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Best of Alan Krigman

Gaming Guru

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Without the players' options, blackjack wouldn't be a serious gamble

22 February 2010

Highly-informed blackjack buffs know the precise house edge they fight by following rigorous Basic Strategy. When the rules allow doubling down on any two cards, resplitting to as many as four hands, and doubling after splitting, it's 0.402225 and 0.429881 percent for six- and eight-deck games, respectively. The edge arises from wins by the house when the player and the dealer both bust. But, what do the values mean in a practical sense?

Technically, per $100 booked, they mean the bosses earn an average just over $0.40 in the first case and a bit under $0.43 in the second. And solid citizens lose this amount, also on the average, per $100 wagered. But the juice tends to be invisible. Partly because the amounts are small compared to money won or lost. And partly because the figures are averages and apply indirectly to round-by-round results for any individual.

It may be more intuitively rewarding to know the likelihood of coups when players are favored, based on their initial hands and the dealer's upcard. Excluding "nonplayable" rounds, where the dealer has a blackjack, prospects are 41.651 percent with six decks and 41.536 percent with eight. Dealers are in the catbird seat on the complementary 58.349 and 58.464 percent. One reason edge is low, despite the wide gap between chances of situations with positive and negative expectations, is the extra half bet players win on uncontested blackjacks. The probabil-ity of a blackjack is 4.749 percent in six- and 4.745 percent in eight-deck games. The half-bet premium trims what would otherwise be the edge by half of these frequencies – 2.374 and 2.372 percent, respectively. This, by the way, explains why casinos can offer goodies in one-deck games where naturals pay only 6-to-5. Blackjacks have 4.826 percent probability with one deck, but the bonus is 1/5 this frequency so edge drops by just 0.965 percent.

Another factor that helps reduce edge is the players' option to stand on potential busts below 17 while dealers must hit such hands. And blackjack bonuses as well as standing against weak dealer upcards are free, they take savvy rather than specie.

Doubles, another player option, are also vital but menace more moolah. All Basic Strategy doubles favor players. Chances of getting suitable hands are 9.643 percent with six and 9.645 percent with eight decks. Soft doubles, where one card is an ace, are less attractive than their hard counterparts. With six decks, probabilities are 1.643 percent soft and 8.000 percent hard. Eight-deck chances are 1.642 percent soft and 8.003 percent hard.

Splits also require additional money at risk. Some players shun certain splits because two underdogs replace one. They understand offensive splits, which make robust hands such as 9-9 vs 4 hardier, or weak hands like 8-8 vs 4 stronger. The problem is defensive splits, having negative expectation however the hand is played; 8-8 vs 10 is the prime example. The key buried in the math is that the split has lower negative expectation overall than the original total. The probability that Basic Strategy will call for a split with six decks is 2.527 percent, 1.753 percent offensive and 0.774 percent defensive. Rates of splits dictated by Basic Strategy with eight decks average 2.556 percent, 1.726 percent offensive and 0.830 percent defensive.

What does all this suggest? First, getting at least your share of blackjacks is vital to keeping the edge in check. The effect is due to not only the obvious guaranteed win on the hand, but – perhaps more critically – the payoff bonus. Corollaries of this are that the one-deck game with a 6-to-5 blackjack payoff is no bargain, and taking even money with insurance may be a worse long-term choice than it appears. Second, know the situations in which you should stand. And third, exploit opportunities to double down and split when they arise. If you hesitate to double or split because of the extra dough you have to put on the line, you're overbetting your bankroll to begin with. You won't find blackjack much fun, either, let alone lucrative. As the perturbingly pedantic poet, Sumner A Ingmark, presciently penned:

To those who discern their chance and grab it,
A gamble becomes a winning habit.

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.