# Thread: Doubling of soft hands from A,2 to A,5

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Working my way through the math! Lots to take in so thanks very much to everyone.

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Originally Posted by DSchles

So the OP's sense of risk aversion is correct, but, as you mention, it doesn't apply to BS.

Don
Yes, this is what I wanted to express.
Thanks for clarifying.

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If you double down with ace 2 and catch a 2, you can't draw again.

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Originally Posted by felix
Basic Strategy Question. Eight Decks. Dealer Stands on all 17s.

Doubling of soft hands from A,2 to A,5. Why? Example with A,4:

If I double on Ace, 4 against dealer's 4, I can only make 5 possible hands: 17, 18, 19, 20, 21. So 5/13 or 38.5% of the time I will make a hand (remembering 17 is never a 'winning' hand, it's either a push or a 'win' over a dealer's bust).

If the dealer starts with a 4 their outcome is 60.5% that they will make a hand of either 17, 18, 19, 20 or 21 and 39.5% that they bust.

So my question is why would I double on my Ace, 4 against a dealer's 4 when 60.5% of the time they will make a hand and I can only make a hand 38.5% of the time by doubling and getting that additional single card?

If I just hit Ace, 4 there are more possibilities of making a hand. For example: A, 4 and I double getting an Ace = 6 or 16. End of hand.

Or Ace, 4 and I hit getting an Ace = 6 or 16, so I have another chance by taking another card...

Interested to hear if I've missed something basic here. New Forum member. Thanks.
Hi Felix! I'd like to point out that your initial analysis only accounts for the immediate possibilities after taking a single card (whether via hitting or via doubling). It neglects to mention the various future possibilities for the player's hands and dealer's hands after taking that card, as well as the payoffs to the player in each case (1x the original bet if hitting versus 2x the original bet if doubling). It is necessary to account for both factors to determine the optimal play. The reason why you didn't is the same why most people didn't before Thorp (Baldwin et al recommended a "hit" in the case of soft 15 versus 4) examined the entirety of the branching possibilities via a computer: only a computer can accurately and quickly account for all outcomes of hitting versus doubling your soft 15 versus 4, weight them according to the payoffs and their associated probabilities of occurrence, and then sum them all to a final total EV. This is why Don, Gronbog, Cacarulo, and others say "just trust the math": the equation is often larger than the human mind can handle. We can trust the logic of the calculation since the same logic holds for other, simpler cases that we can analyze with pencil and paper (e.g. Woolworth blackjack from Griffin's "Theory of Blackjack"), and there is no outstanding reason why we should doubt this since the difference in the complexity of the two problems is one of degree rather than of kind.

This is also, by the way, why I wholeheartedly recommend that an AP should be as mathematically literate as possible. If we're going to be more mathematically literate than the casinos, we should also be savvy enough to be able to consider and properly justify all facets of a problem when devising an optimal strategy before we even wager our first bet.

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Nice post!

Don

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Thanks for the additional replies on this.

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