Liar's Poker: a tricky problem

[big_bad_al]

Liar's Poker is a card game we sometimes play around the office. It's a pretty simple game to learn if you're already familiar with poker hands:

Comments

[inferno0069]

We suspect there's a way of combining these
Did you take any game theory?
http://en.wikipedia.org/wiki/Mixed_strategy
Now I've gotta go work, but I hope to come back and read this in more detail later.

[big_bad_al]

I have not taken any game theory. I strongly suspect there is always a mixed Nash equilibrium, though.

Earlier today I solved the 8-card deck version, and it doesn't matter if you use a pure or a mixed strategy; the best you can do is 3/7 change of winning. I'll hopefully post more details about this soon.

[dhalps]

It sounds like in reality this game, like poker, will have nothing to do with math and everything to do with people.

[big_bad_al]

I agree that in the general case (i.e., when the total number of cards dealt is more than 2), any good program will make predictions based on the past behavior of the opponents, and these predictions will play a critical role in whatever strategy it uses. However, if you go first in the final round, you can't change your behavior based on what your opponent does (by the time he bids, the game is deterministic).

Consequently, I think that for this final round, the best you can do is to use whatever the mathematically optimal strategy is, so that your opponent cannot take advantage of you. I'm assuming that you play the game enough that your opponents can figure out your end-game strategy if they so choose, which is likely to be the case here (the tournament will contain at least thousands of games, if not more).