pomdp

const int N;

module M

	s : [0..2]; // state
	h : [0..3]; // hidden var
	g : [0..N] init N; // num guesses left

	[toss] s=0 -> 0.1:(s'=1)&(h'=1) + 0.3:(s'=1)&(h'=2) + 0.6:(s'=1)&(h'=3);
	[guess1] s=1&g>0 -> (s'=(h=1)?2:s) & (g'=g-1);
	[guess2] s=1&g>0 -> (s'=(h=2)?2:s) & (g'=g-1);
	[guess3] s=1&g>0 -> (s'=(h=3)?2:s) & (g'=g-1);
	[timeup] s=1&g=0 -> (s'=3);
	[loop] s=2 -> true;

endmodule

observables s, g endobservables

label "correct" = s=2;

rewards "guesses"
	[guess1] true : 1;
	[guess2] true : 1;
	[guess3] true : 1;
endrewards