Doubling at Blackjack: The Pros and Cons of too Little or too Much

3 October 2002

By Alan Krigman

Winning or losing doubled-down blackjack hands can make or break a session. Basic Strategy dictates doubling when doing so has higher "expectation" or theoretical profit than other options. Some players, however - veterans who prize their wallet-sized gospel tracts as well as greenhorns who think it's all luck - hit or stand when "D" is indicated, while others do the opposite.

Bettors who balk when doubling is decreed generally worry lest a loss would bust their budgets, and would prefer to win half as much than risk going belly-up. Solid citizens who double when less assertive action is advocated typically perceive they're in a strong position and think this is a clever way to exploit it.

Players face criteria in addition to expectation. As a "zero-sum" analogy, would you rather bet $1 on a 10 percent probability of winning $9 or a 1 percent shot at $99? What about betting $1,000 with a 10 percent chance of winning $9,000 or a 1 percent chance of grabbing $99,000? The money coin clearly has two sides - the pain of how much can be lost and the pleasure of how much might be won. Chance of success or failure is a third point, albeit one given short shrift on casino floors, in lottery ticket lines, and wherever else good folks gather to gamble.

Similar ideas pertain to doubling down in blackjack, although the distinctions are finer and expectation enters the equation. Most players get the money part right. Probabilities are the problem.

To illustrate the case of doubling when Basic Strategy calls for a hit, picture a two-card nine vs seven-up. Players are favored either way. Hitting, chances are 53 percent of winning, 36 percent of losing, and the remaining 11 percent of pushing. Expectation, stated as theoretical profit per dollar bet, is the difference between the chances of winning and losing, each multiplied by $1: ($1 x 0.53) - ($1 x 0.36) = $0.17. Doubling, prospects are 49 percent of winning, 44 percent of losing, and 7 percent of pushing. Expectation is the difference between the chances of winning and losing, each multiplied by $2: ($2 x 0.49) - ($2 x 0.44) = $0.10. Hitting results in smaller bankroll swings than doubling. But expectation is better by $0.07 per dollar and the chance of winning is greater by 53 - 49 = 4 percent.

An example of hitting when doubling is "correct" is shown by a two-card eleven vs a non-blackjack 10-up. Players are again favored either way. Hitting, probabilities are 51 percent to win, 39 percent to lose, and 10 percent to push. Expectation is to earn ($1 x 0.51) - ($1 x 0.39) = $0.12 on the dollar. Doubling, probabilities are 51 percent to win, 42 percent to lose, and 7 percent to push. Expectation is ($2 x 0.51) - ($2 x 0.42) = $0.18 profit on the dollar. Expectation is $0.06 per dollar more by doubling than by hitting. With 11 vs 10, chances of winning are nearly equal but doubling loses more often, 42 percent as opposed to 39 percent, the difference going to pushes. Other doubles may win more often than hits, or win and lose at the same rate.

Basic strategy is postulated purely on maximizing expectation. Transgressing its tenets always trims the statistically expected profit. Hitting when the crib sheet says to double may compensate somewhat for the reduced expectation by raising the chance of winning or lowering the likelihood of losing. Doubling when the experts advocate hitting exacerbates the cut in expectation by decreasing the chance of winning or elevating that of losing.

Boosting what you risk to raise what you hope to gain, or the converse, is subjective and neither right nor wrong. Breaching Basic Strategy by hitting instead of doubling, or vice?versa, sacrifices expectation. The former at least offers the benefit of more wins or fewer losses at the lower level. The latter imposes the penalty of fewer wins or more losses in the higher realm. Which is best for you? Always follow the book? Live dangerously? Take the conservative path? Weigh the implications for your stake and your goals, along with the impact on expectation and the effect on your chances, then decide for yourself. As the venerated versemonger, Sumner A Ingmark, vividly verbalized:

The wisest people tend to act,
In concert both with hope and fact.