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# How Confident Are You of Winning at Blackjack with a 20?

7 April 2000

Blackjack buffs occasionally get frustrated when they're either dealt or manage to pull totals of 20, then can't seem to beat the dealer anyway. Is this situation particularly rare? Something that happens only when the moon is full, a bozo at third base keeps feeding the dealer the right wrong cards, or you've just raised your bet and are really at the cusp of destiny?

The real question is how often you can expect a dealer to push or beat a 20 in the normal course of the game. The accompanying list shows the answers. For each upcard, it gives the likelihood the dealer will finish with 20, 21, or either. In the case of a final 21, blackjacks and other combinations are indicated separately.

 dealer upcard chance of  final 20 chance of final 21 chance of   final 20 or 21 2 12.4% 11.8% 24.2% 3 12.0% 11.5% 23.5% 4 11.6% 11.1% 22.7% 5 11.3% 10.8% 22.1% 6 10.2% 9.7% 19.9% 7 7.9% 7.4% 15.3% 8 6.9% 6.9% 13.8% 9 12.0% 6.1% 18.1% 10 34.2% 3.4%  (non BJ) 37.6% 7.7% (BJ) 7.7% A 13.1% 5.4%   (non BJ) 18.5% 30.7%   (BJ) 30.7% overall 18.0% 7.3%   (non BJ) 25.3% 4.7% (BJ) 4.7%

It shouldn't be a shock to see the figures confirm how vulnerable solid citizens are with 20, when the dealer starts with 10 or ace. All-told, the chance a 20 will push or be beaten is 45.3 percent against 10-up. The probability rises to 49.2 percent when the dealer shows an ace. Despite these risks, players with point totals of 20 are still favored. Expectation, including losses to dealer blackjacks, is a net gain of \$0.44 per dollar bet against 10-up and \$0.15 per dollar against an ace.

Few players, though, realize how often a dealer can be expected to make 20 or 21 starting with what's supposed to be a dog. The data demonstrate that such an event happens on nearly one out of every five appearances of the dealer's weakest upcard -- a six. And frequency rises to one out of every four on a two-up. Expectation correspondingly ranges from a profit of \$0.70 per dollar bet against six-up, down to \$0.64 per dollar vs a two.

The best situation for the player with a 20 occurs -- not when the dealer begins with a stiff -- but with an eight, followed by seven then nine. The figures show that dealers will win or push on only 13.8, 15.3, and 18.1 percent of these starters, respectively. The bettor's matching expectations, in net win per dollar bet, are \$0.79, \$0.77, and \$0.76.

Instances of dealers making 20 or 21 with low upcards tend to be memorable, if not disheartening. The primary reason is that low upcards represent initial conditions players are typically happiest to see and expect to yield winning rounds most often.

The anticipatory euphoria is justified, in general, since two-up through six-up are most apt to cause the dealer to bust. As a result, they offer the greatest promise for players who stand on totals below 17. They're similarly the upcards against which doubles are strongest, given the chance that a poor draw may mean the bettor can only win the round if the dealer goes bye-bye.

But, once stalwarts stand with point totals of 17 or above, there's a particular dealer upcard that gives them the greatest expected profit. And it's only a stiff in one case. Here are the hands and associated expectations per dollar bet. For a player 17 it's six-up at just over \$0.01, for an 18 it's seven-up at \$0.40, for a 19 it's seven-up at \$0.62, for a 20 it's eight-up at \$0.79 as noted above, and for a 21 it's nine-up at \$0.94.

One factor making casinos exciting is the stroke of luck that can turn impending defeat into victory. Another is the risk that a strong position may quickly deteriorate. The money? Well, the way some folks seem to disdain their bankrolls, you'd wonder if it was even a factor. The poet, Sumner A Ingmark, put it like this:

Some gamblers don't care what they earn,
The thrill of the game's what they yearn,
You'd think they had money to burn.

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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.