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Best of Alan Krigman

Gaming Guru

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How Often Can You Expect Doubles to Help You in Blackjack?

10 December 2002

The difference between winning and losing sessions at blackjack often depends on doubles. In particular, it hinges on 10s versus dealers' twos through nines and 11s against twos through 10s. Beating the bosses is greatly facilitated by getting a fair share of these hands, acting aggressively on them, and pulling the right cards when you do.

Sometimes, however, it seems as if you don't fall into enough doubling situations. Or, you encounter plenty, and end up drawing garbage in round after aggravating round. Not that you can't experience a profitable session without doubles. Or by repeatedly doubling on 10s or 11s and getting smacked with fives or less when the dealer is showing high up-cards. It may be exciting to snatch victory from the jaws of defeat occasionally. But nobody likes shoving out extra money then silently or otherwise having to beseech the gambling gods for gifts to save their skins.

The probability of starting with a 10 or 11 against two through nine or two through 10, respectively, is about 7 percent. This is somewhat more than once every 14 hands. Assume you're playing one hand, with three other spots in action at the table. You should average 80 to 85 hands per hour. This means you can expect five or six of the cited opportunities in an hour, subsequently pulling robust third cards in two or three cases and weaklings in the rest. At these nominal levels of occurrence, doubles essentially help you remain afloat. More favorable cases, and you should make money. Less, and, well, let's not talk about it.

How unusual is it to encounter a session in which you get under or over the five or six possible doubles you anticipate for the assumed conditions? The answers can be found in the first of the accompanying lists. The figures account for more than 90 percent of all possibilities. They indicate the likelihood of receiving from two to nine candidate hands in an hour, when the law of averages says five or six are actually expected. The data show that, in fact, five or six should happen about one third of the time, but a sorrowful three or four instances are far from rare - at 23.8 percent, and a joyful seven or eight are roughly as common - at a combined 23.6 percent.

1. Chance of receiving various numbers of 10s or 11s versus dealer 2-9 or 2-10, respectively, per hour when the expected number is five or six

instances probability
2 4.7%
3 9.5%
4 14.3%
5 17.0%
6 16.6%
7 13.8%
8 9.8%
9 6.2%

2. Chance of receiving various numbers of 10- or 11-based doubles and finishing with 20 or 21, per hour, when the expected number is two or three

instances probability
0 10.4%
1 23.8%
2 27.0%
3 20.2%
4 11.2%
5 4.9%
6 1.8%
7 0.5%

The second list shows the chance of receiving from zero to seven 10- or 11-based doubles in which you finish with 20 or 21, per hour, when two to three are expected. The two or three favorable results needed to stay afloat should ensue in about 47.2 percent of all hour-long sessions at tables with four spots in action. Fewer instances, zero or one, occur in about 34.2 percent of all such cases; the four or five well-turned doubles that can boost you over the top should only be anticipated in 16.1 percent.

Solid citizens generally know how to handle sessions with more than the projected number of two-card 10s and 11s, especially when they find themselves drawing well to them. Most forge ahead. Some press their bets, hoping to exploit what they perceive as a hot shoe to the max; others stay on a steady course, taking the profit from the additional money bet under promising conditions.

The opposite case often leads to behavior like switching tables, quitting, or adding spots hoping to change the legendary "flow of the cards." If one or another of these actions serves to calm your nerves, go ahead. But bear in mind the probabilities given in the lists, recognizing you can encounter shoes that seem like history's worst, yet are hardly singular by any reasonable criteria. Here's how the venerable versemonger, Sumner A Ingmark, urged restraint from rashness in such situations:

Ere you dismiss events as strange,
Be sure you know the normal range.

Alan Krigman

Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.
Alan Krigman
Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.