Soft counts

Could someone explain the math behind doubling on soft counts? It seems counterintuitive to me to double on a A,4 when the dealer is showing a 4 or 5. Why is it worth it? Thanks

Acccording to the Wizard of Odds, your expected return from hitting A-4 against 4,5,and 6 is .06, .09, and .12 respectively (rounded to the nearest hundredth.) In other words, on a $10 wager, if you played the hands many thousands of times, you'd average out to a profit of 6 cents, 9 cents, and 12 cents respectively for each time the hand is played.

On the other hand, if you double, your expectation is .06, .13, and .18. So that is why basic strategy calls for a double in that situation. Over time, it makes more money than hitting. In fact, doubling A-4 against a 6 is about 50% better over time than hitting.

I just realized that the numbers are very close on doubling A-4 against a 4 on this chart; and my rounding made them look exactly the same. The actual expectation is .0593 for hitting and .0584 for doubling (carrying the decimal out four places as the site does.) This would appear to me to be a mistake. Unless I am reading something wrong, you'd do slightly better by hitting against the four. This is probably an issue of something that is rule-specific, or specific to the number of decks in play.

This chart is at http://wizardofodds.com/blackjack/bjapx1.html and is based on an infinite deck.

funny you mention this because I use to think the same way. I recently conditioned myself not to think at the table (as you can tell, I don't count cards) and just do basic strategy like it was second nature w/out questioning it

bama,

I just checked bja3, pg 446. correct expectation for A,4 vs 4 is hit .0593 and double .0623, .........checked the numbers near and nothing close to that double figure, so just a typo I guess.

mike

now I see that if you drop down to row A,5 vs 4 for a double you get .0586

hmmmmm

and who said computers never make mistakes?