Re: In a S17, H16 game
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Can anyone tell me why doubling A4 and 5 are mathematically better than doubling A2 and 3?
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I'll try (though you may wish to move this to the appropriate forum for the best answer).
The issue is the ability to rehit. One only doubles down here against stiffs (dealer showing three through six in a 6-deck game). With this in mind, the goal is to maximize EV. Doubling A5 against a stiff is straightforward. An A, 2, 3, 4 and 5 improve the hand (P = 5/13). The other cards have no effect (P = 8/13; a total less than 17 is the same as zero). The downside to doubling down is not getting a third card. Here, it's only an A where you'd like to get one more card (P = 1/13), and an A here isn't horrible, as you still have a chance to push against some of the range where the dealer stands (a 17, of course).
Doubling A2: Improves with 4, 5, 6, 7, and 8 (still P = 5/13). Other cards equal zero (still P = 8/13). The difference is in losing the rehit. Here, you'd like to rehit if you got an A, 2, 3, or 4 (P = 4/13), and only one of these, the 4, allows a push against a dealer 17.
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Ah... I see now. Thank you.
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