games. Lines are drawn in the dirt with sticks to represent the spaces of the game. Binary lots -- cowrie shells, acorn cups, almost anything that can fall easily on one side or another -- are tossed. Some simple algorithm is used to determine what a particular number of up-lots versus down-lots means; players advance their tokens along the track in accordance with the lots thrown. The first player to reach the end of the track wins.
Needless to say, games of this type exist in modern cultures too, many of them deriving directly from Pachisi, an ancient and popular game in India: Parcheesi, an American commercial variant; Ludo, a British commercial variant; Sorry!; Trouble; and so on. Typically, these games add some element of strategy -- blocking, sending pawns back to start, etc. -- but the line of descent -- from track games that seem to exist in almost every Neolithic culture to modern Pachisi variants -- seems clear.
For Neolithic cultures -- and for some people in modern society too -- randomness is not merely a feature of gameplay: It has a magical, in some cases religious aspect. A random test is viewed as divinatory.
In reality of course, "luck" is not an external force. Randomness is randomness, and nothing more; in a sequence of random tests, occasional streaks will show up, but there is no real significance to this fact. It's simply how randomness happens. It's not a consequence of mystical forces.
Ancient cultures, of course, had no concept of statistics, and humans by nature tend to find patterns in things and ascribe meaning to those patterns even when there is none. Hence the very concept of "luck."
The Romans played dice games not merely for the thrill of gambling -- but also as a means of testing their favor with the Gods. Many Neolithic cultures use binary lots or other forms of random number generation as a means of divination, ascribing predictive value to the results. Very likely, track games arose not as entertainments, but as a means of recording the results of a series of divinatory casts. And Cullin documents a number of cases in which games are used by Neolithic cultures as part of their religious practices.
And even today, some people continue the practice: the Ching is a "oracle" consulted via the throw of binary lots, the Tarot uses randomly selected cards in divination. They are not games in themselves, obviously, though games have certainly been devised that use the Tarot deck, and one could, I suppose, make a game of the Ching if you so wished. Though if you take the Ching seriously, I suppose you might be reluctant to mock it thusly.
In the French noir movie Bob le Flambeur, the protagonist, who is a professional gambler, keeps a slot machine in his hall closet. Before going out each day, he inserts a coin and operates it once. If he wins, he considers that he is "lucky," and cheerfully goes off to a day at the casino. If he does not, he finds something else to do with his time. As did the Romans, as do Neolithic cultures, he is using a game for divinatory purposes, and ascribing a magical aspect to its results.
Most of us, of course, scoff at the notion that there is anything significant about the outcome of random tests. And that perhaps is the main reason why serious gamers, at least, tend to view games that are excessively luck-dependent as poor games by nature; unlike primitives, or the superstitious, we see no significance to the outcome of random processes, and therefore no sense of triumph at winning a luck-dependent game. We do not have the favor of the gods, the mystical forces of nature are not aligned in our favor, it is not an omen that our endeavors today will likewise be met with triumph. It was just a game, over which we had no real control, and therefore not a very interesting one.
Skill vs. Chance
The law, at least, divides games into two categories: games of skill and games of chance. Games of skill are always legal. Games of chance, if played for money, are generally illegal, because gambling is viewed as an addictive and destructive vice. Although if that's true, it's hard to reconcile government's suppression of gambling with the promotion of government lotteries; a libertarian would say that government suppresses other forms of gambling because the state doesn't like competition. But perhaps a more accurate statement would be that we have, somewhat confusedly, adopted toward gambling the attitude that some people think we should also adopt to other vices, like recreational drugs and prostitution: People are going to gamble whatever you do, so better that we permit gambling but tax and control it carefully, to limit the damage it does and to prevent organized crime from earning the proceeds. In this light, advertisements for the lottery are an example of a somewhat confused government, part of which wants to limit gambling and part of which wants the revenue it generates.
Just as government is confused about whether it wants to restrict or promote gambling, however, government is also confused about what gambling is. Games like Roulette or Craps (at least when played with honest wheels and people who don't try to manipulate the dice) are indeed pure games of chance, but the same is not true even of all casino games. Blackjack has at least some element of skill, and some Poker players will tell you that their game is absolutely a game of skill. (The claim is, however, not entirely true, as I'll explore later.) And some forms of gambling, such as betting on the horses, are almost entirely a matter of skill.
Horse racing bookmakers use what's called a parimutuel system of betting. In a parimutuel system, the posted odds are dynamically adjusted as bets are made. By contrast, in a game like Roulette, the house earns its money by having some numbers on the wheel (0, and in some cases 00) that do not fall under the conventional bets of even/odd and black/red; and the payoff for betting on a single number (36-to-1) is lower than the actual number of slots on the wheel (37 or 38). Consequently, over repeated spins, the house is guaranteed to come out ahead.
In a parimutuel system, however, the house simply ensures that, regardless of how the horses come in, the total payout, based on posted odds and bets received, will always be smaller than the amount of money bet. As new bets come in, the posted odds are dynamically adjusted. Consequently, the house doesn't care if one bettor is a better "player" of the horses than another, or has some scheme that lets them consistently win; the house's rake is guaranteed.
In fact, it's possible to make a living betting on the horses, and some people do. It isn't easy; it requires a lot of work, and considerable self-discipline. The way to do it is to study the horses, pore over statistics of their performance, learn which do well or poorly in different track conditions, and then pay careful attention to the posted odds. Most bettors are naïve, and will not have the same expert knowledge as you; consequently, you will have a better sense of the likelihood of different outcomes than they, and when a spread opens up between the posted odds and your actual expectation of outcomes, you can take advantage of that by betting against the mass of naïve bettors. It's a form of arbitrage, in other words.
In truth, the outcome of a horse race very rarely depends on chance; it depends on the characteristics of the horses involved, and the condition of the track on which they run, and perhaps more subtle variables; but, pace quantum mechanics, it takes place in the Newtownian phenomenological world, and a sufficiently advanced student of the horses can win consistently, because posted "odds" are not based on actual odds, but on the pattern of betting.
The only element of chance that intrudes, really, is that unexpected events can happen in a universe as complicated as ours; thus, a horse can stumble and fall, say. This isn't 'chance' either, of course, but it's the kind of event that no student of the horses can anticipate -- it's the sort of thing we'd simulate in a game by introducing a chance element.
The common dichotomy between "games of chance" and "games of skill" therefore is something of a false one; there are pure games of chance (such as Roulette) and there are pure games of skill (such as Chess), but almost everything else is some mixture of the two.
Different Aesthetics
Different games appeal to different aesthetics. People who love story-driven Japanese CRPGs will tell you how much they loved the story of Final Fantasy X, while others, blind to this genre, will characterize the game as "interminable cut-scenes separated by boring and repetitive gameplay." A more broadminded gamer may see truth in both viewpoints -- the Final Fantasy games do provide interesting characters, well-written stories, and gorgeously-rendered cut scenes, and players do come to care about the characters surprisingly deeply; yet there's far less variation in moment-to-moment gameplay, and in terms of strategy and puzzle-solving, than in almost every other game genre. Final Fantasy X is a wonderful story, and is also characterized by dull and repetitive gameplay between story elements.
Part of my objective in general is to foster the aesthetic of a "broadminded gamer," able to see what people find appealing in any game; but that's because I'm a game designer and pretentious "ludeaste" (a word I just coined by analogy to cineaste). Most gamers prefer to find games that they like, and often look down on ones they don't, even if enjoyed by others. My games rock; your games suck, and never the twain shall meet. If you don't like Final Fantasy, you're obviously an idiot, or conversely, sucked in by the story and don't really understand what games are really about. This is a short-sighted view.
But to return to the question of randomness, in light of the idea that there are different, and equally valid, aesthetics of "the game." One sort of game aesthetic says: Games should be won by skill and not luck. Hence any recourse to randomness by a game is bad.
Curiously, it's an attitude held by two sorts of gamers who otherwise have very little in common: Fans of abstract strategy games, and fans of first-person shooters.
To an abstract strategy gamer, games like Chess and Go are the n'est plus ultra of gaming: mechanically simple but strategically profound. You can, and people do, spend a lifetime studying and mastering these games. To a serious abstract strategy gamer, a game like Risk is a trivial and even appallingly stupid waste of time, a mere die-rolling exercise; and even something like Backgammon, a game of no little strategic depth in its own right, is inherently suspect, and inferior, because of its reliance on dice. The ideal is a game that pits mind against mind in a clean contest of strategic planning and anticipation of the opponent. Anything that involves even the slightest degree of randomness is inferior, because victory should come through mastery of the game and superior play. The notion that someone might win through luck is almost repulsive. Never mind the fact that factors external to the game itself, such as one player's third margarita the night before or another's existential despair over the affair her husband is having might affect their quality of play; within the magic circle itself, everything should be pure.
Similarly, for an FPS player, winning a deathmatch involves mastery of the interface, perfect knowledge of the level layout and the location of spawn points and power-ups, and superior knowledge of (and ability to perform) tactical tricks of the trade, such as the bunnyhop and the rocket jump.
Chess is about as different a game as you can possibly get from Quake: one is a game of mental domination, and the other a "twitch" game, a game that depends almost entirely on the mastery of a limited set of physical skills.
No Chess player ever leapt from a board shouting "Woot! Ph34r my l33t sk1llz!", and "pwned" is not likely to become synonymous with "checkmate" anytime soon. Yet Chess players, too, prefer to feel that it is their "l33t sk1llz" that bring victory, not any random element.
Gamers often divide games into two categories by the type of skill they require: "player skill" games, like Counter-Strike, depend on physical mastery, while "character skill" games, like Final Fantasy, depend primarily on the characters' stats and the player's choice of special actions to determine outcomes. To a serious FPS gamer, character skill games are obviously inferior; all they take to win is perseverance, while player-skill games reward those who work to master the gameplay.
And yet, if you look under the hood (that is, at the source code) you'll find that weapon damage in FPSes is partly random; typically, weapons do some set amount of damage (X) plus some additional amount of damage determined randomly and linearly between 0 and another factor (Y).
This fact isn't normally perceptible to players, who may assume that any variation in damage is a consequence of variation in accuracy or range; and indeed, in actual play, the randomness of FPS damage has little impact on ultimate outcomes. Except perhaps in very marginal circumstances, it's not enough to let an inferior player beat a superior one. Nor is it particularly clear why id (Quake's developer) felt it necessary to make variable damage part of the game: in the soloplay game, most monsters are killed with a definable number of shots from particular weapons, and the randomness isn't enough to cause any surprises; in deathmatch play, there's enough variability in a system of chaotic fireplay to prevent a non-random system from becoming dull. I suspect the random element of damage derives not from a conscious design choice, but from an unconscious and automatic adoption of a game mechanic -- variable weapons damage -- that stretches back into the tabletop roleplaying and miniatures gaming prehistory of the videogame.
But miniatures gaming, certainly, and tabletop roleplaying, to a lesser degree, need a degree of randomness to sustain player interest. Why might that be?
Value in Simulation
Let's start by examining Little Wars, H.G. Wells's landmark miniatures rules, the first commercial rules published for gaming with toy soldiers. It does not rely on chance, at least on the surface. Infantry may move such-and-so many inches per turn, cavalry somewhat farther, artillery less far. Melee combat is resolved according to a simple, non-random rule: if the two sides are equal, everyone on both sides dies. If unequal, the inferior force is eliminated, doing damage to the inferior force according to this formula:
Thus, if the inferior force has 4 units, and the superior one 6, the superior force loses 2 units: doubling the inferior force gives us 8, and subtracting the superior force of 6 produces 2.
No randomness here.
Artillery fire is, however, resolved in a different way. The rules to the game assume that both players have what Wells describes as "spring breech-loader guns." You slide a stick into the cannon, depress the spring, and aim the cannon, then release the stick. If it strikes an opposing figure, that figure is lost.
It seems clear to me that without this second rule, for artillery, Little Wars would be a very dull game indeed. If melee combat was all it permitted, you could almost predict before play begins who would win: The side with the greater strength, of course. Only poor play by the superior side, or brilliant play by the inferior one, could prevent that outcome.
Artillery changes the equation, however. It's still non-random, in the sense that the effectiveness of your artillery depends on your ability to aim it, your feel for the power of the cannon's spring, and of course your ability to maneuver your troops to leave clear lines of sight from your cannon to opposing units. But all of these are tricky things, not as cut-and-dried as the rules for melee. In the Newtonian universe, they are not random elements -- but they provide, in this context, the sort of variability of outcome essential in any true wargame.
Why do I say that variability of outcome is essential in a wargame? For a simple reason: wargames are supposed to be simulations. They are supposed to represent, with greater or lesser fidelity, a real or hypothetical military conflict. There has never yet been a general who can confidently predict the outcome of battle.
Part of the reason for that is, of course, fog of war; at the inception of battle, both sides generally don't really know how strong the opposing side is (something few games do a good job of simulating). But even if they knew what they were up against down to the last man and piece of equipment, they could not be certain of the outcome. So much is dependent on the actions, or failures, of individual men on the field; so much on vagaries of weather and lighting; so much on improvisational genius or confusion and sloth.
As von Moltke says, "No battle plan survives contact with the enemy." The phenomenological world may be Newtonian, and hence in principle calculable, but thousands of men in desperate struggle is a messy, incalculable situation. "For want of a nail, a kingdom was lost" -- an extreme statement of the situation, but illustrative. You can't know; all you can do is plan, take your best shot, and hope things work out.
"Alea jacta est," Caesar said as he crossed the Rubicon, leading his army to Rome in defiance of the orders of the Senate; the die is cast. Surely he thought he had the power to triumph, as he ultimately did; but he knew also that he was taking a huge risk. As in Poker, military command is a matter of minimizing risks and making the best bets you can -- but as in Poker, you cannot be sure of the outcome.
To properly simulate war, therefore, unpredictability is essential, and the easiest way to ensure unpredictability is to harness the power of randomness; like Caesar, we cast the die, in our case to simulate the impact of all the multifarious factors that no commander can control.
In other words, a wargame that contains no random elements is, by nature, a poorer simulation than one that incorporates randomness. Accuracy, or at least verisimilitude -- the feeling of accuracy -- is essential to the aesthetic of the wargame: When playing a simulation of the Second World War, we want it to feel like the war, to feel that as commanders of one side or the other, we're making decisions about what to do that were within the realm of possibility for the opposing sides. If things happen that strike us as ludicrously infeasible -- like, say,
Sweden conquering Russia in 1943 -- then it's clear that the game is flawed. To a wargamer, at this point it doesn't matter whether the game system is strategically deep, or provides an interesting narrative, or satisfies any of the other aesthetic criteria that some bring to games: it's a bad game, because it's a bad simulation, and for a wargamer, value as a simulation is a major part of his aesthetic.
The notion that randomness is bad is an aesthetic one, and appropriate to games characterized a spartan commitment to pure strategy; but that is only one valid aesthetic lens. A wargamer might, in fact, consider a game like Chess too dry, too moldy in antiquity, and ultimately uninteresting because of its lack of color, aesthetically unsatisfying because of its severe divorce from anything real. It simulates not, neither does it spin (the dice).
The use of chance as an element in heightening the realism of a simulation isn't unique to wargames; indeed, almost any game that purports to simulate real world phenomena uses chance to a degree. In Roller Coaster Tycoon, when one of the little people wandering about your theme park completes their current action, the game chooses a new action for them to perform that is partly dependent on the character's current stats and partly based on a random factor. In SimCity, the paths taken by individual "sims" through the city are determined semi-randomly. In Kremlin, whether or not one of your geriatric Politbureau members dies this year is determined by a die-roll. Just as war is too complex to simulate accurately through an entirely non-random system, so are almost all real-world phenomena, at least addressed at a high level, and thus a degree of randomness increases the simulation's fidelity.
When Chance isn't Random: Regression to the Mean
In reality, the reliance by games on chance does not necessarily mean that the game's final outcome is random. In a game with chance elements, there will typically be dozens or hundreds of random tests over the course of the game -- many, many times in which dice rolled, or an algorithm that uses a random number as an input applied.
Paradoxically, the greater the number of random tests, the less effect chance has on the outcome. Over time, random systems regress to the mean.
Consider a single die-roll: there is exactly a 1/6th chance of each possible result. Now consider a 2D6 roll (that is, rolling two six sided dice and summing the numbers rolled): There is a 1/6th chance of rolling a 7, but only a 1/36th chance of rolling a 2 or 12. A single die-roll produces a flat curve, with all outcomes equally probable; a 2D6 roll produces a bell curve, with numbers toward the center of the curve more probable, and the extremes less likely. Adding more dice increases the sharpness of the curve.
In other words, the more random tests, the lower the likelihood that the outcome will be at one extreme of the bell curve, and the more likely that it will be near the center.
Suppose that the outcome of a game is based on a single random test that can go either way -- 50/50 odds. In this case, I will win 50% of the time, and you will win 50% of the time. The outcome of the game is purely random.
Let us suppose instead that, over the course of the game, we have 100 random, 50/50 tests -- but in addition to those tests, there's an element of strategy -- in a wargame, the element of strategy might depend on choosing where and how to maneuver, taking advantage of terrain, deciding where to follow up success and where to retreat, and so on. Over the course of the game, the likelihood is that I will win roughly half of those random tests, and you will win roughly half. It's possible, though highly unlikely, for me to win every one, and therefore the game, purely by luck. It's far likelier that the random tests will give no player any strong advantage, and that instead, strategy will dominate -- that victory will, as in a purely non-random game, go to the superior player.
Or to put it another way, if a game contains even a small element of strategy, then as the number of random tests approaches infinity, the outcome of the game is more and more likely to be dictated by strategy than by chance. The point at which strategy begins to dominate over randomness depends on how much effect strategy has -- in a game where random elements are small and strategy vital, strategy dominates with even a handful of random tests, while if strategy is a relatively modest dictator of outcomes, then many random tests are required before strategy dominates.
But the net effect is clear: in a game that relies on chance to some degree, has many random tests, and also has highly strategic elements -- typical of all sorts of simulations -- the outcome will only in very rare cases be dictated by chance.
Mind you, this analysis presupposes that each random test has roughly the same impact on the game as every other such test; there are cases when this is very much untrue. It might be that a handful of random tests are critical. As an example, in Jim Dunnigan's Empires of the Middle Ages, the players' success is critically affected by the military, administrative, and diplomatic capabilities of their monarchs, each represented by a number from 1 to 9. When a monarch dies -- which happens only a handful of times during a game -- the new monarch's stats are randomly generated. Being lucky in monarch generation is so important that it overwhelms almost every other factor of the game; strategy still plays an important role, but if one player has a 9-9-9 monarch for most of the game, he's very likely to win, almost no matter what the other players do.
Dunnigan would doubtless argue that in this regard, Empires is an accurate simulation of conditions in the Medieval era, that the characteristics of monarchs were critical to their nations' success or lack thereof; and indeed, the color and historicity of the game are sufficient to make the game enjoyable despite its largely random path. But considered as a game qua game, as opposed to a simulation, this is undeniably a design flaw: if you have bad luck, it's frustrating to play, and if you have good luck, it's hard to feel a sense of accomplishment at winning.
Empires is, however, an outlier in this regard; most wargames are consciously designed to take advantage of regression to the mean, in order to preserve the simulation value of randomness in a military context, while also ensuring that the game remains strategically interesting to the players.
The point remains: the criticism by strategy-purists of games that involve some degree of chance is not wholly valid, not only because random tests can improve other aspects of the game, such as fidelity of simulation, but also because if chance is used sufficiently frequently, and with sufficient care, strategic elements will still dominate outcomes. Thus, strategy and not luck will remain the most important factor in play.
Poker: Strategy as the Epiphenomenon of Randomness
Poker is a perfect illustration of this point. On the surface, Poker appears to be an entirely random game: cards are allocated randomly, and the best hand wins. Hard to get more random than that.
Of course, we've described only two of the game's mechanics: card distribution, and hand comparison. What transforms Poker from a random game to one that is highly dependent on player skill is, for the main part, one thing: betting strategy.
Versions of Poker vary, but in all cases, there are multiple rounds of betting before hands are revealed. Each round, some information is revealed to the players; in Draw Poker, after one round of betting, players may discard some cards and request more, and the number of cards discarded by your opponents gives you a bit of a clue as to what they hold. In Stud, cards are dealt out to the players each round of betting, with some displayed face-up. In Texas Hold'Em, "community" cards that are shared by players are revealed over several betting rounds.
Thus, in all cases, players gain information during the hand that, while imperfect, gives them some sense of the odds. They know what they have, they have some clues as to what the other players may have, and they can drop out after any round of betting. And of course, there's also the information provided by the facial expressions and body language of the other players.
The trick, then, is to minimize your losses when the cards are against you, while maximizing the pot when you have the cards. One typical strategy is "fold early, and bet aggressively;" don't hold onto weak cards, and if you have a strong hand relative to what you see on the table, work to maximize your potential win.
Let us imagine a game between several average players and one superior player -- a player who knows the odds backwards and forwards, and reads other players well. If only one hand is played, the outcome of that hand -- in terms of who wins -- is wholly random. The flow of money in that hand is not; in all likelihood, the superior player will fold early on a weak hand, and ramp up the betting to win substantially on a strong one. That's only "in all likelihood," however; the superior player could have a Flush (an excellent hand in most versions of Poker), bet aggressively, and still be beaten out by an inferior player who, this hand, just had the luck to get a Full House. In a single hand, the superior player has an advantage, but the advantage is modest.
Poker is almost never played for a single hand. It's typically played for many hands in succession. The superior player's edge in a single hand is modest, but over time, that modest edge means that, all things being equal, the pile of chips in front of him will grow, while the piles in front of the other players will shrink.
Random tests regress to the mean. The superior player can be beaten by luck over a small number of plays, but over a lifetime of play, he will dominate.
As with the horses, there are people who make their living playing Poker, and as with the horses, doing so requires work and commitment, and either the ability to calculate odds quickly on the fly, or a strong gut feel for odds learned by long-time play. In this regard, Poker players and racetrack bettors rely on something very similar: for the horses, the arbitrage opportunities opened up by naïve bettors in a parimutuel system; for Poker, the opportunities created by the inferior strategies of more naïve players.
Is Poker a game of skill or chance? If Roulette is the measure, it is unquestionably a game of skill. Yet even in, say, a typical Texas Hold'Em tournament, with a single buy-in and a relatively limited number of hands, a perfect player can still be defeated by the luck of the draw. Poker is a mix, but over the long term, strategy beats luck.
And, please note: the strategy of Poker is based on its randomness. Without random card allocation, it would be an entirely different, and inferior game. The strategy of Poker lies in understanding the statistical nature of the game, and managing statistical outcomes. That's true, to a lesser degree, of many other games that rely on random factors; in a board wargame, for example, you always know the probabilities of different outcomes before you commit to an attack. But Poker is almost unique in its pure reliance on probability as the creator of real strategic depth. Poker in particular belies the abstract strategy gamer's idea that randomness is in opposition to strategy: in Poker, strategy is an epiphenomenon of randomness.
Randomness as a Way to Break Symmetry
Chess and Go, the abstract strategy games par excellence, are almost perfectly symmetrical: both players have equal forces, with equal positions and equal capabilities. The only element of asymmetry is their turn-based nature, which gives one player a turn-order advantage -- in both of these games, the first player has a slight advantage, but in some other games, the last player, or some other player in the order, may have some advantage.
Symmetry, at least in terms of starting position, is common, though not universal, in virtually all games that involve two or more players. In multiplayer games, players prefer to feel that they begin on a level playing-field, and the easiest way to ensure that they do is to start them off equally.
Symmetry is also a real danger in any game design. Symmetry can lead to a host of ills. Symmetry works in Chess and Go because these are games of enormous strategic depth, and symmetry is quickly broken by the moves or placements of the players.
Contrast this with John Nash's Hex or Alex Randolph's Twixt (which, despite minor variations in tessellation and play, are extremely similar games). The object of both games is to build a connected line from your side of the board to your opponent's, with the opponent trying to do the reverse, with neither player able to play through the other player's line.
At first, this may appear interesting, but in actuality, the game has an optimum strategy -- a fact mathematically proven up to 9x9 Hex grids. Given optimum play, the first mover wins. The problem with Hex is that it has nothing like the strategic depth of Chess or Go; symmetry never gets broken.
Games in which all players pursue the same strategy result in a win by the player who makes the fewest mistakes -- or, if none, by the player who has the player-order advantage.
This is dull.
To make a symmetrical game interesting, you need to break the symmetry as quickly as possible. You need to put the players into somewhat different positions, so that they have different concerns to think about, and different strategies to adopt. Chess begins symmetrical, but with a single exchange of moves, it begins to open up; your first pawn move opens a line of potential attack for a bishop, while my first move signals a potential castling. Immediately, it's a different game.
Chess can pull this off because of its strategic complexity. Chess has been refined over centuries, pondered by millions of minds. Good luck to you in devising a game of equivalent depth.
How else can you break symmetry? One way is by providing slight asymmetry in starting positions. Puerto Rico does this by having different players start with different plantations, and by forcing players to adopt different actions each turn. But one easy way to break symmetry is to provide a degree of randomness -- and in fact, almost every Eurogame does so.
This seems paradoxical on the face of it: the Eurogame aesthetic prizes strategy and disparages luck, and yet at the core, many games in the genre depend on some degree of randomness.
In Settlers of Catan, for example, new players are advised to set up the board as per a diagram in the rules that provides a balanced, symmetrical arrangement of terrain -- but more advanced players are encouraged to lay out the board in a random fashion. Discs with different numbers are distributed semi-randomly across the board's hexagonal tessellation, and dice are rolled each turn, and compared to those numbers, to see which areas produce resources. The players begin with symmetrical resources, but the asymmetry of the board, coupled with the random nature of resource production, quickly produce asymmetries as players settle different areas of the board.
Or consider Torres, which at heart is a purely symmetrical abstract strategy game -- but breaks the symmetry by giving players "action cards," each of which provides some special benefit. Different players hold different action cards, and the opportunities they offer therefore provide them with an incentive to adopt slightly different tactics during play, opening up what would otherwise be a pretty dull game.
Similarly, in Ticket to Ride, players begin with a number of "route" cards, and the victory points they earn mainly (though not exclusively) come from completing routes (e.g., New York to Los Angeles). Played without the route cards, Ticket to Ride would be a dull exercise in trying to complete the longest rail lines first; with the route cards, each player is striving for different objectives in an asymmetrical landscape, and therefore the game has far greater strategic depth.
The danger with the use of randomness as provider of asymmetry is that the game becomes too chance-dependent, which in a genre like the Eurostyle is a flaw, since the aesthetic of the genre prizes strategy and planning. There are, however, three ways to harness the virtues of randomness without falling into the trap of allowing randomness to determine the winner: Regression to the mean, as we've discussed; ensuring that random elements are "balanced;" and ensuring that random elements face all players with the same opportunities.
Let's start with "balance," a term I used advisedly: it's an awkward term to use, because "balance" can mean many different things in the context of a game, depending on exactly what you're talking about. In this context, what I mean is that if randomness is used to open up different possibilities to different players, thereby fostering different approaches to the game, but if all opportunities opened up are of roughly equivalent game value, then the random element does not unbalance the game, that is, make it luck-dependent.
As an example, the action cards in Torres allow players to do different things but, at least a priori, none of the actions they permit is obviously better or worse than the others. In addition, to draw a new action card, a player must forgo taking some other action in the game, so the question of whether or not to draw a card becomes a strategic concern. Chance is not entirely eliminated through this scheme, however; in a particular strategic situation, drawing a new action card might provide you with an ability that is precisely what you need at this moment, or something that is of no immediate benefit -- and so luck continues to play a role.
The route cards of Ticket to Ride, and how they have evolved over the course of the game's expansion, are particularly interesting here. In the original game (set in North America), your original draw of route cards has a huge impact on your likelihood of winning or losing. If you have cards that involve nice, high-value, long-haul routes that overlap to a high degree, so that you can complete them with a relatively few number of rail car placements, you are likely to win. Conversely, if you are stuck with short-haul routes in the central US that do not lay the groundwork for later long haul successes, you are most likely screwed.
Alan Moon, the game's designer seems to have recognized the problem here; subsequent versions of the game, such as the European board and the "Mega Game" that replaces the original North American card set, are designed to ameliorate the problem. On the European board, all players are guaranteed one long-haul route with their initial route cards; and the Mega Game provides players with a choice of more cards initially, making it less likely that you will be stuck with duds, while also giving bonus points to the player who completes the most routes, providing more benefit to the short-haul route cards. Both games are far more balanced, in the sense that initial card distribution is less likely to determine the outcome.
The concept of "balance" in this context assumes that the game's random elements apply to individual players; but it is possible to have random elements that offer the same opportunities to all players. Think of these elements as akin to the weather; you and I are equally subject to the rain.
Consider Reiner Knizia's Medici; in this game, competing Medieval merchants bid on lots of luxury trade goods. At the beginning of each round, counters representing the trade goods are placed in a cloth bag. On his turn, a player draws between one and three goods from the bag, and these become a lot on which all players bid.
Clearly, there's a random element here, because goods are drawn blindly, that is, at random. Yet all players are bidding on the same lot of goods; the distribution of goods does not, in itself, offer any immediate advantage or disadvantage to any player. Though this is random, the randomness does not in itself have any immediate impact on the game's outcome.
In Medici, you earn points both for the raw value of the goods that are shipped -- but also for shipping more goods of a particular type (say, spices) than other players. This is, in fact, how Knizia breaks the symmetry of an otherwise perfectly symmetrical game with perfect information: different goods suddenly become more valuable to you than others, because you have previously purchased or shipped goods of a particular type. But this in itself is not chance dependent -- it depends purely on your decisions, that is, on what lots you bid on.
Randomness isn't being used here as the key way to break symmetry -- Knizia does that with his scoring system. Instead, randomness is being used to ensure that players cannot predict what goods will be auctioned next, and to ensure that each auction is likely to be somewhat different from the previous one, thus preventing the game from becoming static and predictable.
In summary, adding a random element to any game creates a risk that the outcome will depend on luck rather than strategy; but it also helps to break open a symmetrical game, which is essential to prevent it from degenerating into strategic gridlock.
Too, designers can adopt strategies to minimize the impact that luck has on outcomes, such as balance among random elements, exposing all players equally to random elements, and/or regression to the mean.
Leveling the Playing Field
In children's games, in particular, randomness is often used as a way of leveling the playing field -- that is, of ensuring that everyone has an equal chance of winning, regardless of age or skill.
Please note that we're talking about yet another game aesthetic here: for most styles of games, and for most gamers, the idea that everyone should have an equal chance of winning regardless of skill is tantamount to saying "this is barely a game." You might as well roll a die to see who wins. Why even play?
Suppose, however, that you are a parent with a small child, with whom you want to play a game. You could choose Chess, I suppose, but unless you purposefully play badly, you will beat your child every time. And very likely, will wind up trying to comfort a crying child who will never, ever, want to play a game with Daddy again.
Consider Snakes and Ladders, a classic and centuries-old game of childhood (popularized in the US as the commercial title Chutes and Ladders). Everyone begins at square 1, and strives to reach square 100, in a 10x10 matrix of squares numbered sequentially. Each turn, you roll a die (or use a spinner), and advance your token as many spaces as the number generated. At various points on the board are "snakes" (or "chutes") that cause you to slide from one square to a lower one -- or "ladders" that cause you to advance from one square to a higher one. The first to square 100 wins.
A moment's thought will show that there is no strategy to the game; the outcome is purely dependent on chance. This fact is not readily apparent to a small child, however, who may well experience a moment of fiero when landing on a ladder, and momentary annoyance when landing on a chute -- and will be gleeful if and when she beats her Dad.
From the perspective of an abstract strategy gamer, say, Snakes and Ladders is nugatory, a degenerate game, not worth the time to play. But it is actually perfectly suited to its niche in the ecosystem of games. Playing Snakes and Ladders, a child learns how to take turns, make moves, experience some of the emotions that games evoke, gains practice with counting -- and also learns to internalize the "magic circle," the idea that what happens in the game stays in the game, that you strive to win but loss has no consequences external to the game and is therefore not to breed ill feeling.
Examine almost any halfway decent game designed for small children, and you'll find the same factor at work. Candyland, 3D Labyrinth, and the innumerable forgettable licensed "track" games that appear each year are all, in the final analysis, dependent wholly on luck. And even games aimed at slightly older children are generally mostly a function of luck, thought they start to add strategic options: Go Fish, Sorry, Uno, Parcheesi, and Ludo all have minor strategic elements, but luck is the main determinant of outcome.
Even in sophisticated games, the use of randomness as a leveling factor has a role to play. Poker is a good example here. Every Poker player knows that better players win more over time -- but also know that, this hand, you have some shot at winning, even if you're not one of the elite. The game's randomness doesn't level the playing field entirely, as it does in Snakes and Ladders, but it does given you a reason to play, and a hope of winning, even if you are not a studious master of the game. The leveling nature of randomness, for Poker, serves a highly important function, and one that sophisticated players of the game prize rather than despise: It keeps the suckers playing.
Wild Cards
B-17: Queen of the Skies, a long out of print game from Avalon Hill, simulates the military career of the crew of a single B-17 bomber engaged in repeated raids over Germany during the Second World War. As a game, it is a little more than a series of tables on which the player (it's a single-player game) rolls dice. Dice are rolled to determine the player's mission, what opposition in terms of German fighters, flak, and so on the crew faces during the mission, the effects of combat with enemy fighters, how successful the aircraft is in damaging its targets during bombing runs, which crew members get killed or injured, and how badly, and so on. There are almost no decisions to be made, just dice to be rolled. It sold relatively well during its lifetime (by board wargaming standards).
Part of the reason for that was undoubtedly that there are very few solitaire board wargames (a mainly two-player genre); but part of it was that B-17 was, in its own weird way, fun to play. There was some enjoyment to be gained by rolling the dice and seeing what came next.
Interestingly, I don't think a digital adaptation would be remotely popular; you'd just click "next" and see the next event. The process of operating the game system, of physically rolling the dice and looking up the results, felt something like gameplay, even though it wasn't, really. The mechanization of resolution that digital games provide would make the underlying dullness of the game obvious.
B-17 is an example of randomly-generated algorithmic content. What made it (mildly) interesting was that interesting stuff happened in the game -- even though your ability to respond to or manage that stuff was, well, essentially non-existent.
I'm not holding it out as an example of good game design; it's not. But it is a good demonstration of another utility of randomness: providing variety of encounter, a mechanism for letting "interesting stuff happen."
As an example of digital games with something of the same dynamic, consider Rogue-likes. Rogue-like games are single-character, hack-and-slash, dungeon-crawling RPGs in which almost everything is randomly generated. Each level of the dungeon is laid out according to algorithms that rely on a random seed; the level is populated with monsters and treasure generated by tables referred to with a random index. Almost nothing is "level-designed," in the sense of most digital games, though some Rogue-likes, such as NetHack, intersperse a handful of levels with designed elements among the randomly-generated ones.
Rogue-likes are highly luck dependent; you are often faced with hordes of monsters, or other problems that you cannot overcome, and can contrariwise (though not often) gain some key magic items that let you advance quickly. But they are far from devoid of strategy; they're turn-based, and every turn you typically have a choice of a wide variety of actions -- not just the usual movement and attack, but things like using spells or potions, praying to your god, locking doors behind you, and so on. There are a host of tactical tricks to learn, counters to special monster abilities, and so on. If the mark of the superior strategy game is that it makes you stop and think about your next move, then Rogue-likes qualify -- even though they are so heavily luck-dependent.
In exchange for accepting an almost perverse level of chance, Rogue-likes offer an almost unparalleled level of variety. Because they are randomly generated, no two play sessions are identical. They typically have dozens or hundreds of different monsters, magic items, and other capabilities, and quite often dozens of "verbs," actions the player may trigger. Some of the more involved Rogue-likes, such as NetHack, contain so much rococo detail, handle so many unlikely possibilities, that even after years of play you may discover new features. As an example, in NetHack, if you toss a ring down the sink, the sound the sink makes in response may give you a clue as to what that kind of ring does -- one of NetHack's innumerable coders (it's a long-standing open-source project) having a bit of fun, there.
Obviously, you cannot play a Rogue-like with the kind of seriousness that a Chess master brings to that game; no matter how experienced a player, the next corner may bring you face to face with instant death. It requires a sort of cheerful resignation, a willingness to enjoy the often humorous ways in which you die ("gnawed to death by rats on level 17 while paralyzed").
Despite the randomness of the game, the sheer variability it offers means that it is infinitely replayable. Games like Diablo -- a commercial, graphical dungeon-crawler, similar in many ways, but with designed levels -- is hardly worth playing more than once. You might try it a second time with a different sort of character, but the challenges and story elements will be the same. By contrast, NetHack is one of only two games that has been on the hard drive of every computer I've owned since I first encountered in. (The other is Civilization.)
There's a lot to be said for sheer variety of encounter, and random shuffling of game elements is perhaps the easiest way to provide it.
So. Randomness: Bane or blight? It all depends. If randomness dictates outcomes, many players will find the game unsatisfying. But there are times when a degree of randomness plays an important, and useful, role in a design.
thanks!
Excellent, thought-provoking post. More like this, please!
Another point that strikes me in relation to randomly-generated content in videogames (a la Nethack) is that it can relieve the developer of a lot of work - rather than having to create enough content for 40+ (or whatever) hours of gameplay, he or she creates a set of procedural rules for the game itself to create content on the fly, which, if you're clever enough, is less time-consuming.
I first encounted this point in an interview with one of the guys from Introversion - he explicitly said that the reason that all Introversion games have featured, to a greater or lesser extent, procedurally-generated content, is because Introversion is a small, independent team working on a low budget, and procedurally-generated content is the only way they can provide a gaming experience interesting enough to compete on commercial terms with the big-budget titles.
Uses of randomness
Thank you for posting this presentation--it was a fascinating read, and, for me, one of the most interesing entries on playthisthing for a while (then again, I read it mostly for musings about games rather than to find new games to play).
I have a few comments ranging from serious to nitpicks:
1)Some uses of randomness result from games' different positioning regarding their social status: from competition to pastime (which, I suppose, would be a different way of conceptualizing differing game aesthetics). Apart from the last proposed aesthetic (and some aspects of simulation aesthetics), you treat games as primarily focused on competition, either between players, or between player(s) and system. I tend to believe that most games (and most reasons for gameplaying) involve a hefty dose of both, with a very common emphasis on socializing, both in face-to-face games and in online environments. Consequently (and this is hinted at in your discussion of levelling the playing field), there is commonly a need to relieve social tensions which tend to build up in competitive situations. Randomness is one way of doing that: I win because of my brilliant play, and lose because of bad luck. And then we have the whole genre of tabletop rpgs, largely (though not always, of course--D&D has competitive elements, Rune and Donjon foreground them)non-competitive, even though character skill might be an important factor in determining game progress (and session results can, of course, be interpreted in terms of success/failure).
2) Your wargamer aesthetic blends together historicity and immersion which I believe to be rather different issues, if just because I tend to like immersive games (i.e. ones with plot and setting that draws me in, even at the expense of pure gameplay) but tend to dislike historical simulations (which I find dull). This gets more muddled, though, when the simulated reality is not historical: the success of the design of, say, Starcraft the boardgame depends on how much it feels like the videogame. This, incidentally, includes both game design and graphic design of the product (to the extent they can be separated).
3) nec plus ultra. It's Latin, not French. Also, it's never jacta. EDIT: Apparently, it sometimes is jacta. Which I thought I edited out before posting, but apparently didn't. My bad. Serves me right for nitpicking.
Good stuff. The discussion
Good stuff. The discussion of randomness to break symmetry is particularly interesting. Thanks for posting it.
As a casino game designer, the goal for me is to imply other things in a game of pure luck: intention, choice, strategy, meaning. This is a small problem, and largely an aesthetic one. The truth is that players of luck games are making their own stories up as they play, and creating their own meanings... just like poor Bob (le Flambeur.) Everyone has their own magic circle.
Ta
Cheers! Very interesting.
I like the sound of B-17, it sounds like the sort of pleasure-of-performing-a-system-correctly game. Dice Cricket springs to mind, as oddly does the character generation system from Traveller; That was an entire game in itself, and one of the few you could lose before even reaching the game proper.
Good read - minor correction.
A very thorough article, I very much enjoyed reading it.
I do think you used a poor example in Diablo, which does actually feature levels, monsters, and items that are generated randomly. Indeed, I feel that the Diablo series offers exceptional replay value due to this, and I think you could make a real case that Diablo represents the most commercially successful roguelike to date.
It's missing certain elements that 'roguelike' normally implies (most notably perma-death) and adds some that it normally doesn't (real time, click-based combat), but I think it does a great job of translating the core experience into a modern (for the time), commercially viable package.
Motivation
I'm really surprised you don't get into the psychology of motivation. It's been shown in hundreds of studies that a variable ratio rewards schedule - where reinforcement for the behavior happens seemingly at random - is the easiest way to increase motivation for a task. Dogs, for instance, develop worse begging habits if they're given scraps (rewarded for begging) occasionally and unpredictably, rather than never, or at every meal, or only at dinner, etc.
Additionally, an important element of psychological addiction is internalizing the motivation for a task. Random reward schedules are great at this. World of Warcraft is extremely addictive because the rewards come at random intervals. When they DON'T come, the player still has to justify his actions to himself. The only justification is, "I'm killing bears over and over because I like to do this."
What you cover is very insightful but I feel this is a simple, but key angle that needs to be explored. After all, the question isn't really "How much randomness makes a game good?", it's "How much randomness makes people want to keep playing?"
A nice meta-TableTop
A nice meta-TableTop Tuesday.
I thought I'd briefly add the gist of Nassim Taleb's writing on this issue, since he goes into depth on the epistemological problems with prediction and chaos in the world, and was a pretty good player at the options game. His strategy was to put the vast majority of your money in hyper-safe things like Treasury Bonds and collect a few % on that, then use that % to make up for what you spend on these deep-out-of-the-money options, basically lottery tickets that a market will go really really far away from where it is now, farther than its ever gone. They cost like $30 for a single contract, maybe even less, and if say the price of oil in the summer of '08 were to crash all the way down to $50 a barrel, seemingly inconceivable at the time, then your $30 contract would be worth like $2000. So his strategy was to hang on what you can predict while speculating with the extremely unlikely because the world is more chaotic than we give it credit for and we've been getting these 100-year-flood events like every 18 months.
Mark Rosewater on randomness
Nice article.
Just in case you're interested, Mark Rosewater wrote an article on the same topic a while ago. He also argues that Chess is not without randomness, via pairings - which incidentally introduces the idea that any metagame at all inherently introduces randomness - and also that players lookahead is always limited and hence a player's choice may or may not match the "ideal" play via luck alone.
Very nice. Thanks. Also... randomness spurs concentration
Excellent post; would have loved to have seen the presentation live. The balance of skill and randomness is, indeed, very important to games. Also to the plots of stories, be they novels or screenplays. If you throw too much "weird s**t" into a plot for no reason, it seems, er... well... random and disconnected. If everything is predictable, though... probably even worse. That's a whole 'nother post, though.
One related link for you:
http://www.sciencedaily.com/releases/2009/09/090915174455.htm
[clip]
According to research by psychologists at UC Santa Barbara and the University of British Columbia, exposure to the surrealism in, say, Kafka's "The Country Doctor" or Lynch's "Blue Velvet" enhances the cognitive mechanisms that oversee implicit learning functions...
"The idea is that when you're exposed to a meaning threat –– something that fundamentally does not make sense –– your brain is going to respond by looking for some other kind of structure within your environment...And, it turns out, that structure can be completely unrelated to the meaning threat."
[clip]
Perhaps another useful element of randomness in games is somewhat related: when we are forced to deal with chaotic or random events in a game, it makes us look harder for important patterns. In chess/go, the only activity you need to take into consideration (besides your own actions) is the moves of the other player. If, however, you are imagining and planning based on contingencies that are both player- and random-driven, you need to do more planning.
Plus, as you state, we love to see and create patterns where none really exist. Taking a random event like a die roll and making it conform to a very rigid, narrow set of circumstances (move X spaces forward) is, in a sense, a way to "control" chaos. As if we're saying to ourselves, "Yes, the universe can't be predicted... but at least *this* universe, this game, channels that randomness."
Anyway. Nice piece all around.
Tales of the Arabian Nights
Similar to B-17, I call out Tales of the Arabian Nights as an interesting data point, both the 80s version and the new release. There is some strategy, but picking the most likely "successful" option is usually obvious. Games between beginners tend to be highly random as their choices are poorly informed and the results unpredictable. Among a group of more experienced players (just two or three games), the best choices become relatively obvious. There is so much luck involved that it drowns out the occasional bits of insight by a beginner, or occasional errors in judgement by an experienced player. None-the-less, it's an enormously fun game full of replay value. Why? Because there is so much to see! The beggar you assault on the street might be a criminal, a vizier in disguise, a genie, or an actual beggar. Being toss off a ship at sea might lead to washing up ashore and being lost, or you might be rescued by mer-people and convince them to go to war! The joy is in the manipulation of the game (like B-17, I expect it would be less fun with a computer moderating despite the significant speed gain) and the enjoyment of the resulting genre appropriate adventures.
As JeremyT notes, Diablo does feature random generation, even down to the dungeon levels and the outdoor levels in Diablo 2. The two games do survive at least a few replays pretty well. However, Diablo has far fewer nouns (monsters, items, scenary) to select from at any given point compared to NetHack, so one is likely to find it repetitive earlier than NetHack.
Okay, now I feel a bit silly
Okay, now I feel a bit silly suggesting that costik consider Tales of the Arabian Nights.
Hex and Twixt are dull?
Thanks for your hard work! As I scrolled down and read, I was delighted to see your section on my two favorite games, Hex and Twixt. You even used a Twixt image I created (with POVray) of a game I won! Clearly I have a biased viewpoint here. When I read your apparent conclusion that these games are dull, I was less delighted.
You say
"... the game has an optimum strategy -- a fact mathematically proven up to 9x9 Hex grids."
It is true that computer analysis has found a way to win for the first player on 9x9 grids. But this analysis ignores the pie rule, also known as the swap rule or one move equalization. Every Hex server implements this rule. After the very first token is placed on the board, the second player has the option, at that moment only, to swap sides. This greatly reduces the imbalance created by the first move. In fact, with this rule, theoretically, the second player has a win, but in practice both sides have close to equal chances. It is called the pie rule because it is like when two people want to share the remains of a pie. One person cuts the pie into two slices, and the other chooses which slice to eat. Some US editions of Twixt do not mention a pie rule, but it was included in all later editions.
With the pie rule included, the largest size Hex grid solved by computer so far is 7x7. Many humans regard 11x11 as the standard size. Some prefer grids as large as 19x19. The strongest known computer Hex opponent, Six, is nowhere near to the strength of the best human players.
You say
"The problem with Hex is that it has nothing like the strategic depth of Chess or Go; symmetry never gets broken."
I don't understand this at all. Look at the Hex image you posted. Does that position look symmetric to you? I'm glad you did not make a similar claim about Twixt.
With regard to strategic depth, I would like to make three points.
First, Hex has been around for about 67 years now, and Twixt about 52. Most people, even among those who like to play their chosen abstracts, have not even heard of these games. I would like to believe their popularity will increase eventually. The Net has been a great facilitator. I submit that they have not been studied enough to make definitive conclusions about how deep they really are.
Second, look at the ELO rating performances of some of the best Hex and Twixt players on the Little Golem turn-based server. ELO is a rating system generally regarded as a statistically accurate method of comparing the strengths of players. It is somewhat misleading to compare ELO ratings between different games, but the ratings of the strongest players arguably can be viewed as a measure of how deep that game is. In face to face chess, The strongest players are rated around 2800. This is rating not ranking; a higher value indicates a stronger player. On Little Golem, Hex is divided into two games, 13x13 and 19x19. One player is currently ranked number one in both these grid sizes as well as Twixt. His name is Maciej Celuch.
In Hex 13x13, his rating is now 2481, 48 points above his nearest rival.
In Hex 19x19, his rating is now 2385, 332 points above #2 (me.)
In Twixt, his rating is now 2504 (!) 59 points ahead of #2.
I believe the main reason his rating in each of these games is not still higher is that no one is pushing him hard enough. This is especially true for 19x19 Hex. If just a few more players of his quality were to join in the fracas, I am sure the highest rating would push up considerably.
I feel sure that many of the top players could win virtually 100% of the time if they move first, even against Maciej, if there were no swap rule. But I also doubt that any of the top players would agree to play a rated game without swap.
The third point I want to make about strategic depth is, as grid size increases, the depth of these games dramatically increases. I believe 19x19 Hex, or 30x30 Twixt, could be as deep as chess in some sense.
Overall, these points are not important to your discussion about luck versus skill. Thanks for reading this far!
David "they call me Mister Twixt" Bush
Aesthetics
Hoist by my own petard, here, of course; some people find Hex and Twixt fascinating; I find them dull. But of course that's an aesthetic choice, and here I am trying to claim I'm above that such particularist aesthetic judgments.
Random, Fun, and (no) AI
The solitaire war board/card game Fields of Fire, from 2008, has this really fun setup phase before each mission when you get to create the map by placing a few rows of terrain cards on the table. Of course the same mechanic would be a lot less fun watching on a computer (although I do remember one fun aspect of Civilization was exploring the map just to see what it looked like in each new game).
One weird thing about wargamers and randomness is that it seems from my experience that a lot (most?) of them think that in a computer game it is very important that when playing single player the computer simulates a "fair" two-player game with some sort of made-up pretended virtual opponent sitting across a virtual table. It's like the aesthetics from abstract strategy games somehow got mixed into how wargames should be played on a computer, maybe in the early years of computer games when those genres were defined on computers.
To me that is really odd since I got into wargames later, from RPGs, and to me the important aspect was always being immersed into a gameworld and reacting to problems in-game. Why must turn-based wargames still have to pretend to be some kind of fair chess-like games, rather than just throwing random enemies at the player (like B-17, or probably better Fields of Fire, or Red Beach One, or some other more interesting solitaire board wargame that is not only made up of dierolling)?
I don't think a wargame would be less fun if enemy units were randomly spawned along the frontline. Kill all those "this game sucks since the AI is so weak" debates as well.
I have never heard anyone be upset because the "AI player" in Super Mario Bros is "cheating" for instance. Really, almost any other genre I can think of it is perfectly OK to throw random obstacles at the player while focusing on the game world, story etc. The worst thing about this is that in many cases it is very bad for the suspension of belief, with all the "AI Player" stuff said out loudly on-screen, and it makes it more difficult for me to go into the gameworld as a general, rather makes me feel like playing a game where I pretend that I am a player at a virtual table playing a simulated boardgame, which sucks.
Not to nitpick, but...
...aren't "bane" and "blight" both negative things? Shouldn't it be "bane or boon" or "boon or blight"? Sorry, but this confused me. Great article, though. Very though provoking.
That's a joke, son.
That's a joke, son.
Single player
Great post.
Nethack and its variants are interesting because, despite being bred from almost purely random elements, they provide one of the most enjoyably replayable single player experiences that I know if. The apparently dependence on chance is very strong, but the player's ability to assess and deal with situations is so important that it is almost impossible to win without investing hundreds of hours in learning the gameplay.
Solitaire card games are similar to a degree. The odds of winning a game of Klondike or Canfield without investing previous time in understanding how to take the advantages you're given is almost nil. Compare to the "pure" abstracts like Hi-Q or the Icosian Game - I know almost nobody who actually plays those for fun.
Game AI
Pelle,
I would agree that there is (for me) no need to have a virtual human player across the board in computer strategy games but, for me, AI in strategy games is an important part of game immersion: I would have no problem with enemy units being created right at the frontline if and only if I could believe in them getting there within the logic of the simulated world. Otherwise, the game starts looking silly and I lose interest. But then, I am not a great fan of strategy games, so probably my view is not particularly representative.
But you get the same AI discussions in FPS games: enemy intelligence is discussed to no end, and so is their fairness (i.e. dumb but strong enemy is supposedly not conducive to a fun, challenging experience). And I believe I've found that in cRPG discussions as well (but, I suppose, only to the extent cRPG fights are, at heart, strategy game wannabes).
wargame ai
I agree about the "if and only if" part. I understand that not all scales and themes would work equally well. For instance the tactical solitaire game Fields of Fire works very well with random enemy units being triggered by player units moving onto cards containing Possible Contact markers. The scale and somewhat abstract map helps. I can't think of a situation in that game where I would think the game is cheating because enemies appeared from nowhere in some unrealistic way. On the other hand in a strategic game you would need more logic/AI to make sure enemy units don't just pop up from nowhere in areas they could not realistically have moved to.
About FPS AI someone said something very enlightening in some blog/article a while ago (would love to read that again if someone has a link) that FPS AI has gone from cheating with enemies showing up at random everywhere, to stupid but non-cheating AI, to AI that is so good that now enemies show up at random everywhere again (sneaking behind players in clever ways) which to the player is completely impossible to distinguish from the old games with randomly spawned enemies, only now the games are much more difficult to develop and require much more CPU... Perhaps given enough development resources wargames could also go full circle like that, but it seems they are currently stuck somewhere in the "stupid but non-cheating AI" part.
Randomness is a third player
Before I begin, my two cents on the Latin debate. "Alea Jacta Est" is acceptable medieval church Latin, but not Roman Latin. The J was a Germanic innovation. (Indeed, his name was Iulius Caesar). So one CAN write Alea Jacta Est, but you're translating. Also, "The die is cast" does not imply randomness. It actually refers to the die used to cast coins, not numbered cubes, so the connotation is not one of entrusting oneself to the divine, but actually of making a firm, irrevocable decision (crossing the Rubicon under arms, and therefore declaring war upon the Roman republic). Other than that, though, your remarks about randomness to ancient cultures seem pretty spot-on.
It's worth recognising that for these cultures the random elements were in some sense divine themselves, not merely divinely influenced. Dice were not controlled by the gods, they were in themselves magical artifacts. Similarly, idols were not representations of the divine, they were divinities, so on and so forth.
Randomness, then, was viewed as another player in the game. Solitaire was considered to be playing cards against Lucifer. It's interesting to note that modern game theory (by which I mean maths, not ludology) also considers randomness to act as an extra player in a game for purposes of analysis. While mathematicians obviously don't hold this as a conscious belief, it remains the most effective way to approach randomness. As Zizek points out about ideology, it doesn't matter what you claim to believe, but what you act as though you believe.
Given this, we can reformulate your approach to randomness in games from an aesthetic choice to a question of control. Chess is "abstract" precisely because Lucifer doesn't get to make his move, whereas generals (armchair or otherwise) know that he always does in war. In Snakes and Ladders, you allow the invisible player to act as a judge and mediator in the game. It may still decide that poor little Johnny gets whooped every game, but we trust the gods not to let that happen too much.
I've never held too much stake in the "long odds" approach to wargaming, precisely for the reasons you outline. Not only can one die-roll disproportionately influence the game, but it also influences on what other occasions dice will be rolled, and under what conditions. It might be more useful to look at this as a "random walk:" a particle starts at 0,0 on the coordinate plane and starts wandering at random. In terms of averages, over the long term you don't expect the particle to move. But in actual fact the chance of the average result surfacing is practically nil, and every step the particle wanders away reduces it even more.
There's a trend in the actual conduct of war towards trying to contain the "random player" more and more. A supply train represents a general's refusal to rely on forage, a weather satellite represents a general's refusal to be ignorant of incoming weather conditions. All of the science of strategy is an effort to subject the chaos of war to human design. Chess represents utter mastery of the random, where the only factors are the wills of two sovereigns pitted against one another; dice are the utter surrender to outside forces. There's a medieval fable where a king asks his adviser which is the best game for kings to play: chess, dice, or backgammon. The adviser eventually decides it's backgammon, since it admits that there ARE uncontrollable elements that may wreck a plan, and good rulership is about learning to control them.
On an entirely different note, I've been meditating on games like Chess lately, or symmetrical abstract strategy games as you call them, and I've ended up inverting the way we tend to look at these games. Usually, we say the game starts off symmetrical and proceeds towards asymmetry. I would say it's just the opposite. Chess and its ilk start from the premise of an imbalance of power: white takes the first move which represents an invasion of black territory. Without that initial disruption, without that initial asymmetry of who gets the first move, there would be no game. The game proceeds not to the disruption of balance, but rather to its restoration: either one side is routed or a stalemate results. In either case, the impetus for fighting ends and a new power balance results. It helps to remember that Chess isn't just a strategy game, it's the definitive war game.
Breaking the illusionary symmetry
Came here from Rock, Paper, Shotgun; loved the article.
The most enlightening aspect of the article, to me, was that it made me think much more clearly about what lenses I look through when thinking about certain types of games. I believe it conducive to a good discussion to be very clear about the lens one is looking through.
So yes, I come to this with a very, very specific case in mind: Civilization, the PC game (specifically Civilization 4), played competitively.
When I play computer games, it is almost always multiplayer. It didn't use to be that way, but I somehow slipped into this mode of playing, and it's what I enjoy most now. I loved Fallout 3, for instance, but halfway through I found myself not playing the game anymore. It wasn't so much that it had bored me or that I had ever really closed the game thinking "yawn, I don't need any more of this"; it was more that when I sat down to game and asked myself "what do I feel like playing?", other answers presented themselves. Team Fortress 2. Civilization 4. Sins of a Solar Empire. More recently, League of Legends. And yes, all of them in multiplayer, and all of them played very competitively.
(I feel myself slipping into an entirely different post here; I should probably write this up somewhere else.)
So yes, I play to win. I enjoy losing them too, especially if I know why I was beaten, and if I get a chance to try again and improve. There is nothing more addictive to me than the feeling of "I was bad at this before, now I am clearly better; I can now defeat people who used to defeat me." Pure Fiero.
So this is my lens. In this case I guess it's abstract strategy, but I would say that the same applies to twitch-based games. You were very right and insightful to point out that abstract strategy gamers and fps gamers agree on the role of randomness. I know from my experience with TF2 that there are a lot of people playing on "no crit" servers, and that these people are convinced they are playing a purer, superior version of the game. Critical hits are one of the very few random elements in TF2; there is weapon damage spread as well, but the spread is VERY narrow (and whenever it is mentioned in patch notes it is to say that it has been made narrower still). And I find myself agreeing with these people: where's the accomplishment in winning a round just because your scout had two consecutive crits with his Scattergun? In a fairer game, we should have won.
League of Legends is somewhere between the two; there is a LOT of twitch involved, a lot of keeping a cool head (do I run or fight? Do I keep bashing the guy I'm currently bashing on or do I switch to a squishier target with more dps?), but also an interesting element of strategy (our melee dps char is always hit by a stun first thing in a team fight, so he buys the "block one negative spell every 30s" item, stun baits, and then initiates).
And yet, League of Legends has a lot of random elements. True, there is no damage spread (at ALL; great design decision!), but the game has both critical hits and dodges. The former represent a non-predictable damage spike, the latter a random defense against one attack. The frustrating and confusing element to me, from a pure game design point of view, is that the two functions ("increase damage output" and "increase defense") are already filled plenty by existing options (buy more attack damage/attack speed/armor penetration for damage output; buy more health/armor/magic resist for defense). So why do we need these random functions that fill the same roles? (I don't have an answer; this is an honest question)
Let's come finally to my main point: Civilization 4. God how addicted I am to that game. I started playing it with the friend I play most games with; we soon started checking out mods and for a very long time played what must be the biggest mod for Civ4: Fall From Heaven.
FfH is what we used to call a Total Conversion of Civ4 into a fantasy game. We played an insane number of games against each other before one thing became apparent: The game is horribly unbalanced (and, as I've decided after a lot of thinking about it, unbalanceable). I don't want to digress too much again, but it's interesting to examine why it took us so long to discover this very obvious fact. I put it down to "Explore Mode". Essentially, there were so many new releases of FfH and each one of them contained so much weird and interesting content that half of the time we were discovering things. Both of us being rather careful thinkers, we tried hard not to jump to conclusions before being intimately familiar with the game.
So we had decided that FfH is completely unbalanced (some races are way more powerful than others; some strategies so good that to not choose them is tantamount to surrender) and, due to its size and complexity, unbalanceable. I believe, and this is only a gut feeling, in a complexity event horizon. Cross that, and there is no way you can balance your game anymore. But that, again, is beside the point.
So we went back to the core game. The most recent expansion was now Beyond the Sword. We played against each other and quickly noticed other things that marred our game experience. For instance, one of us might spawn next to two gold resources and have iron and copper within easy reach, while the other would start with nothing useful. There are options to equalize your starting positions resource-wise, but we found even that insufficient. The next logical step was mirrored maps. The game provides a few, but a Polish fan has made a much, much better mirror map script (eradicating almost ALL of the "why didn't this resource get mirrored?" bugs). So we used that. Now we were getting somewhere.
And then there was that game where my friend attacked me with a stack of doom that should most definitely have wiped me out. My first city under attack had a few longbowmen; pretty good defense units, ESPECIALLY when they've levelled up a bit, but not nearly enough to hold him back. Or it shouldn't have been. Due to sheer luck I won a fair number of combats where the odds were around 80-90% in his favour. Not only did that stop his initial stack dead in its tracks, it also allowed me to level up the longbowmen, making them much, much better defenders. That city had just become unassailable.
This is a classic case of a single (or a few) roll(s) being much more important than the average. We'd noticed this in FfH before, where the effect was more pronounced still: FfH has the concept of heroes, very powerful, unique units that can grow to truly epic levels of awesomeness through experience. Losing a hero is a game-ending moment since so much of your army's power is tied up in this ONE unit, and once it's gone, it's gone (with very very few exceptions; I believe there is a ritual where you sacrifice a few mana nodes to resurrect a hero? At any rate, nothing you could easily do). This lead to neither of us using a hero offensively unless the odds were 95% or higher. This, again, led to a very stale, dull game experience. We'd argued our case on the FfH forums and I'd even made a patch that seriously dialed down the randomness (an ugly hack if ever there was one; a fight in Civ4 is a series of dice rolls where each turn one unit has a chance to inflict damage on the other. The chance AND the amount of damage depend on the power differential between the units. The only thing I'd changed was to simply dial up every single unit's hitpoints from 100 to 1000. This is a classic case of using regression to the mean.) but eventually it became clear that there really wasn't anyone interested in playing FfH competitively. We'd move on to BtS to escape the tyranny of "single random event determining outcome of game", but found that we hadn't.
I think this kind of event seriously limits the usefulness of regression to the mean. But this is not my main point: my main point is, why do we need randomness at all? Seen through my lens, the regression to the mean argument sounds a little like this: yes, if you rub dog faeces into your clothes, you will smell pretty badly, but we can mask that with perfume, and anyway if everyone does it hardly anyone will notice.
The question that a reasonable person must ask being: why rub faeces into your clothes in the first place?
Again, I loved this article, but if there's one thing I didn't like it was how much the entire issue of "breaking the symmetry" was glossed over.
The basic assumption is that if you have a fair and symmetrical game with no element of randomness to it that there then must be a discoverable optimum strategy and that all improvement in gameplay is just getting closer to that strategy. You say that in Chess or Go the symmetry is quickly broken:
Symmetry works in Chess and Go because these are games of enormous strategic depth, and symmetry is quickly broken by the moves or placements of the players.
I'd call you out on that phrasing. Just *what* aspect of their strategic depth is it that allows them to have symmetry broken by player moves? What is this thing that is missing from, say, Hex? It can't just be the amount of valid moves at every stage of the game, right? Because then we could just turn up the size of the hex grid. As David Bush points out (and man did that post make me want to give Hex a try!) there is a simple workaround to this problem (the side switching option).
By the way, I don't mean to say that you're WRONG; I am just trying to figure out what characteristic of chess or go give them that magical quality of allowing SYMMETRY without developing into DULL SYMMETRY.
Chess could theoretically be solved, right? (Again, I'm not firm in mathematical game theory at all) Given unlimited computing power, every single position could be analyzed to the point where a computer could play a perfect game; a game where the first mover always wins. Or is that not so?
At any rate, the point I am trying to make is that this question (can a game be solved so that knowing all the possible positions a first mover can always win) is of purely philosophical or mathematical interest. It need not interest us as human players at all as long as there is sufficient complexity that no human could ever come close to playing the "perfect strategy" at any given time.
Most people know how to force a draw at tic-tac-toe. In that way there is an optimum strategy (even though the endgame is Do Not Lose rather than Win) and it does become the contest to make "the fewest mistakes" you describe. I agree that this is dull. However, school children still play the game. As long as you don't know the optimal strategy, there is some fun in the game.
The idea that a game as complex as Civilization could have an easily discoverable "optimum strategy" (given symmetrical starts) is clearly absurd. It may very well have a perfect strategy where at any given point you can take one specific decision that leads down a fractally forking path of future decisions where again at each stage there is one thing you can do to eventually secure victory. This is very interesting mathematically (and if I'm wrong about this, it only makes my argument stronger), but irrelevant to a human player. We cannot make useful predictions beyond a round or two in Civilization. Even if we DID know everything our enemy is doing (which we don't), there are always so many options that the amount of outcomes grows too quickly for us. I do not see how this is different from chess or go. I'm not putting Civilization on one level with those classics (well, maybe I am ;P), but I'm saying that I believe the characteristic of these games that allows them to have self-breaking symmetry is simply their complexity. Every move can have so many answers that it is never totally clear which is the "best" move at any given moment, meaning you cannot predict your enemy's turn, meaning you cannot plan further ahead with any amount of precision. In a game of Civilization 4 with no randomness and absolutely symmetrical starts (same civilization, same leader, same starting units and techs, perfectly mirrored map) the players' moves would very quickly break the symmetry, just as they would in Chess or Go.
I return then to my last big question: why rub faeces into your clothes in the first place? If it is not for "breaking the symmetry", what could be the motivation?
The two arguments most often flung at you (to stay with the faecal metaphor) on fan forums are, as I would phrase them:
1) Dulling the edges of imbalance
and
2) Surprise! Excitement!
Let's start with 2). Somehow many gamers find that predictable combat outcomes are dull. If I know that in a hundred out of a hundred combats where a strength 4 unit attacks a strength 3 unit the strength 4 unit wins (and takes 75% damage), then somehow that is dull. What these people miss is the context. What options did that player sacrifice to have a strength 4 unit when the other player only had a strength 3 unit? Does the player with the inferior unit maybe have a second unit ready, or sneaking into the other player's territory? There is a lot more to a war than a simple skirmish, and to miss that is to miss the point of the game.
Something that also enters into argument 2) is what you mentioned in your article: verisimilitude. I reject this outright and remind the gentle reader of my open confession to wearing the abstract strategy gamer's lenses. Just because it feels more realistic does not make it a more exciting contest of skills. Quite the opposite.
So, 1) then. I find the same idea SOMEWHAT implied in your above-quoted section on Chess and Go; also in this one:
Chess can pull this off because of its strategic complexity. Chess has been refined over centuries, pondered by millions of minds. Good luck to you in devising a game of equivalent depth.
It's the mysterious strategic depth again. Not just the amount of valid moves at any moment, I gather, but also their rough equivalence for the game; any move you may make could theoretically be as good as another, while in Civilization the investment of Research and Resources into Horse Archers may simply not be worth it. (I don't think that this really is what is necessary to break the Symmetry; or rather, that this PERFECT balance worked out over centuries is absolutely necessary for games to develop asymmetrically on their own.) So one answer to the "Civilization will never be completely balanced" problem is that "randomness dulls the sharply imbalanced outcomes of certain events." Maybe for the same resources invested Horse Archers are inferior to Macemen. But if sometimes, through sheer luck, a certain investment in Horse Archers can still beat the same investment of Macemen, well, it's not so bad, then. Right?
Wrong. Randomness goes in both directions and, if anything, exacerbates this problem. Randomness does not dull the game impact of imbalance; it dulls the perception of imbalance, making it much harder for players to judge whether they lost due to bad decision making or whether they just weren't lucky enough.
I had started a mod once that strived to remove, as far as possible, all elements of luck from Civ4. It was also going to do a lot of other things that I really shouldn't get into (because then I'll be here another hour). Unfortunately I was distracted by other projects/simply too lazy to finish it. But I would bet a lot of money that games in that mod, with a perfectly symmetrical start, would not become dull. Maybe if one were to replay the same map over and over again, maybe then a "quickest build to Meditation" or a "fewest years to a stack of 10 axemen build" would surface. And maybe one or the other would seem, for a time, like the non plus ultra (if I may use the Latin *I* learned in school). But even that has a simple fix (randomly generate the mirror map before each game), and even if it didn't there is no reason to assume that human ingenuity wouldn't come up with a perfect counter to one of those.
Have I really been ranting here for an hour and a half? Dear God, I must care about this subject. Here's the tl;dr:
* Luck BAD, Skill GOOD! Or else!
* Symmetry needs to be broken only in very simple games where an optimum strategy is clearly visible to a HUMAN MIND.
* There was no need for random battle outcomes in Civilization 4.
* Pick up after your dog!
Thank you,
Daniel Klein
IANALatinScholar, but...
Also, "The die is cast" does not imply randomness. It actually refers to the die used to cast coins, not numbered cubes
But Caesar, even notionally, didn't say "the die is cast" in English, so I don't think the double meanings of the English words used to translate are relevant.
All the English words I can think of that derive from 'iecta' seem to connote throwing, not stamping -- eject (throw out), reject (throw back), inject (throw in), etc. Does 'iecta' ever mean 'stamp' in Latin?
Likewise, alea- as a modern English prefix always connotes chance/randomness, not minting of coins.
Does 'alea' actually refer to a coin-stamping die, or is there a different word for that?
Alea
I hope I can help out on this one - Caesar didn't say "alea iacta est" or "alea jacta est". He was saying something important, so he said it in Greek - specifically, he said (transliterating roughly) "anerriphtho kubos". "Kubos", as you might expect, means "die" as in solid cube-like form used for gaming.
"alea" doesn't mean "die" at all, except metaphorically - the Latin for (six-sided) die is "tessera" (I know that makes no sense, and I have nothing but sympathy for your position - at a guess, it's because Roman dice started out with four faces and two rounded ends, and were then flattened to have six faces, the older form being called "tali"). "Alea" is a game played with dice - hence "aleatory", which means dictated by chance.
So, "iacta alea est" is what he have in Suetonius, transcribed by monks as "jacta alea est", which is probably a _mistranscription_ of "alea iacta esto", which would mirror the form of "anerriphtho" and would mean "let the game of dice begin", roughly.
Very interesting article, in any case.
Controlled unpredictability
I was going to say that, only I wouldn't exactly call it "randomness". In chess, the complexity of the choice of moves quickly surpasses the human ability of conscious thought. At that point, you're forced to play "with principles", that is your moves are subject to a higher order, more abstract set of rules, what we call strategy. This is similar to how in Poker you have to rely on the laws of probability and statistics to plan your moves, because you can't predict everything.
So, randomness and complexity are two methods of introducing controlled unpredictability/uncertainty to a game, which forces the players to not plan their actions by calculating moves but by developing small abstract theories. Essentially, one could argue that this is the difference between tactics and strategy.
On the subject of Latin
I always thought the phrase was "ne plus ultra" (Latin-ish), not "n'est plus ultra" (French-ish). I guess maybe it's both? :)
non-random lens
I found Daniel's post about his view through an abstract strategy game and competitive fps game lens interesting, if somewhat difficult for me to understand. Reading about mirrored maps in a Civ-game almost made me cry. Through my non-abstract strategy game lens, having symmetric maps is completely out of the question. And non-random combat...Again, through my lens that sounds very very dull. I want the uncertainty of real battle (or fantasy battles, presumably), knowing that I might have a 80-90 % chance of victory, but being forced to plan for also the risk of a 10-20 % defeat. The story of the longbowmen holding out in a city against overwhelming odds was good, and to me it shows exactly the reason for playing games: for the great stories and memories it creates, when things like that happen.
Also for historic wargames (and probably also fantasy/sf wargames) I want the historic possibility to gamble. I might know that I have only 33 % chance to win a battle, but it might be worth attacking anyway since a victory will open up for a spectacular strategic victory of the entire game (and make for a good story to retell later), and if lost I still have a good backup plan and will not be much worse off. To me that kind of reasoning brings me more into the game-world, into the roleplaying of some historic event, and that is what I find most important in a strategy game.
Man, that last paragraph is a mess...
Apologies, v. tired yesterday. Should have read:
"So, "iacta alea est" is what we have in the text we have of Suetonius as a Latin translation of the Greek phrase (quoting Menander) that, according to Plutarch, Julius C. actually spoke, transcribed by monks as "jacta alea est". However, that is quite possibly a _mistranscription_ of "iacta alea esto", which would mirror the form of "anerriphtho" and would mean "let the game of dice begin", roughly.
Regarding Sweden conquering Russia (in 1943, when totally incredible, rather than, say, 1701) - I'm reminded of an 8-bit wargame called Theatre Europe - http://www.gb64.com/oldsite/gameofweek/2/gotw_theatreurope.htm - which first had to be specifically made (in the view of the creators) unrealistic, because a realistic simulation of a land war in Europe between NATO and the Warsaw Pact using the same rules always resulted in the Warsaw Pact obliterating NATO's European defence forces, so that the only response available to the player was to launch a full nuclear strike on Russia. Having been thus gamed, it did allow for a very canny and/or very lucky player (combat results being to some extent randomised, although there was also a very dull skill-based minigame which could influence results) to beat back the Warsaw Pact advance and start pushing back into Eastern Europe and towards Russia - at which point the game would cause a nuclear armageddon. Effectively, realism in the game was protected not by the mechanics of the game itself but by a failsafe which meant that victory for the player had to be seen in terms of holding the line, rather than making a decisive military advance, despite the relative strengths of the two forces having been tweaked away from realism to make it competitive.
Awesome article! You make
Awesome article! You make me sad that I didn't go to the GDC, if all the presentations were like this... Please write more gaming articles like this in the future!
Roguelike = poker not chess?
Obviously, you cannot play a Rogue-like with the kind of seriousness that a Chess master brings to that game; no matter how experienced a player, the next corner may bring you face to face with instant death. It requires a sort of cheerful resignation, a willingness to enjoy the often humorous ways in which you die ("gnawed to death by rats on level 17 while paralyzed").
Yes, it's not like chess, but from your list of game varieties it shares distinct parallels with poker:
.. the strategy of Poker is based on its randomness. Without random card allocation, it would be an entirely different, and inferior game. The strategy of Poker lies in understanding the statistical nature of the game, and managing statistical outcomes.
As with roguelikes. They are more about managing risk than charging in blindly to any situation that has been generated for you. At any time you COULD be staring down a bad beat, but on the whole skill has far more influence on the success of your character than luck.
Another area that caught my eye was randomness in FPS games:
.. in deathmatch play, there's enough variability in a system of chaotic fireplay to prevent a non-random system from becoming dull. I suspect the random element of damage derives not from a conscious design choice, but from an unconscious and automatic adoption of a game mechanic -- variable weapons damage -- that stretches back into the tabletop roleplaying and miniatures gaming prehistory of the videogame.
Although you were talking about Quake, there is a clear case of design choice for placing randomness into a game with Team Fortress 2's critical hits. Valve purposefully placed crits into the game to give opportunity for variety, breakthroughs, streaks and rampages. These were seen as adding 'memorable' events to help form positive experiences around, while also breaking up a 'boring' stalemate. The reception of random criticals in the professional eSport scene was not good though, and virtually all competitive games of TF2 now play without crits. An in-depth analysis of the transition between these two standpoints would also be enlightening on the acceptability of randomness in games. Quite ironic when the competitive FPS community seemed to gloss right over the random spray pattern of counterstrike weapons. It's accepted as part of the game and more realistic.
... and statistics.
I really enjoyed this article. It seems like the good aspects of randomness in games are usually drowned out by complaints of unfairness or even cheating by the computer. So I especially liked the parts about how randomness adds to realism and variety of encounter. The history lesson was new to me, too.
However, I think that the sections about the cumulative effect of many random events are misleading. The idea that more random tests causes less overall effect of randomness seems counter-intuitive on the surface, and I don't think that the statistics prove otherwise.
For an intuitive example, let's add one random event to chess: on a given turn, each player has an equal random chance of gaining one pawn, losing one pawn, or nothing happening (this happens only once per game). The most extreme outcome for this event would be for one player to lose a pawn and the other player to gain a pawn. If the two players are playing nearly equally well, this event could affect who ultimately wins, but otherwise skillful play will decide who wins.
Now let's edit the rules of chess again. Use the same random event, but now it happens 20 times during the game. Intuitively, this will have a much greater effect on the outcome of the game, right? At worst, these 20 events will cause one player to lose 20 pawns, and the other player to gain 20 pawns. This is extremely unlikely. But it would be fairly likely for one player to have a net gain of one pawn or more while the other player has a net loss of one or more. That's an equal or greater difference than you could possibly get with the single random event.
Also, the article discusses rogue-likes because they are so highly random that winning or even surviving for a while depends on good luck. Part of this is because a single random event can be so powerful (like gaining or losing knights or queens in chess). But having many random events doesn't reduce the overall randomness. Things just get crazier as the game gets longer, rather than evening out.
OK, all the intuition in the world doesn't matter if the math proves otherwise. The argument in the article is "the greater the number of random tests, the less effect chance has on the outcome." The cumulative result of random events (I'll call it R) is represented as the sum of the results of a number (N) of die rolls. What we want to know is how often and by how much R differs from the expected cumulative result of the die rolls (E). To do this, we can graph R on the horizontal axis and the probablility of each possible value of R on the vertical axis.
The conclusion is reached by examining the shape of these graphs. The examples given are a graph of 2 D6 rolls, and a graph of 40 D6 rolls in which the graph of 40 rolls is much pointier. This is meant to show that the result of 40 rolls is more likely to be nearer to the expected value.
The problem is that the two graphs use different scales on the axes. The pictures are too small to read the numbers, but the possible values of R for 2 D6 rolls range from 2 to 12, and R for 40 D6 rolls ranges from 40 to 240, and each graph shows the whole range on the horizontal axis. There is a similar problem on the vertical axis because the chance of getting any single value of R much smaller with 40 dice. If we used the same scales on both graphs, the 40 rolls graph would be much shorter and much wider than the 2 rolls graph. Even if you ignore the tails of the 40 rolls graph, it looks like the graph would have to range from R values of 100 to 180 to include most of the likely R values. That's a very rough estimate, but it's a much bigger range of likely R than for the 2 D6 graph. That indicates that more rolls causes more randomness.
But I promised MATH and so far I've just talked about the shapes of graphs and rough estimates because that's the argument used in the article. To go beyond that, we need an exact definition of the total effect of randomness that we're calculating. Instead of looking at the graph of the distribution of R, we'll calculate its Standard Deviation. I'll call it S.
In our current example, each possible Ri has a probability of ocurring, Pi. (These are what we have been graphing.) E is still the average and expected value of R. So the definition of S is:
S = squareroot[ sum over all i( Pi * {Ri - E}squared ) ]
Basically, it goes over each Ri based on its probability and sums up its deviation from the mean squared. An unlikely Ri far from the mean increases S much more than a likely Ri close to the mean. And S is in the same units as R. The end result is that most Ri will be found between the values (E - S) and (E + S).
So, this will prove that more random tests causes more total randomness. I won't do the dice rolling example because it is a lot of work to do with pen and paper. I'll compare the standard deviation of two coin flips to the standard deviation of four coin flips because those have nice round numbers that are easy to do with pen and paper. Heads = 0 and tails = 1. Each Ri is the sum of the flipped coins.
For two coin flips, the possible results are:
2 heads. R1 = 0. P1 = 1/4.
1 heads, 1 tails. R2 = 1. P2 = 1/2.
2 tails. R3 = 2. P3 = 1/4.
E = 1.
S = squareroot[ P1 * (R1-E)^2 + P2 * (R2-E)^2 + P3 * (R3-E)^2 ]
S = squareroot[ 1/4 * 1 + 0 + 1/4 * 1]
S = squareroot[1/2]
S ~ .707
Then for four flips, the pairs of (Ri, Pi) are (0, 1/16), (1, 1/4), (2, 6/16), (3, 1/4), (4, 1/16) and E = 2.
End result is:
S = 1
Four flips has higher standard deviation than two flips, so the results support the theory that more random events cause more total randomness. There is nothing special about coin flips compared to other random number generators, so there's no reason to suspect that this theory is not universal. You are welcome to test it.
So are the "regression to the mean" and law of averages wrong? No, those are about doing repeated random events and how the mean of those results approaches the expected mean as the number of tests increases. But we were not interested mean of those random events, we were interested in R, the cumulative effect of the random events, the sum. R divided by the number of events is equal to the mean, and that is the difference.
Alright I'm done. I first read this article days ago, and since then it has been bothering me that a conclusion that sounds so counter-intuitive could be true. But I couldn't immediately think of why it was wrong. And it really did take me hours to write this post while reasoning through it myself. I didn't even realize that connection between sum and mean in the last paragraph until I was writing that paragraph. So maybe this post is a waste of everyone else's time, but I enjoyed(?!) writing it.
Latin
Okay, according to Notre Dame's online Latin dictionary, I'm wrong. My mistake! But I blame it on my old Latin teacher, who told me story I repeated here.
Statistics are fun!
I liked it, nullspace.
I believe nullspace is
I believe nullspace is forgetting the most important factor: skill. More random events makes a game less random if (and only if) players have some way of influencing the odds in their favor, or preparing to handle the different outcomes to be slightly better off than the opponent given any result. In a wargame with only one battle for example, if I by skillful play can get the odds of that (highly decisive, probably) battle up to 60 % chance of me winning, then the game is still pretty random, even though I will on average win 60 % of the games played. But if the game has 200 battles on average, and by skill I can get 60 % chance of winning each battle, then I will probably have almost 100 % chance of winning the game.
Even if I have no chance of improving the odds of each battle, I can be better at setting up units to not be as badly hurt by a defeat, or to cause more damage to the enemy when winning. The classic example in many wargames is by surrounding an enemy unit so that if it is forced to retreat it will be eliminated... The better player will manage to do that a lot, while being able to retreat his own units safetly away from lost battles, so even if the players win 100 battles each, one player might have lost 80 units while the other only lost 5.
Any board wargamer can assure you that it works very well in practice. One of the most dice-heavy games of all, Advanced Squad Leader, is also one of few wargames that is popular to play competitively at tournaments, and the best player almost always wins every game (and tournament).
Even in the case of chess with random spawning of pawns, if there is a way for a player to prepare for that possibility in some way, to get more of an advantage of being given a pawn and/or less of a disadvantage when the opponent is given a pawn, then I believe that even in that game the better player would gain more of an advantage the more such evens there were, the odds of winning the game slightly drifting in his favor the more pawns was spawned.
The same goes for the FPS critical hit example. If many hits are scored, the player that hits most time will also score more critical hits, but the fewer hits there are the risk increases that the worse player will be lucky and score more critical hits than the better player.