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Best of Alan Krigman

Gaming Guru

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Playing It Smart: Can you believe 'the book' on how to play proper blackjack?

9 December 2008

Even blackjack buffs who know their Basic Strategy inside and out sometimes balk at a few of its dictates. They're aware that "the book" says to hit 16 against a dealer's 10-up and 12 against 2-up. The most astute recognize that these hands are underdogs either way so it's a question of magnitude rather than kind. But, some wonder about risking immediate suicide by hitting, when standing would keep them alive to be there if the dealer busts.

Players in this position may speculate whether "the book" was written by the casino bosses, or their flunkies, who ultimately want solid citizens to lose but try to be cute about it. The enlightened minority who know the rules are based on the laws of math and weren't just "made up" or matters of opinion, have been overheard mumbling that whoever printed the original version must have typed it wrong and everyone else copied the mistakes.

Here are the figures for the two situations. For simplicity (mine, in doing the calculations), they assume that each rank in the shoe always has one chance out of 13 of being drawn.

For 12 against 2-up, a blackjack buff who stands will win if the dealer busts and will lose otherwise. A 12 can't push.

This puts the probability of winning at 35.36 percent and of losing at the complementary 100.00 - 35.36 = 64.64 percent. The average net loss per $100 is therefore $64.64 - $35.36 = $29.28.

A person hitting this hand can expect to push 4.98 percent of the time. Wins occur if the player finishes between 17 and 21 and the dealer busts or stops at a lower total; this eventuality has a chance of 34.84 percent. And losses result if the player busts or ends below the dealer a 60.18 percent likelihood. The average net loss per $100 is consequently $60.18 - $34.84 = $25.34.

Bettors standing on 16 against 10-up similarly can't push. They succeed if the dealer busts and fail otherwise. The following figures are based on "playable" hands those in which the dealer does not have a blackjack since these lose either way.

The shot at winning by standing on 16 against 10-up, that of the dealer busting, is 21.21 percent. The complementary chance of losing is 100.00 - 21.21 = 78.79 percent. So the average loss per $100 is $78.79 - $21.21 = $57.58.

Hitting gives players 5.92 percent prospects of pushing by matching the dealer between 17 and 21. It leads to probabilities of 20.05 percent they'll win, and the remaining 74.03 percent they'll lose. The resulting projected net loss per $100 is accordingly $74.03 - $20.05 = $53.98.

With both of these hands, hitting the decision dictated by Basic Strategy yields fewer wins than standing. For 12 versus 2-up, the shortfall is 35.36 - 34.84 = 0.52 percent. For 16 versus 10-up, it's 21.21 - 20.05 = 1.16 percent. However, hitting can also lead to pushes, such that losses are also less frequent. The deficit on 12 versus 2-up is 64.64 - 60.18 = 4.46 percent. On 16 versus 10-up, it's 78.79 - 74.03 = 4.76 percent. So the reduced expectation of losses exceeds that of wins, yielding a net reduction in the average penalty.

Notice something else. Basic Strategy calls for surrender, when it's offered, on 16 against 10-up. The figures show why this is the case. The theoretical loss per $100 by standing is $57.58 and by hitting is $53.59. Mathematically, a certain loss of $50.00 is superior to chances of 78.79 percent of losing and only 21.21 percent of winning $100 by standing, and similarly, 74.03 percent of losing and 20.05 of winning $100 by hitting.

Or, do you tell yourself you're in the casino "to gamble and not to surrender"? Making you into one of the folks the wiseguys often refer to as "our preferred patrons." This, for reasons it's easier to fathom by thinking in terms of "the other guy."

For, as the punter's poet, Sumner A Ingmark, perceptively penned:

Gamblers who are in the know,
Reap the fruits of what they sow,
Guarding carefully their dough,
Circumventing tales of woe.

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.