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// Knuth's model of a fair die using only fair coins
mdp
module die
// local state
s : [0..7] init 0;
// value of the dice
d : [0..6] init 0;
[fair] s=0 -> 0.5 : (s'=1) + 0.5 : (s'=2);
[ufair1] s=0 -> 0.6 : (s'=1) + 0.4 : (s'=2);
[ufair2] s=0 -> 0.7 : (s'=1) + 0.3 : (s'=2);
[fair] s=1 -> 0.5 : (s'=3) + 0.5 : (s'=4);
[ufair1] s=1 -> 0.6 : (s'=3) + 0.4 : (s'=4);
[ufair2] s=1 -> 0.7 : (s'=3) + 0.3 : (s'=4);
[fair] s=2 -> 0.5 : (s'=5) + 0.5 : (s'=6);
[ufair1] s=2 -> 0.6 : (s'=5) + 0.4 : (s'=6);
[ufair2] s=2 -> 0.7 : (s'=5) + 0.3 : (s'=6);
[fair] s=3 -> 0.5 : (s'=1) + 0.5 : (s'=7) & (d'=1);
[ufair1] s=3 -> 0.6 : (s'=1) + 0.4 : (s'=7) & (d'=1);
[ufair2] s=3 -> 0.7 : (s'=1) + 0.3 : (s'=7) & (d'=1);
[fair] s=4 -> 0.5 : (s'=7) & (d'=2) + 0.5 : (s'=7) & (d'=3);
[ufair1] s=4 -> 0.6 : (s'=7) & (d'=2) + 0.4 : (s'=7) & (d'=3);
[ufair2] s=4 -> 0.7 : (s'=7) & (d'=2) + 0.3 : (s'=7) & (d'=3);
[fair] s=5 -> 0.5 : (s'=7) & (d'=4) + 0.5 : (s'=7) & (d'=5);
[ufair1] s=5 -> 0.6 : (s'=7) & (d'=4) + 0.4 : (s'=7) & (d'=5);
[ufair2] s=5 -> 0.7 : (s'=7) & (d'=4) + 0.3 : (s'=7) & (d'=5);
[] s=7 -> 1: (s'=7);
endmodule
rewards "coin_flips"
[fair] s<7 : 1;
[ufair1] s<7 : 1;
[ufair2] s<7 : 1;
endrewards
label "one" = s=7&d=1;
label "two" = s=7&d=2;
label "three" = s=7&d=3;
label "four" = s=7&d=4;
label "five" = s=7&d=5;
label "six" = s=7&d=6;
label "done" = s=7;