Andy's Math/CS page

Sunday, April 15, 2007

Money Colliding at High Speeds

Are there any gamers among my vast readership? Here is a simple auction-based card game I once toyed with; I'm curious what others think, and how it might be souped up for greater replay value.

For two or three players. Each receives all 13 cards in a suit, which they hold privately; the remaining suit (diamonds) is shuffled and put face down. On each round, a diamond card is flipped face up; players simultaneously submit a 'bid' card from their suit. The highest bid gets the diamond (ties can be handled in one of several ways, suit yourselves), and all bid cards used get discarded.

To score when all diamonds have been auctioned: each player gets m points for the m of diamonds, 11 for the jack, etc.

This game can reach a maniacal level of second-guessing--exciting, but perhaps too little in the way of underlying strategy and calculation. It is easy to show that no deterministic strategy is 'undominated' (i.e. there is always a victorious counter-strategy); but I don't see that any simple randomized strategy is undominated either.

Suggestions? Pointers to successful auction games already on the market? I'd look into them myself, but then half of my attraction to the auction genre is that I'm a cheapskate.

• Interesting game.

I'd be inclined to work it out completely for the two card game (ie, a 'suit' has just twos and threes in it), then do the 2,3,4 game, etc.

By  Thane, at 11:38 PM