"A game for Vulcan children" is how Kevin Maroney once described Hare and Tortoise (Hase und Igel in the German -- apparently German hares race hedgehogs). It's an apt description; the game has the external indicia of a child's game -- cute little animals drawn from a childhood fable -- but actually, it's a game of exceptional mathematical and logical rigor.
It's a race game, meaning it's played on a track, and the first player to advance his token across the finish line is the winner. Most race games are, of course, purely luck-dependent (and brain dead). Hare and Tortoise is anything but.
You begin with 65 carrots, and on your turn, you choose how many carrots to spend advancing along the track. The cost in carrots is the triangular number of the number of spaces moved. Interesting to me, because triangular numbers show up in a lot of my designs too -- they increase faster than linearly, but not as fast as squares, and are therefore useful in a lot of cases. A triangular number is the sum of that number and all prior numbers down to 1; that is, the triangular number of 2 is 3 (2+1), of 3 it is 6 (3+2+1), and so on. Or if you prefer, cost = (n^2 + n)/2.
Thus, you can zip quite far down the track, but at prohibitive cost. There are ways of acquiring additional carrots -- indeed, you must do so to win -- but laggards can more easily acquire carrots than leaders (a balancing feature), and in any event, gaining carrots is a double-edged sword. You see, you may not pass the finish line (as the winner) with more than 10 carrots remaining. Thus, gaining carrots can cost you, too.
The third major piece of the puzzle is that a track square can only be occupied by one player at a time, and certain squares are critically important to gaining carrots (and to getting rid of the three lettuce markers you begin which, which you must also do before crossing the finish line). Thus, each turn you're not just faced with the calculational problem of winning, but also with the practical problem that critical squares up or down the track may be occupied at present, so figuring the optimal action this turn is tricky.
Hare and Tortoise won the Spiel des Jahres in 1979, the award's first year, and is an excellent design; it is also, at present, only in print in German, but English-language editions can still be found from a number of vendors for less than $20.
I find I like games -
I find I like games - role-playing games, at least - that use triangular numbers for things like skill level progression. With the breadth of skills available in many RPGs, it seems to provide a reasonable balance between having a lot of skills at a small level versus devoting a lot of energy into developing expert skill level in something. It also provides a progression where players find it easy to know how much experience (or whatever) they need to improve something to the next level - one more each time.
As much as the probabilistics nerd in me loved the Earthdawn RPG for its Fibonacci sequences and its step table resolution (i.e. having a "step 18" roll meant rolling a number of multi-sided dice with a mean expected value approximating 18), the system was not kind to the non-mathematicians for whom a 500/800/1300/2100/3400 Legend Point progression wasn't natural.
Hare and Tortoise is in print in English now
There is a Ravensburger 2008 edition (pictured above with the hedge hog) available in German. However, because the of the abundance of Abacus Spiel 2000 English edition, it is likely that Ravensburger edition will not be printed in English until the Abacus Spiel edition become scarce in the US.
The key difference in editions besides the artwork and usability (interface) is how much luck is included when landing on a Hare square. It is my understanding that the author submitted the game to be zero luck and different publishers tinkered to add luck in the game. I heard that the Vulcan edition has not tinkered with the design, having zero luck. However this is unconfirmed because shipping cost cost are so high from Vulcan homeworld, I do not have a copy.
The newest, Ravensburger 2008 edition, you draw a card when you land on a Hare square. The card can be getting more carrots to losing a turn. The cards were used fix some imbalances in the luck of the previous editions.
The older, Abacus Spiel 2000 edition, you rolled dice. A dice roll on a chart determined from losing a turn to gaining more carrots when you land on a Hare square. Some people felt that there were imbalances in the luck of the dice chart.
When I emailed the author about the which of edition he prefers on how luck is handled when you land on a Hare square and he said:
"... you can land on them [Hare squares], but must miss a turn. This would be the equivalent of the hare taking a nap, as in Aesop's fable. This is the rule I most favour and would prefer it to simply not landing on them at all, ..."
Thus get the English edition Abacus Spiel/Rio Grande 2000 and play with this zero luck variant (patch)
* Nap time--landing on a Hare square causes the player to take a nap and lose one turn.
Designer's Notes > http://www.davidparlett.co.uk/haretort/index.html
Different editions compared: > http://www.thegamesjournal.com/articles/Hare&Tortoise.shtml