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Best of Alan Krigman
How often can you expect a favorable hand at blackjack?19 October 2009
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, 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 of everything but aces). These figures are good to know. If, only to impress one's 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. Being 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. Make believe 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?
Further, edge is a result of several factors acting in concert. These are the chance any combina-tion of player's and dealer's cards will occur, and 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 then winning or losing hands on which they are strong or weak.
In six-deck games, the likelihood of a favorable hand is 41.6 percent. In eight-deckers, the outlook declines slightly to 41.5 percent. The probabilities are broken out by the move dictated by Basic Strategy in the accompanying chart.
Probabilities of hands, classified by Basic Strategy dictum
Here's an example of interpreting the data. The chance of hands on which Basic Strategy says to hit at an eight-deck game is 42.4 percent; the player will be favored on 13.1 percent of these.
All Basic Strategy doubles are favorable. Some splits see bettors risk additional money even though the prospects are adverse; the reason is that the hands are projected to lose less, on the average, when split than played in an alternate way. The data for stands and hits may come as a surprise. Bettors are generally favored on hands for which standing is in order, by 54.7-to-45.3. They're underdogs when hitting is recommended, by 86.8-to-13.2.
The primary incentive for knowing these figures is in a greater understanding of the ebb and flow of a game. Knowing what to expect can help a gambler maintain a rational outlook when the heat is on. And, of course, to be realistic before blurting out some choice phrases such as "this is the coldest blankety-blank table I've even seen." Here's how that perennially perceptive poet, Sumner A Ingmark, envisioned this form of enlightenment.
When 'tween cause and effect, some chance interposes, Know how much to expect in nettles and roses.
Best of Alan Krigman