// Simple POMDP guessing a hidden variable (multiple attempts)

pomdp

// Number of guesses allowed (N=1,2,3,4)
const int N;

observables s, g endobservables

module M

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

	// Assign hidden variable randomly
	[toss] s=0 -> 0.1:(s'=1)&(h'=1) + 0.3:(s'=1)&(h'=2) + 0.6:(s'=1)&(h'=3);
	// Guess the value of the hidden variable
	[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);
	// No more guesses left
	[timeup] s=1&g=0 -> (s'=3);
	// Done
	[loop] s=2 -> true;

endmodule

label "correct" = s=2;

// Number of guesses made
rewards "guesses"
	[guess1] true : 1;
	[guess2] true : 1;
	[guess3] true : 1;
endrewards