[matt42s]

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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.

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This sounds right, but is ignoring the premise - that is, allocating the cards with the correct frequency. If P2 is given KQ, then you would have to deal the remaining deck to P1 an average of 204 times before P1 is given AA. If P2 is given AK, you have to deal 408 times before P1 is given AA. We cannot ignore that difference.

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"P(P2|AK)=5/12 and P(P2|KQ)=7/12"

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these numbers follow on from the previous error.

The only answer is P(AK)=1/3 P(KQ)=2/3 and we need an algorithm which will generate that distribution of cards