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# How Often Do Blackjack Dealers Make Good Hands?

13 September 1999

How Often Do Blackjack Dealers Make Good Hands?

Picture yourself in the heat of one of those cold blackjack games you wish you hadn't started. 'Fess up. Haven't you wondered whether the cards are conspiring amongst themselves to give the dealer good hands regardless of the starting point? You squeeze a three- or four-card 19 out of a two-card 12, and are counting your money against a seven-up; the dealer finesses you with 20. Or, you double on six-three against a five and pull that best of all possible aces for a 20; you think you're sitting pretty until the dealer passes you with 21. Rare outcomes? Not really. Chances of these dealer results were 7.9 and 10.8 percent, respectively.

Few blackjack buffs have a good idea of how often the dealer is expected to make good hands or bust in a normal game. The list below shows the chances of various endpoints. The first column gives averages for all upcards, and the second indicates what to anticipate when the dealer starts with a "stiff" two through six.

dealer  chances of achieving hand (%)
finish  all upcards  2- through 6-up
17 14.5 13.9
18 13.9 12.4
19 13.4 12.0
20 18.0 11.5
non-BJ 21 7.3  11.0
BJ 4.7 0.0
total non-bust 71.8 60.8
bust 28.2 39.2

Here are some examples of how to interpret the data. Overall, the dealer has an 18 percent chance of finishing with a point total of 20. Starting with an upcard from two through six, the dealer has an 11.5 percent chance of finishing with a 20.

These figures indicate why dealers seem to bust less frequently than most bettors imagine. Overall, dealers should break on fewer than three out of every 10 hands. And, starting with low upcards, they should bust on fewer than four out of every 10.

The numbers can also give solid citizens a picture of how often they ought to win, push, or lose in various situations. As an illustration, say you correctly stand with 14 against a stiff upcard. You can't push, will win if the dealer busts, and will lose otherwise. You have a 39.2 percent chance of winning and a complementary 70.8 percent chance of losing.

Notice how your fate improves when your total hits 17, then rises toward 21. Assume you have 17 instead of 14 against a low upcard. You'll win only if the dealer busts -- the likelihood is still 39.2 percent. But, you'll push if the dealer finishes with 17 -- the chance is 13.9 percent, and will lose on a dealer's 18 through 21 -- the chance is 12.4 + 12.0 + 11.5 + 11.0 = 46.9 percent. Your probability of winning hasn't grown, but your chance of losing has shrunk from 70.8 to 46.9 percent.

See what happens if your total is 18 against a stiff upcard. Now, you'll win if the dealer busts or finishes with 17 -- a chance of 39.2 + 13.9 = 53.1 percent. You'll push if the dealer ends on 18 -- the chance is 12.4 percent, and will lose on a dealer's 19 through 21 -- the chance is 12.0 + 11.5 + 11.0 = 34.5 percent. With a total of 18 rather than 17, your chances of winning rise from 39.2 to 53.1 percent, of pushing drop slightly from 13.9 to 12.4 percent, and of losing plummet from 46.9 to 34.5 percent.

Your prospects always brighten when you get to 17, then rise through 21, against any upcard. When the dealer starts by showing seven through ace, the effect is strong enough to warrant your hitting to 17, even though you may risk breaking by doing so. However, don't goof by guessing you can outgun the gurus if you hit stiffs against dealer two through six when Basic Strategy says to stand. The likelihood you'll bust and automatically lose before the dealer acts more than outweighs the expected benefits in these cases. It's as the sage songster, Sumner A Ingmark, succinctly summarized:

Those who scorn the laws of science,
Dearly pay for their defiance.
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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.