HOW OFTEN CAN YOU EXPECT
A FAVORABLE HAND?
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 athttp://www.iconworldwide.com/winningways/search.php.
Most sophisticated blackjack buffs follow Basic Strategy in deciding whether to stand, hit, double down, split pairs, or surrender. Even acutely adept card counters introduce few variations to the rules – and, then, relatively infrequently. This is because the benefit of counting is chiefly derived from raising bets when the composition of the shoe suggests the overall statistical expectation increases, and conversely.
By adhering to Basic Strategy and betting the same amount every round, or varying wagers pretty much by guess or by gosh, solid citizens can hold the house advantage – the edge – to about 0.40 and 0.43 percent in six- and eight-deck games, respectively (with standard rules including resplitting allowed to four hands on everything but aces). These figures are good to know if you want to impress your friends and in-laws. Unfortunately, they tend to be abstractions and don't contribute much to players' comprehension or anticipation of the ebb and flow of a session.
Technically, 0.40 and 0.43 percent mean that the house earns an average of 40 and 43 hundredths a cent respectively per dollar wagered, prior to the deal. Since they are averages, the percentages don't represent real dough the casino actually squeezes out of the folks at the table. They reflect the net the casino takes in over what it gives out when the bean counters tally the activity on the game over a long period. Knowing the edge, therefore, doesn't help bettors make decisions in the midst of the melee.
Another limitation of applying edge during a game is that the associated amounts are small compared to what individuals pick up or drop on any coup. Suppose a gambler bets $10. Depending on the hand and the way it's executed, the player can push; win $10, $15, $20, or maybe more; or lose $5, $10, $20, or sometimes more. Who'd notice 4.0 or 4.3 cents grabbed by the greedy bosses?
Furthermore, edge is a result of several factors acting in concert. These are 1) the chance any combination of player's and dealer's cards will occur, and 2) the probabilities of winning and losing the amounts involved. Ultimately, of course, players will judge their performance in a particular session by the rise and fall of their fortunes. They may, however, gain more intuition about blackjack in general, and better justify comfort or worry about their progress in a given instance, knowing the probability of getting and then winning or losing hands on which they are strong or weak.
In six-deck games, the likelihood of a favorable hand is...
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