// sum of two dice as the asynchronous parallel composition of
// two copies of Knuth's model of a fair die using only fair coins

mdp

module die1

	// local state
	s1 : [0..7] init 0;
	// value of the dice
	d1 : [0..6] init 0;

	[] s1=0 -> 0.5 : (s1'=1) + 0.5 : (s1'=2);
	[] s1=1 -> 0.5 : (s1'=3) + 0.5 : (s1'=4);
	[] s1=2 -> 0.5 : (s1'=5) + 0.5 : (s1'=6);
	[] s1=3 -> 0.5 : (s1'=1) + 0.5 : (s1'=7) & (d1'=1);
	[] s1=4 -> 0.5 : (s1'=7) & (d1'=2) + 0.5 : (s1'=7) & (d1'=3);
	[] s1=5 -> 0.5 : (s1'=7) & (d1'=4) + 0.5 : (s1'=7) & (d1'=5);
	[] s1=6 -> 0.5 : (s1'=2) + 0.5 : (s1'=7) & (d1'=6);
	[] s1=7 & s2=7 -> (s1'=7);
endmodule

module die2 = die1 [ s1=s2, s2=s1, d1=d2 ] endmodule

rewards "coinflips"
	s1<7 | s2<7 : 1;
endrewards

label "done" = s1=7 & s2=7;
label "two" = s1=7 & s2=7 & d1+d2=2;
label "three" = s1=7 & s2=7 & d1+d2=3;
label "four" = s1=7 & s2=7 & d1+d2=4;
label "five" = s1=7 & s2=7 & d1+d2=5;
label "six" = s1=7 & s2=7 & d1+d2=6;
label "seven" = s1=7 & s2=7 & d1+d2=7;
label "eight" = s1=7 & s2=7 & d1+d2=8;
label "nine" = s1=7 & s2=7 & d1+d2=9;
label "ten" = s1=7 & s2=7 & d1+d2=10;
label "eleven" = s1=7 & s2=7 & d1+d2=11;
label "twelve" = s1=7 & s2=7 & d1+d2=12;