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Best of Alan Krigman

Gaming Guru

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How vulnerable are blackjack dealers with fives- or sixes-up?

30 August 2010

Most blackjack buffs breathe a sigh of relief when the dealer pulls a five- or six-up. These are, indeed, the weakest dealer upcards. If nothing else, sophisticated solid citizens know that proper Basic Strategy is to stand against them on any non-paired hard total of 12 or above, waiting out the dealer's actions and not risking a premature bust by hitting a feeble 16 or below.

Many bettors, however, start counting their money when they see these cards, then find they have the short end of the stick after the dust finally settles. Does this mean they're in an unusually cold game? Or are their expectations of triumph too optimistic?

The fundamental problem is rooted in false perceptions. Players see a five- or six-up and think "the dealer has 15 or 16, has to hit, and will bust more often than not." It's the same conceptual error that causes players to hesitate before hitting a 12 against a two-up; in that situation, folks tend to consider themselves on equal footing with the dealer at a total of 12.

Plain and simple, a five-up becomes a 15, a six-up a 16, and a two-up a 12 in less than one third of all rounds. Frequently enough to be remembered, but hardly a sure thing.

The chance of a dealer busting with five- or six-up turns out to be less than 50-50. When the dealer has to stand on soft 17, with a five-up, the probability of busting is 41.8 percent; with a six-up, it's 42.3 percent. These percentages equal the chances of winning for players who stop with totals of 16 or less.

A player's 17 through 21 is stronger than 12 through 16 against five- or six-up, but less so than commonly imagined. The likelihoods of dealers finishing at various levels with these upcards are shown in the accompanying table. The figures are for eight-deck shoes, but are almost the same for six-deck games.

Probability of a blackjack dealer with five- or six-up finishing at various points

end point     five-up     six-up
       17       12.2%      16.6%
       18       12.2%      10.6%
       19       11.8%      10.6%
       20       11.2%      10.2%
       21       10.8%       9.7%
     bust       41.8%      42.3%

Make believe you've squeaked by with a 17 and confidently stand. How can you realistically expect to fare?

You'll push if the dealer also has 17. The table shows this has a probability of 12.2 percent on five-up and 16.6 percent on six-up; the offset between the two results from the dreaded ace in the hole in the latter case. You'll only win if the dealer busts -- 41.8 and 42.3 percent shots on fives and sixes respectively. Everything else will lose because the dealer ends between 18 and 21 -- at 46.0 percent on a five and 41.1 percent on a six.

Maybe you're stronger. Say you have 19 and the dealer six-up. You think you're sitting pretty. But what are your actual prospects?

You'll push if the dealer finishes with 19 -- 10.6 percent. And you'll win if the dealer busts or stops with 17 or 18. That's 42.3 percent for a bust, 16.6 percent for a 17, and 10.6 percent for an 18 -- a total of 69.5 percent. Not bad, but you still have 10.2 plus 9.7 or 19.1 percent risk of losing to a 20 or 21.

The danger is not insignificant even if you have a 20. With this total against a six, the probabili-ties are 10.2 percent of pushing, 80.1 percent of winning, and the other 9.7 percent of earning the right to mutter "unbelievable!" by losing to a 21.

It also surprises many blackjack aficionados to learn that a dealer's five- or six-up is more apt to lead to a 21 than supposedly better upcards -- seven through ace -- excluding hands that aren't played because the dealer has a blackjack. This doesn't seem like the good guys are getting much of a break, just when they think they are. But whoever said that casinos gave out breaks? In fact, the poet, Sumner A Ingmark oppositely observed:

The bosses act quite queasily,
When players win too easily.

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.