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Dreidel modeling
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dtmc | |
const int M; //starting money | |
formula Players = 4; //Players | |
formula maxval = M*Players; | |
formula done = (p1=0) | (p2=0) | (p3=0) | (p4=0); | |
formula halfpot = ceil(pot/2); | |
module dreidel | |
p1 : [0..maxval] init M; | |
p2 : [0..maxval] init M; | |
p3 : [0..maxval] init M; | |
p4 : [0..maxval] init M; | |
pot: [0..maxval] init 0; | |
turn: [1..4] init 1; | |
[spin] ((pot != 0) & !done & (turn = 1)) -> | |
0.25: (p1' = p1-1) & (pot' = min(pot+1, maxval)) & (turn' = 2) //shin | |
+ 0.25: (turn' = 2) //nun | |
+ 0.25: (p1' = min(p1+halfpot,maxval)) & (pot' = pot-halfpot) & (turn' = 2) // hay | |
+ 0.25: (p1' = min(p1+pot,maxval)) & (pot' = 0) & (turn' = 2); //gimmel | |
[spin] ((pot != 0) & !done & (turn = 2)) -> | |
0.25: (p2' = p2-1) & (pot' = min(pot+1, maxval)) & (turn' = 3) //shin | |
+ 0.25: (turn' = 3) //nun | |
+ 0.25: (p2' = min(p2+halfpot, maxval)) & (pot' = pot-halfpot) & (turn' = 3) // hay | |
+ 0.25: (p2' = min(p2+pot, maxval)) & (pot' = 0) & (turn' = 3); //gimmel | |
[spin] ((pot != 0) & !done & (turn = 3)) -> | |
0.25: (p3' = p3-1) & (pot' = min(pot+1, maxval)) & (turn' = 4) //shin | |
+ 0.25: (turn' = 4) //nun | |
+ 0.25: (p3' = min(p3+halfpot, maxval)) & (pot' = pot-halfpot) & (turn' = 4) // hay | |
+ 0.25: (p3' = min(p3+pot, maxval)) & (pot' = 0) & (turn' = 4); //gimmel | |
[spin] ((pot != 0) & !done & (turn = 4)) -> | |
0.25: (p4' = p4-1) & (pot' = min(pot+1, maxval)) & (turn' = 1) //shin | |
+ 0.25: (turn' = 1) //nun | |
+ 0.25: (p4' = min(p4+halfpot, maxval)) & (pot' = pot-halfpot) & (turn' = 1) // hay | |
+ 0.25: (p4' = min(p4+pot, maxval)) & (pot' = 0) & (turn' = 1); //gimmel | |
[ante] (pot = 0) & !done -> (pot'=pot+4) & (p1' = p1-1) & (p2' = p2-1) & (p3' = p3-1) & (p4' = p4-1); | |
[done] done -> true; | |
endmodule | |
rewards "num_spins" | |
[spin] true : 1; | |
endrewards |
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