% Nicos, 2003.
% These are predicate definitions for the Monty Hall problem.
% For reletated publications see http://stoics.org.uk/~nicos/pbs
% eg. http://stoics.org.uk/~nicos/pbs/Ismis03.ps.gz
%     http://stoics.org.uk/~nicos/pbs/Qapl01.ps.gz


% to use: 
% ?- use_module( library(pfd)).
% ?- pfd_demo.
% ?- [pack(pfd_demo/examples/curtains)].
% ?- curtains( Strategy, Probability ).
% 
% Probability=1/3,
% Strategy=alpha ? 
% 
% 
% Probability=2/3,
% Strategy=beta ? 
% 
% nope
% 
% Here alpha is the =, ie dont switch, strategy and beta is the #, strategy.
%
% curtains( alpha, Pr ) :- 
curtains( alpha, Pr ) :-
	Gift ~ uniform([1,2,3]),
	First ~ uniform([1,2,3]),
	Reveal ~ uniform([1,2,3]),
	Reveal \# Gift,
	Reveal \# First, 
	Second = First,
	Pr is p(Second=Gift).

curtains( beta, Pr ) :- 
	Gift ~ uniform([1,2,3]),
	First ~ uniform([1,2,3]),
	Reveal ~ uniform([1,2,3]),
	Reveal \# Gift,
	Reveal \# First, 
	Second ~ uniform([1,2,3]),
	Second \# Reveal,
	% Second \# 1 :: First, % alternatively
	Second \# First,
	Pr is p(Second=Gift).