[BruceZ]

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No. Now there are 24 cards that can help you. If you get one of the 12 that pair you (A, 2, 3 or 4), there are 22 cards that can go with it.

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There are 21 cards that go with it, not 22. A-4 (12-3=9) + 5-7 (12) = 21.


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If you get one of the other 12 (5, 6 or 7), there are now 21.

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There are now 20, not 21. A-4(12) + 5-7(12-4=8) = 20.


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That comes out to a 26% chance.

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24.8%. Only 0.6% better than A23x. I didn't believe it myself at first, but that's because it only allows for additional specific 2 card combinations which have relatively low probability. We also lose all the combinations with one of the fours.