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Playing It Smart: The premium paid for a blackjack means more than you think

12 February 2008

Most blackjack buffs, even those with considerable experience, underestimate the significance of ace-10 "naturals." Sure, everyone likes to pull a fair share of these hands. The rationale typically hinges on two factors. First, the combination can't lose; it pushes a simultaneous dealer blackjack and wins automatically when it's uncontested. Second, the payoff normally includes a bonus; rather than even-money, solid citizens get 1.5-to-1 in standard multi-deck versions of the game.

These features are indeed desirable. But although they are behind the true benefit of the hand, they're actually just tangential to it. The ultimate value of 1.5-to-1 blackjacks is in cutting the edge in the game substantially, no matter how a person plays.

At an eight deck table, ignoring cards removed in earlier rounds, the chance that any hand will be an uncontested blackjack is slightly over 4.5 percent. This is about once every 22 rounds. The probability of such a hand, of course, is the same for dealers and players. The difference arises in the payoff. Say a player bets \$10. When the dealer has an uncontested blackjack, the player loses \$10. When the bettor gets the brass ring, the win earns \$15 under the standard rules.

Picture 1,000 rounds with \$10 bets. Dealers and players should each average 45 uncontested blackjacks. The dealer will lock up \$10 x 45 = \$450; the player will pick up \$15 x \$45 = \$675. The player finishes \$225 ahead. That's a \$225 advantage for a gross wager of \$10 x 1,000 = \$10,000. And \$225/\$10,000 = 0.0225 or 2.25 percent knocked off whatever edge the casino would otherwise have. The reduction in edge equals half the expected frequency of uncontested blackjacks, a consequence of players winning half again as much as they lose depending on who gets the hand.

Say that an uncontested player blackjack was a certain win but at only even money. Dealer and player blackjacks would balance, on the average. The 2.25 percent benefit in edge would therefore be reclaimed by the house. With eight decks and 1.5-to-1 blackjacks, good Basic Strategy gives the house a low 0.5 percent. Even-money blackjacks would raise this to a high 0.5 + 1.25 = 2.75 percent.

In a single-deck game with standard rules such as resplitting, doubling after splitting, and doubling on any two cards, perfect Basic Strategy with a 1.5-to-1 payoff for winning blackjacks gives the house essentially zero edge. Which explains why single-deck blackjack is either a relic of gambling history, or offered with a covert catch to deceive the naive.

An illustration of this skulduggery is the single-deck game offered in some casinos with 6-to-5 (1.2-to-1) rather than 1.5-to-1 payoffs on blackjacks. Earnings of \$12 rather than \$15 on a \$10 bet, on a hand that still has the appeal of being unbeatable, may seem like a minor change. What's \$3 every once in a while?

A lot more than the chump change you may at first suspect. The chance of an uncontested blackjack with one deck is 4.65 percent slightly greater than that with eight decks. Eliminating the bonus altogether by paying even money for a blackjack, the bosses get back the edge reduction equal to half the theoretical rate of occurrence. With a single deck, this would bring the house advantage up from zero to 2.325 percent. The 1.2-to-1 bonus means that players win 20 percent more when they have blackjacks than they lose when the dealer gets the natural. So the 6-to-5 payoff cuts the edge back down by 20 percent of the projected incidence frequency, 0.2 x 4.65 = 0.93 percent. This leaves 2.325 - 0.93 = 1.422 percent. Large, considering a plain vanilla eight-deck game paying 1.5-to-1 on a blackjack has only 0.4 percent edge.

People gamble at single-deck 6-to-5 tables, though. Greenhorns who haven't a clue what they're doing. And also veterans who've heard that one-deck games are good but neither understand why nor care to be confused by facts. Some even smugly believe they're pulling a fast one on the bosses who inadvertently opened up this loophole. Here's what the poet Sumner A Ingmark thought:

Casinos are genuine places of dreams,

Where rude reawakenings nullify schemes,

Since nothing there's really quite like what it seems.

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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.