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# Which Are the Weakest Dealer Upcards in Blackjack?

19 October 1998

The other day, I overheard two venerable blackjack veterans debating which was the weakest dealer upcard. They figured it for five or six. The first said six, having "read somewhere" that dealers break with it most often. The other disagreed because the dealer could have an ace in the hole and make a pat hand with a six, but always had to draw to a five.

The bettor who thought the dealer was more vulnerable with six than five was right. Not that it affects how hands are played, since there are no situations in which the optimum decision on a player's total differs for one or the other. But solid citizens who like to know the nuances of the game should be aware of how the dealer's upcard affects their prospects going into a round.

The following list shows the probability that dealers will bust in six-deck games when they have to stand on soft 17, in order from most to least likely. The chance the dealer will break is most important when players stand on "stiffs" - totals below 17 - because hands can't push and this is the only way to win. As an example of interpreting the data, say you have a 14 and stand against a dealer's four-up. The list indicates you have a 39.6 percent chance of winning; the complementary 60.4 percent is your chance of losing. Your "expectation" under these circumstances is to lose 60.4 - 39.6 = 20.8 cents per dollar bet.

 up-card probability of busting (%) 6 42.3 5 41.8 4 39.6 3 37.4 2 35.4 7 26.2 8 24.4 9 22.9 10 21.2 A 11.5

The dealer's chance of busting isn't the sole factor determining the wisdom or folly of counting your chickens before a round hatches, of course. Your starting hand and the way you play are also considerations - owing to the possibility you'll bust regardless of what the dealer does, push or beat a 17 to 21, and split or double under appropriate conditions.

The next list shows the player's overall edge for various dealer upcards, assuming perfect basic strategy. Figures are percent advantage (+) or disadvantage (-) in order from most to least favorable. The data are for six-deck games in which dealers must stand on soft 17, where pairs can only be split once, and doubles are allowed on any two cards including the hands formed by splits. Values for upcards of 10 and ace do not include cases in which the dealer has a blackjack.

 up-card overall player edge (%) 6 + 23.4 5 + 20.2 4 + 16.2 7 + 14.4 3 + 12.6 2 + 9.2 8 + 5.7 9 - 4.1 10 - 17.3 A - 34.2

The list shows that players have a net edge for all dealer upcards from two through eight. Of course, specifics vary with player starting hand. For instance, hard 15 is an underdog versus all dealer upcards despite the overall advantage for two through eight, expecting to lose over 15 cents per dollar bet against a six, 42 cents against an eight, and 48 cents against an ace.

Note how the rankings in the bust and expectation lists differ. If you dread seeing the dealer expose a two or three, you'll be glad to learn these upcards aren't quite as dangerous as you may have imagined, but are still stronger for dealers than sevens.

Percentages aside, gamblers good and poor alike know that when the next card is drawn, anything can happen. But the good ones know it's best to play the percentages, anyway. Sumner A Ingmark, the Tennyson of Twenty-One, said this in his Ode to Odds:

I'll venture to prophesy,
Not but the ultimate curtain,
Odds on this bet aren't just high,
Here is a case where they're certain.

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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.