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Best of Alan Krigman
How Doubling in Blackjack Wins More by Winning Less26 January 1998
I'll cite a few examples.
o Three-seven against four-up. Hitting, expectation is a profit of $0.24 per dollar bet. Doubling, it's $0.48.
o Six-five against 10-up. Hitting, expectation is to win $0.12 per dollar bet. Doubling, it's to gain $0.18.
o Ace-four against five-up. Hitting, expectation is to earn $0.09 per dollar bet. Doubling, it's to net $0.13.
o Ace-seven against six-up. Standing, expectation is a return of $0.28 per dollar bet. Doubling, it's above $0.38.
In some doubling situations, you have the same chance of winning whether you go for broke or hold back and take the more conservative option. These are hands on which your alternative is to hit, and on which you'd only draw a single card regardless of its value. This occurs exclusively on two-card totals of 10 or 11 versus dealer four through six.
In all other cases, you have less chance to win by doubling than hitting. Why? Because the draw could yield a total at which the probability of winning would be raised by taking another card.
Here are some illustrations:
Doubling has twice the expectation of hitting when the odds of winning are equal. Otherwise, the advantage is less than twice - still double the money, but less chance of winning it.
Restriction to drawing a single card diminishes the benefits of doubling most severely on soft hands, especially low totals. For instance, starting with ace-three versus five, expectation is about $0.02 per dollar higher for doubling than hitting. With ace-two versus five, the improvement is less than a penny.
How can you use this knowledge? First, if you're scraping the bottom of your bankroll, recognize that winning at all may be worth more than winning twice as much; maximizing your chances may therefore be better for you than maximizing your expectation. Next, forget about "doubling for less" except, possibly, on 10 or 11 versus four through six; on all other hands, this will cut your expectation two ways, reducing both the amount you'll win and also your chances. And last, when your gut says something and the gurus something else, ponder the perspicacity of this pronouncement from the pencil of the pensive poet, Sumner A Ingmark:
Best of Alan Krigman