Winning hands!

Apr 23, 2002 7:40 AM

Most connoisseurs of casino blackjack know that the house edge in the game arises because the dealer acts after the players. This has nothing to do with the kitchen table advantage of seeing everyone else’s totals before deciding how to proceed. Casino blackjack dealers follow strict rules, which in most places dictate hitting below 17 and standing on and above this level. Rather, acting last means that players lose if they go over 21, regardless of whether the dealer subsequently breaks. Therefore, the double-bust situation isn’t balanced, but goes to the dealer.

With the hit-to-17 rule, dealers can be expected to bust 28.2 percent of the time. Were players to rigorously mimic the house’s strategy, hitting below 17 and standing otherwise, never doubling down or splitting pairs, they’d also have a 28.2 percent bust rate. The probability of player and dealer both busting on the same round would then equal 0.282 times 0.282, or 7.95 percent. This would be the edge in an even-money version of the game.

The beneficent bosses graciously lop about 2.26 percent off this edge by paying 3-to-2 on uncontested player blackjacks. But even the residual 5.69 percent would suffice to send the game to the scrap heap of gambling history. The perennial popularity of blackjack is due to gains solid citizens derive from available options. These include ability to split pairs either defensively or offensively, to double-down when doing so would improve the expected profit on a hand, to hit soft 17 and soft 18, and to stop with totals below 17 against low dealer upcards.

Properly utilized, the last of these alternatives is the most powerful. It ultimately trims 3.2 percent from the inherent edge, compared with 1.6 percent for doubling, 0.4 percent for splitting, and 0.3 percent for the soft 17 and 18 plays.

The importance of standing with tallies below 17 against dealer "stiffs" can be discerned from the accompanying table. The data, excerpted from Blackjack Attack by Don Schlesinger, show the likelihood of dealers and players finishing with various totals under standard house rules and Basic Strategy, respectively. Uncompleted hands are those that terminate prematurely because the dealer has blackjack and the player does not.

The most evident divergence between dealer and player final hand probabilities is in totals from 11 to 16. The dealer has none in this range. Players should finish here, hoping to win by default, in 20.3 percent of all rounds; of these, 16.4 percent result from standing against low dealer upcards and only 3.9 percent from doubles gone kablooie. The next greatest contrast involves the chance of breaking. By standing below 17, when appropriate, players should bust at an average rate of only 15.9 percent instead of the 28.2 percent obtained with house rules.

Many novices hit totals below 17 when standing would be preferable. Their error is in thinking that getting closer to 21 is more critical than staying in contention and letting the dealer bust. Experienced players sometimes make the opposite mistake. They stand below 17, particularly on totals of 16 or 15, when hitting would be more opportune because the odds favor trying to push or beat a dealer’s finish between 17 and 21.

It’s possible to win, even to triumph gloriously, mocking the math in one of these ways or the other. But, why rely on a windfall any more than necessary when the laws of the universe are there to help? As the bard beloved of betting buffs, Sumner A. Ingmark, succinctly scribbled:

A modicum of luck,
while surely needed,
Is no excuse for leaving
sense unheeded.

Probability of Dealer
Following House Rules
& Players Adhering to Basic
With Various
Final Hands




11 to 16















21 (non BJ)