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Best of Alan Krigman

Gaming Guru

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Never-Bust Blackjack Strategies Can Cost You Money

27 April 1998

In blackjack, stiff hands are hard totals of 12 through 16. Some blackjack buffs won't draw to stiffs regardless of the dealer's up-card. Basic strategy has it otherwise. Playing "by the book" in multi-deck games dictates hitting stiffs when the dealer shows seven or above, and also drawing to hard 12 against two or three.

The "theory" behind never-bust blackjack goes like this. a) Stiffs are underdogs, stand or hit. b) Hitting, there's a good chance of busting. c) Standing, the player stays in the running and will win if the dealer exceeds 21.

These statements are true. But they don't lead to the conclusion that never-bust blackjack is some secret the casino bosses would like to suppress. Not busting and getting the best chance of winning are horses of entirely different hues.

The objective in blackjack is normally to maximize expected return on every bet; this is the criterion on which basic strategy is built. Departures from the standard may turn out serendipitously well on one or more individual hands, and may be ideal under specialized circumstances. But, in the long run, they cost bettors money.

Say the dealer has nine-up. Chance of busting with this exposed card is 23 percent. So, in 1000 hands, players who stand against nine with less than 17 can expect to win 230 and lose the other 770. The corresponding expectation is a net loss of $770 - $230 = $540 per $1000 wagered. Likewise, seven-up gives the dealer 26 percent chance of busting. In 1000 hands, players who stand with stiffs against seven can anticipate winning 260 and losing 740; expected net loss is $740 - $260 = $480 per $1000 wagered.

Expected effects are trickier to calculate if a solid citizen hits a stiff. Now, the math must account for the chances of the player as well as the dealer busting or ending with various point totals. The hands can push as well as win or lose. And starting value is significant. For instance, with all factors weighed, hitting 15 against a dealer's nine leads to an expected net loss of $470 per $1000 wagered - $70 milder than the $540 characteristic of standing. But starting with 13 against the nine leads to an expected net loss of $380 - a $160 gain over the $540 for standing.


Comparing expected net losses for combinations of stiff starting hands and dealer up-cards confirms that hitting is less onerous than standing when so specified in basic strategy. The theoretical penalties for flouting these rules range from $10 per $1000 wagered for 16 versus 10 to $310 per $1000 wagered for 12 versus ace. Never-bust strategies get more punishing as players' starting hands drop from 16 to 12 and as dealers' up-cards go from 10 to 7 and then ace.

The following list shows the average cost of each stiff when players stand rather than hit against dealer sevens and above.

player starting
total
decreased expectation
per $1000 bet
12
$200
13
160
14
120
15
75
16
45

 

In a universe governed by probabilities, anything can happen on a particular trial. A blackjack player in the last gasp of a tournament, who must win and not push the final round to grab the grand prize, can hit a 20 against a 10-up and draw a miracle ace. But gambling typically involves repeated decisions, and is therefore an environment in which modest but relentless differences in probability can tip the balance between agony and ecstasy. Carried to the extreme, it's how casinos pay their bills. And it can work for players, not so evidently hand-to-hand but at the session level and certainly over the long term.

Sumner A Ingmark, the Wordsworth of the wagering world, said it like this:


Respect small forces, unremitting,
Ere nature's laws you try outwitting.

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.