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# Should you flout Basic Strategy in blackjack – and, if so, when and why?

29 November 2010

Even blackjack players who are a mite shaky on the fine points of Basic Strategy know "you're supposed to" double on an 11 facing anything except an ace, and on a 10 against anything but an ace or 10. The reason has to do with what the gurus call "expectation." Whichever option on a hand gives a bettor the greatest positive or the least negative expectation determines the rule.

Expectation is a statistical term involving probabilities of alternate draws by players and dealers, chances of those draws leading to triumph or tragedy, and the corresponding amounts. For intuitive purposes, think of it as the total that solid citizens win or lose divided by the gross wager after many tries, handling a situation in a given manner. Further, while expectation is usually stated as a percentage, it's more readily pictured as average gain or loss per dollar bet at the start of a round.

Here are the expectations for 11 versus ace-up off the top of an eight-deck shoe, or anywhere in such a shoe if it's uncounted. The data are for "playable" hands, excluding the probability of dealer blackjacks, because bettors will lose only their initial wagers when this occurs. The figures show that, on the average, hitting yield \$0.02 to \$0.03 greater profit per dollar bet than doubling. Note, though, expectation is positive – bettors are favored – for either action.

Expectations for hitting or doubling on 11 vs ace-up
```Player's cards      hit     double    hit minus double
9-2              14.611%   11.836%     2.775%
8-3              14.620%   12.030%     2.590%
7-4              14.625%   12.227%     2.398%
6-5              14.643%   12.450%     2.193%
```

Enquiring minds surely want to know whether the benefit of doubling on 11 versus ace, a greater chance to win than lose twice the money, is worth the penalty of \$0.03 per dollar less profit averaged over more hands than they may play in their gambling lives. In deciding, it may help to know not only expectation but also the actual chance of winning or losing the hit or double.

As an example, consider the values for a hand of 6-5 and neglect the probabilities of the dealer having a blackjack as well as of pushing. Evaluating only the chance of winning as opposed to losing, prospects of success are just over 57 percent hitting and roughly 53 percent doubling.

A two-card 10 versus ace-up is a different kettle of fish. Basic Strategy says to hit. Expectation when doing so is positive and amounts to somewhat over \$0.08 average profit on the dollar. Conversely, doubling is unfavorable. Not by much, however; the average loss for this move is a hair under \$0.01 per dollar initial bet. So the difference between orthodoxy and heresy is on the order of \$0.09 per dollar. As for the probabilities of winning or losing the hand, they exceed 54 percent hitting and are a tad below 50 percent doubling.

What about a two-card 10 versus 10-up? The gaming gospel ordains a hit for this hand. Expectations for hitting show profits and those for doubling project losses. Differences are greater than those for 11 versus ace-up, but are still relatively small. The values are as follows.

Expectations for hitting or doubling on 10 vs 10-up
```Player's cards   hit     double   hit minus double
8-2             2.597%  -0.694%     3.291%
7-3             2.589%  -0.596%     3.185%
6-4             2.642%  -0.638%     3.280%
5-5             2.667%  -0.521%     3.188%
```

The chances of winning and losing are likewise close. Again, neglecting the probabilities of pushes and rounds in which the dealer has a blackjack, prospects are somewhat over 51 percent for hitting and a fraction under 50 percent for doubling.

A strong argument can be and often is made that blackjack buffs should stick strictly to Basic Strategy. For those who don't count cards or track shuffles, this gives the bosses the least edge. Presumably, it therefore affords players the most likelihood that the inherent volatility of the game will carry them over the top during the span of single or several sessions or casino visits.

Purism aside, it can be rationalized that edge is swamped by volatility over the short term. Take 100 trials, for instance. Per dollar bet at the start of each round, edge in blackjack played rigorously by the book represents an average loss of \$4. Volatility in the same session is characterized by a bankroll swing – up or down since it can work in both directions – exceeding \$11. Does it make sense to adopt a strategy that boosts the house's edge, if it raises the volatility under circumstances when swings are more likely to be positive or equally-weighted than negative – that is, when players have better or about the same prospects of winning than losing?

There's no simple answer to this question. Ultimately, it's a matter of why you gamble – your goals and tolerance of or aversion to the risk of losing various sums of money. How to decide? Well, it might help to remember this rhyme from the pencil of the poet, Sumner A Ingmark:

Those who break the rules but don't know why,
Are the ones most apt to go awry,
While a person who defies the norm,
With good reason may quite well perform.