[hoopkidups]

Hi,

I'm making a small arcade game that works like this:

A dollar bill ranging from $1 to $6 in value is placed in the middle. (Once that type of bill has been used, it cannot be used again.)

The human player and the computer player both have bills ranging from $1 to $6 in their hands. When the bounty is placed in the middle, the human player will be prompted to select a bill. The computer will do the same thing, and the player who chooses the higher value will will the bounty, plus the other player's bet. If both players bet the same value, all of the cash (Bounty + Human's Bet + Computer's Bet) remains in the middle, and both players will bet again.

The player with the most money at the end of the game will win.

Now that you know how the game is played, I'm hoping that someone will be able to help me with the computer AI. It was easy enough to have the computer make relatively stupid choices, but now I'm trying to make a mode where the computer will choose the BEST possible option to bet.

I did some research, and this game is very similar to a card game called Goofspiel. According to an analysis of the game, a payoff matrix must be created, and then analyzed. This is where I'm having trouble - I can't figure out how to translate the matrix to computer terms, especially since there are so many possibilities.

If anyone knows anything about payoff matrices, then I would really appreciate it if they could shed some light on the problem I'm having.

-Thanks

[bpmurray]

I'm not familiar with Goofspiel, but you need to read up on what's known as "combinatorial game theory" which addresses this situation, i.e. 2 players who each take turns when you have all the information, as opposed to "classical game theory" which refers to games which have a hidden part to them.

The payoff matrix can only be used when you have a fixed amount of money, i.e. the computer loses & the player wins that amount. I just checked wikipedia, and it has a good description of the idea on http://en.wikipedia.org/wiki/Payoff_matrix