Pig Visualizations( home  game  solution  links ) 
Thumbnail  Description  Media 

A cross section of the optimal policy when the opponent's score is 30. The optimal boundary is the black line. The player should roll again at any turn total below that boundary and hold for any total above. The gray areas show the scores and turn totals that are actually reachable by the optimal player. 
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The entire roll/hold boundary for the optimal Pig play policy. 
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A view of all of the states reachable by an optimal player. Notice that an optimal player (shown as player 1) will never hold with a value between 0 and 21. 
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Reachable states where rolling is optimal. 
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Probability contours in Pig space. The contours show where the probability of player 1 winning is 3%, 9%, 27% and 81%. 
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Author: Clif Presser