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Best of Alan Krigman

Gaming Guru

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Basic Strategy in Blackjack Accounts for All Unseen Cards

22 January 1996

The influence bettors exert by deciding how to play their hands heightens the mystique of blackjack. Players who go "by the book" take pleasure in mastery of a sophisticated game. Those who covet splits and doubles, even when they're longshots, relish opportunities to raise bets after seeing their initial hands and the dealer's up-cards. Yet others, who depend on luck as they inch anxiously toward 21, enjoy the thrill of acting on their hunches.

All these approaches can and do send solid citizens home flush. They also can and do send bettors home broke. But not in equal proportions. Mathematically, there's a "best" way to attack blackjack. It's codified in basic strategy, rules giving decisions for every player-dealer combination. Basic strategy doesn't ensure results; nothing can do that. Basic strategy minimizes house edge and maximizes players' chances to win.

Players are full of misconceptions about the origins of basic strategy. Did it come from assuming "unseen" cards -- the next to be drawn or exposed -- are 10-valued? Was it invented by casino bosses to help fill their own pockets? Did someone watch millions of games to see what worked best? Was it something a prospector found chiseled in stone in the Nevada desert? None of the above!

You can view the rules as articles of faith. But maybe you're losing too many well-played hands. Or a few items in the chart ring false -- like hitting 12 against dealer two-up, surrendering 16 on dealer ace, or splitting eights into a 10. Then, you need confidence to keep on the straight and narrow. You need to know that basic strategy was derived using sound mathematics by considering actual probabilities of all possible unseen cards.

As an example, say the dealer has nine-up. Everyone is thinking "19." But probability calculations show the chance of 19 is only 35.1 percent -- 30.8 percent with a 10 in the hole and 4.3 percent with different groups of cards. Other results? Bust: 22.8 percent; 17, 18, or 20: 12 percent each; and 21: 6.1 percent.

What if you face the nine with 17? Stand? You lose if the dealer gets 18 through 21 (the figures above say to expect this 65.2 percent of the time), you win when the dealer busts (22.8 percent), and you tie on a dealer 17 (12 percent). With $10 bets, expect a hundred such hands to unburden you of $652-$228=$424.

You could surrender when this option is available. By doing so, you'll lose $5 each time so a hundred plays set you back $500.

Since standing is so bad, why not draw? You'll bust with anything over four; the likelihood of this is 9/13 or 69.2 percent. Probability of getting 18, 19, 20, or 21 is 1/13 or 7.7 percent each; on these draws, you'll lose if the dealer has more, win if the dealer has less or busts, and tie if the dealer has the same. I'll skip the nitty gritty and go to the results. Draw, and you expect to lose 69.2 percent by busting and 6 percent to higher dealer hands, win 19.8 percent, and tie 5 percent. Statistically, a hundred such $10 hands should cost you $692+$60-$198=$554.

The laws of probability show that 17 is vulnerable to nine no matter how it's played. In a hundred instances at $10 each, expect to forfeit $554 by hitting, $500 by surrendering, and $424 by standing. So basic strategy says stand and cut your losses.

Similar calculations for all player-dealer combinations lead to the complete basic strategy. You can get wallet-sized charts tabulating optimum decisions from casino shops, gaming bookstores, or even friendly pit bosses. And most casinos will let you use a chart while you play, even though basic strategy cuts their edge.

The benefit of statistically-correct play is huge on some player-dealer combinations, tiny on others. Either way, decisions on individual hands may ultimately count less than having the time and bankroll to outride the normal downswings of a game, the sense to quit with reasonable earnings, and the luck of the draw. Still, giving the casino more edge than necessary is giving away money. As Sumner A Ingmark, minstrel to the gaming minions, once mused:

Letting basic strategy determine how you play,
Cannot guarantee you'll win but often saves the day.
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.