Selecting a valid hand configuration for Monte-Carlo simulation

[jukofyork]

Also, the more I think about this the more side-tracked I'm getting with the question I originally asked myself:

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If P2 acts after P1 there will be: Ax, Ay, Kh, Ks, Kc, Kd, Qh, Qs, Qc, and Qd left for him to get dealt without causing a collision and if you keep re-sampling each time one of player 1's aces are chosen you end up with 8xAK and 16xKQ hands for P2 to get dealt, therefore P(P2|AK)=1/3 and P(P2|KQ)=2/3.

If P2 acts first he will have all 4 aces, kings and queens free, so he will end up with P(P2|AK)=1/2 and P(P2|KQ)=1/2 and since P1 only plays AA he will just re-sample until he gets AA whatever P1 chooses before him.

If you were to sample from all possible configurations by doing a full "discard and re-sample" each time then P(P2|AK)=(1/3+1/2)/2=5/12 and P(P2|KQ)=(2/3+1/2)/2=7/12.

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I still can't see anything to refute the fact that if player 2 is always assigned his cards before player 1, then P(P2|AK)=1/2 and P(P2|KQ)=1/2 which seems to go against both the "P(P2|AK)=1/3 and P(P2|KQ)=1/3" and the "P(P2|AK)=5/12 and P(P2|KQ)=7/12" ideas?

The partial re-sampling using a fixed ordering seems to lead to the "P(P2|AK)=1/2 and P(P2|KQ)=1/2" result and the partial re-sampling using a pre-defined permuated ordering seems to lead to the "P(P2|AK)=5/12 and P(P2|KQ)=7/12" result, so maybe they are both biased? [img]/images/graemlins/confused.gif[/img]

Juk [img]/images/graemlins/smile.gif[/img]