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PREMUM FOR A BLACKJACK-
MORE THAN YOU THINK
By Alan Krigman
Alan Krigman, and his poetic sidekick Sumner A. Ingmark, have been illuminating the dark recesses of casino gambling for more than a dozen years. Mr. Krigman is especially well known for sharing his insights into the mathematics underlying the various games (including blackjack), the influence of volatility and skewness as well as edge on bankroll during the course of a session, and the impact of betting as well as decision strategies on expected performance. A searchable archive of Mr. Krigman's prose and Mr. Ingmark's muse is online at
http://www.iconworldwide.com/winningways/search.php.Most blackjack buffs, even those with considerable experience, underestimate the significance of ace-10 "naturals" to their game. Sure, everyone likes to pull a fair share of naturals. The rationale typically hinges on two factors. First, a natural 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 substantially cutting the house edge in the game, no matter how well or poorly a person plays.
If you ignore cards removed in earlier rounds in an eight-deck game, 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 the dealer and players. The difference, however, 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 with an uncontested blackjack, the win earns not $10, but $15 under the standard rules. See the difference?
Picture 1,000 rounds with $10 bets on each round...
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