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// Knuth's model of a fair die using only fair coins |
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mdp |
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module die |
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// local state |
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s : [0..7] init 0; |
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// value of the dice |
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d : [0..6] init 0; |
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[a] s=0 -> 0.5 : (s'=1) + 0.5 : (s'=2); |
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[b] s=0 -> 0.2 : (s'=1) + 0.8 : (s'=2); |
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[] s=1 -> 0.5 : (s'=3) + 0.5 : (s'=4); |
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[] s=2 -> 0.5 : (s'=5) + 0.5 : (s'=6); |
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[] s=3 -> 0.5 : (s'=1) + 0.5 : (s'=7) & (d'=1); |
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[] s=4 -> 0.5 : (s'=7) & (d'=2) + 0.5 : (s'=7) & (d'=3); |
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[] s=5 -> 0.5 : (s'=7) & (d'=4) + 0.5 : (s'=7) & (d'=5); |
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[] s=6 -> 0.5 : (s'=2) + 0.5 : (s'=7) & (d'=6); |
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[] s=7 -> 1: (s'=7); |
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endmodule |
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rewards "coin_flips" |
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[] s<7 : 1; |
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endrewards |
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label "one" = s=7&d=1; |
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label "two" = s=7&d=2; |
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label "three" = s=7&d=3; |
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label "four" = s=7&d=4; |
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label "five" = s=7&d=5; |
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label "six" = s=7&d=6; |
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label "done" = s=7; |