Selecting a valid hand configuration for Monte-Carlo simulation

[matt42s]

I think we need to do a full re-sample AND permute the player orders on every collision, the frequencies will then work themselves out.

ie. our target frequency is P(P2|AK)=1/3
P1 is dealt first and receives 1 of 6 AA combinations.
P2 chooses 1 of 16 AK or 16 KQ combinations. 8 of the AK combinations 'collide' with P1's cards and the deal is invalidated. 8 of the AK's are OK and all 16 KQ's are OK.

When P2 is dealt first, he receives 1 of 16 AK or 16 KQ's
P2 chooses 1 of 6 AA combinations. 50% of the time P2 has KQ and any AA is valid. 50% of the time P2 has AK and a collision will occur 50% of those times. 25% of deals are invalid. The makeup of the remaining 75% is 2/3 KQ and 1/3 AK. Re-sampling P1's cards at this point, leaving P2 with AK in his hand is where the bias is introduced. When a collision occurs we have to take AK out of his hand and shuffle the play order.