You May Have an Edge in Blackjack after the Deal

But edge depends on a priori chances of winning various amounts, before cards are dealt. After the deal, some combinations of player hands and dealer up-cards give bettors the best of it.

Edge isn't money in the bank, no matter who has it. Rather, it measures expected win or loss per dollar of initial bet over the long haul. Mathematically, expectation is the probability of victory times the spoils, minus the probability of defeat times the penalty. Positive values anticipate profits, negative values forecast losses. Expectation is often given as a decimal fraction or percentage; some folks find cents won or lost per dollar bet before the deal more intuitively pleasing.

I'll illustrate by making up some numbers.

Say hitting a certain hand has 48 percent chance of winning even money, 44 percent chance of losing, and 8 percent chance of pushing. Expectation is (0.48 x 1) - (0.44 x 1) or 0.04 - four cents per dollar bet. What if doubling on the same hand had 47 percent chance of winning, 46 percent chance of losing, and 7 percent chance of pushing? Expectation would be (0.47 x 2) - (0.46 x 2) or 0.02 - two cents per dollar. Both expectations are are positive, but hitting would be worth more than doubling.

Players have an edge in the following starting situations. This list is for games using multiple decks with the normal rules for splitting and doubling, when the dealer does not have a blackjack and the player adheres faithfully to basic strategy.

Expected profits per dollar bet for the five weakest yet still favorable hands are a) eight versus three-up: 0.8 cents; b) four versus six-up: 1.1 cents; c) seven versus six-up: 2.7 cents; d) eight versus four-up: 3.9 cents; e) 19 versus 10-up: 6.3 cents.

At the high end, the five strongest starting points all involve the player holding a hard or soft 20. Expectations for these hands per dollar bet are 20 versus a) dealer eight-up: 79.2 cents; b) dealer seven-up: 77.3 cents; c) dealer nine-up: 75.8 cents; d) dealer six-up: 70.4 cents; e) dealer five-up: 67 cents.

What are the worst hands - with the greatest negative expectations, the biggest losers? Players who understand the surrender option of basic strategy will recognize the answer. Four hands have expected losses exceeding 50 cents on the dollar; they are accordingly better surrendered than played for lower expectations. These hands and their corresponding expected losses are a) 16 versus 10-up: 54 cents; b) 16 versus ace-up: 51.7 cents; c) 16 versus nine-up: 50.9 cents; d) 15 versus 10-up: 50.4 cents.

Of course, part of the excitement of gambling is in its uncertainty. You can sit sullenly with a 17 versus a dealer two-up - an expected loss of 47.8 cents per dollar bet - but gather the green when the dealer busts. And you can double down delightedly on an 11 versus a dealer six-up - an expected profit of 66.7 cents per dollar initial bet - and watch both wagers disappear when you draw a five and the dealer turns over an ace.

Sumner A Ingmark, who is to gaming tables what Aesop was to moral fables, fathomed the fickleness of fate in his famous fiat

A lot like chickens ere they're hatched,
Propitious bets may be dispatched,
So don't count winnings 'til they're snatched.