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THE SKINNY ON PLAYING OPTIONS

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.

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. However, what do the values mean in a practical sense?

Technically, per $100 booked, it means the casino bosses earn an average just over $0.40 in the six-deck game and a bit under $0.43 in the eight-deck game. In addition, solid citizens lose this amount, also on the average, per $100 wagered. However, the juice tends to be invisible, partly because the amounts are small compared to the actual amount of 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 "non-playable" rounds where the dealer has a blackjack, prospects are 41.651 percent of winning 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 that players win on uncontested blackjacks. The probability of a blackjack is 4.749 percent in six-deck games 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. Moreover, 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 are. 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 hardier (such as 9-9 vs. 4), or weak hands stronger (like 8-8 vs. 4). The problem is defensive splits that have negative expectation no matter how 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 over betting your bankroll to begin with. You won't find blackjack much fun, either, let alone lucrative. As the perturbing pedantic poet, Sumner A Ingmark, presciently penned:

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

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