Re: Selecting a valid hand configuration for Monte-Carlo simulation
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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.
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I can see why this explains that you have to do a full re-sample each time, but whats the reason you need to permute the player order aswell? It looks like it is because when P1 is first we get a collision 1/3 of the time and when P2 is first we only get one 1/4 of the time? (Bear in mind I've just woken up and might just be stating the obvious or be reading this wrong...). If this is so then this must explain the discrepancy in the pokerstove results you found.
Juk [img]/images/graemlins/smile.gif[/img]
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