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# Playing it Smart - Some blackjack hands call for making the best of a bad situation

5 November 2007

Blackjack buffs rightfully rue a dealer's 10-up. Especially when their own hands total 15, 16, or 17. They recognize the dilemma, intuitively if not mathematically. Standing, they can't win unless the dealer busts which doesn't seem to happen often. Hitting, they need a card high enough to beat the dealer but not go over 21 possible but not especially promising.

The worst of these player hands is 16. Basic Strategy says to hit. And almost everyone dutifully does. Absent knowledge of the proportions of ranks left in the shoe when you have to make the decision, this choice will average the least loss. But you might be surprised at how little the difference is between the options.

For simplicity, ignore shoe size, ranks comprising the 16, and rounds in which the dealer has blackjack. The dealer then has 22.98 percent probability of busting, which is your chance of winning by standing. You can't push, so not winning means losing. This represents the other 77.02 percent. Since the bet is for even money, edge equals the chance of winning minus that of losing 22.98 - 77.02 or -54.04 percent (the minus shows that the house is favored). In monetary terms, for every buck at risk when you see 16 versus 10, you'll average a loss of 54.04 cents.

Hitting, your prospects of busting and losing immediately are 61.54 percent. Or, you may not bust, but lose anyway by finishing below the dealer. This eventuality comes in at 12.49 percent. Overall, the probability of defeat is 74.03 percent. On the upside, the likelihood of finishing between 17 and 21, and having the dealer bust or end lower, is 20.05 percent. The remaining 5.92 percent accounts for pushes. Edge is 20.05 - 74.03 or 53.98 percent an average loss of 53.98 cents on the dollar.

Three conclusions emerge from these figures. 1) Basic Strategy is right in that hitting is better than standing. 2) The difference is only six hundredths of a cent per dollar on the table, so solid citizens aren't incurring an excessive penalty by defying the dogma. 3) If surrender sacrificing half your bet rather than playing out the hand is offered, using it will save an average of about four cents on the dollar.

Similar reasoning can be used to distinguish the options for 15 against 10. Standing, the statistics are the same as with 16 (win 22.98 and lose 77.02 percent for 54.04 percent edge). This, because you only win on a dealer bust and lose otherwise. However, hitting 15, the likelihood of exceeding 21 and losing immediately declines from 61.54 to 58.58 percent while that of making a final hand at each level rises accordingly. Averages for wins, losses, and pushes by hitting are 21.59, 72.03, and 6.38 percent, respectively. Edge is therefore 21.59 - 72.03 or 50.44 percent, an average loss of \$0.5044 on the dollar. So hitting beats standing by 3.60 percent 3.60 cents on the dollar.

Surrender is superior to hitting 15 versus 10 although the impact is small. So small, in fact, that when the cards forming the 15 and the finite size of the shoe aren't ignored, hitting beats surrender on 8-7 against 10 in games with seven or fewer decks.

Perceptive players may also ponder 17 versus 10; like lower totals, this hand can't win unless the dealer busts. Here, the chance of pushing by standing and the greater likelihood of going over 21 by hitting become factors. Standing on 17, chances of winning, losing, and pushing are 22.98, 64.95, and 12.07 percent, respectively. Hitting, the respective probabilities are 18.28, 76.72, and 5.00 percent. So edge standing is 22.98 - 64.95 or 41.97 percent. Hitting, it's 18.28 - 76.72 or 58.45 percent. You're an underdog either way, but standing is less onerous than hitting and surrender by 16.48 and 8.03 percent, respectively.

The luck of the draw is a big factor in blackjack. Which is why experts can lose and amateurs win. But, ordinarily, players will get good cards and bad. Playing the latter in a manner that minimizes losses can sometimes snatch triumph from the teeth of tragedy. As the bettor's beloved bard, Sumner A Ingmark, noted:
Not just by chance is your fate molded,

You actions guide how it's unfolded.

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Best of Alan Krigman
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.