## The game of Spoof

This game for two players requires only six matches. Each player gets three matches to start with. In one round of the game each player chooses a number of his/her matches to hold in his/her hand. This number has to be concealed from the other player. Then the players bid on how many matches there are altogether, with the one constraint that the bid of the second player has to be different from that of the first player. Once both players have given their bids, they reveal the matches in their hands. If the total number of matches equals the bid of one of the players, this player wins the round, which means that he/she loses one match and gets to start the next round. If no bid equals the total, both players keep all their matches and the order of bidding is the same as before. The game goes on until one player has no more matches. This player wins the game.

These two influence diagrams are models to help the two players, assuming that player A always bids first. Ah means A's hand, Ac means A's choice, Ab means A's bid, and similarly for Bh, Bc and Bb.

### Player A

This network has been installed on your computer with the Hugin software. Open the network in Hugin (Note: not all browsers can open Hugin directly). You can find the network in the directory where you installed Hugin (eg. C:/Program Files/Hugin/Hugin Light/Samples).

You can also find the samples at the Hugin download area.

If in Bh and Ah you enter the amounts of matches left, a propagation will yield the expected utilities for choices of matches in Ac. If you then enter the choice of player A in Ac, a propagation will yield the expected utilities for the opening bid.

The utilities are: 1 for correct bid, 0 for correct bid by opponent and 0.5 for no party being correct.

The Const-utility ensures that forbidden choices get negative utilities.

### Player B

This network has been installed on your computer with the Hugin software. Open the network in Hugin (Note: not all browsers can open Hugin directly). You can find the network in the directory where you installed Hugin (eg. C:/Program Files/Hugin/Hugin Light/Samples).

You can also find the samples at the Hugin download area.

| HUGIN Expert A/S | , 1998

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