How Doubling in Blackjack Wins More by Winning Less

Doubling down on blackjack hands can be highly profitable. Expectation - the average net of wins minus losses for the same bet over a long period - is always positive for proper doubles. And it exceeds that of playing the hand any other way.

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.

To clarify, say you have 10 or 11 and the dealer has four, five, or six. Double, and you get a single card. Hit, and your result will necessarily be between twelve and 21 - values on which you would then stand. Either way you'd draw just once.

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:
o Five-five versus two- or three-up. Pulling a deuce gives you 12. Many solid citizens stand on 12 versus two or three, but proper basic strategy is to draw again.
o Three-eight versus seven- through 10-up. If you receive ace through five, you'd have 12 through 16 and would appreciate being able to ask for an additional card.
o Two-seven versus three- through six-up. If a two appears, you'd be sitting with 11 - weak if you had to stop, strong if you could hit again.
o Ace-two through ace-five versus six-up. If an ace falls, you'd certainly draw again if you could.

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.

To see the effect, imagine you're dealt four-seven. Against six, the hand would take one card either way and expectations are $0.34 and $0.68 per dollar for hitting and doubling, respectively. Against seven, draws of deuce through five would warrant further hits if allowed; expectations are $0.29 for hitting and not $0.58 but $0.47 per dollar for doubling.

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:

Winning more by winning less,
Causes gamblers great distress.
How it's done, most will confess,
Calls for facts they don't possess.