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# How Often Should You Expect a Blackjack Dealer to Bust?

30 July 2002

The balance between ecstasy and agony at blackjack often hinges on the frequency with which the dealer busts. In multideck games, dealers who must stand on any 17 or above should break an average of 28.2 percent of the time. Likelihood varies with upcard, the dealer being most liable to go blooie with six-up and least so with ace-up, as shown in the following list.

 Probability that the Dealer will bust in a multideck game, standing on all 17s or above upcard probability of breaking (%) 2 35.4 3 37.4 4 39.4 5 41.6 6 42.3 7 26.2 8 24.5 9 22.8 10 21.2 A 11.5

Disasters are looming if dealers keep pulling unbelievable irons out of the fire with low upcards, and therefore don't go over 21 anywhere near the theoretical 35.4 to 42.3 percent rates for "stiffs." Conversely, sessions can be richly rewarding when dealers start with aces or faces but flip garbage and exceed 21 much more regularly than the expected 11.5 or 21.2 percent.

Chance, alone, may account for a run of hands in which a dealer breaks far less or more often than expected. But, there's another factor. Various cards are unavailable in the shoe because they've been used in previous rounds or are already on the table when the dealer acts. This removal alters the probability of the dealer bombing out. For instance, say a dealer has a 10-up. When players have lots of low cards showing, the dealer's odds of busting decreases; when the board is loaded with high cards, the dealer's odds of breaking increases. The accompanying chart summarizes the effect for each dealer upcard. In the chart, "i" signifies increases and "d" decreases in the chance of crashing, and "*" highlights cases when the influence is especially strong.

Effect of unavailable cards on the dealer will bust (i: increased chance, d: decreased chance, *: strong effect)

 upcard cards un available to the dealer A 2 3 4 5 6 7 8 9 10 2 i i i i *i* *i* i i i *d* 3 i i i *i* *i* *i* i i *d* *d* 4 i i *i* *i* *i* *i* *i* d *d* *d* 5 i *i* *i* *i* *i* *i* d d *d* *d* 6 *i* *i* *i* *i* *i* d d d *d* *d* 7 i i i i d d d d *d* i 8 i i i d d d d *d* i i 9 i i d d d d d i i i 10 i d d d d d i i i i A d d i i i *i* *i* i i d

This chart includes both good news and bad news.

Assume a dealer has nine- or 10-up while players at the table all have strong hands - like two-card 19s or 20s. The dealer is more apt than usual to break because of the unavailable nines or 10s held by the solid citizens. Bettors' strong hands get better. Likewise, make believe the dealer has a four- or five-up and players have an abundance of low multi-card totals featuring lots of aces, twos, threes, and fours. Here, again, the dealer's probability of breaking increases so players' weak hands improve.

The opposite occurs, as an example, when the dealer sports a nine or 10 and the players' hands eat up a bunch of threes, fours, fives, and sixes but are still vulnerable with totals of 17, 18, and 19. Now the dealer has less than the nominal chance of breaking and players' prospects go from bad to worse. Likewise when the dealer starts weak, with six-up, but the players are sitting on nines and 10s. The players are still strong, but not as much as with the same totals formed from low cards, because removal of nines and 10s makes the dealer less apt to bust.

What does this all imply? Imagine yourself and a gaggle of gamblers, all sitting pretty - each with two 10s, for totals of 20, against a dealer's five. The heroes are all strong and the villain is tied to the tracks. But those six 10s smiling at you from the felt may actually be smirking because they raise the chance of the dealer ending with a viable total. The great enigma of blackjack is that cards work both ways. A puzzle poignantly put by the punters' poet, Sumner A Ingmark, when he penciled:

Remember when you hope for something, you may get it,
But often when you do, you find that you regret it.

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Best of Alan Krigman
Alan Krigman

Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.
Alan Krigman
Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.