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Best of Alan Krigman

Gaming Guru

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How different are your strongest and weakest blackjack starting hands?

5 December 2011

The strongest playable blackjack hand is 20 versus eight-up. Ignoring rounds in which the dealer has a blackjack, your expectation by standing with this combination is to win an average of 79.1 cents per dollar bet. Many players would assume a 20 to be their best total but would suppose it would be most favorable against a six, the card on which the dealer is likeliest to break. In fact, average profit for 20 versus a dealer’s six is hefty, but less so at 70.3 cents on the dollar.

The weakest hand is 16 versus 10; the projected long-term loss on this set, maintaining the exclusion of dealer blackjacks, is 53.5 cents per dollar. Some players sweat more over 16 against two–up. By standing, they can’t push and will lose unless the dealer busts – which doesn’t seem to happen very often. The statistical expectation is, indeed, negative in this situation. The average cost is 29.3 cents on the dollar – worse than the result of standing against three through six but less adverse than on any of the upcards on which hitting is recommended. A seven up, the least onerous of the latter, is projected to exact an average penalty of 39.2 cents per dollar.

Expectation, a theoretical average, is the usual measure invoked to express the relative quality of a gamble. Blackjack buffs who focus on the here and now, rather than on extended action they’re not ever apt to personally experience, may more interested in the probability that a hand will win, lose, or push. In the case of 20 versus eight-up, the chances are 86.13 percent to win, 6.95 percent to lose, and 6.92 percent to push. Bettors therefore have a heavy advantage, but shouldn’t conclude something’s amiss if the hand pushes or loses. Analogously for 16 versus 10, chances are 20.08 percent to win, 74.00 percent to lose, and 5.92 percent to push. So solid citizens oughtn’t get their hopes up too high, but a 20.08 percent shot at victory isn’t to be sniffed at.

Overall, regardless of what the dealer is showing, 20s are encouraging and 16s discouraging. And, notwithstanding small shifts according to how the totals are formed – say ace-nine, 10-10, or four-nine-seven for the 20 – these generalizations hold regardless of the dealer’s upcard.

The upcard, however, does affect how good or bad a total might be. For instance, upcards of eight, followed by seven and nine, are most beneficial when players have 20s, even though dealers are more vulnerable to breaking on twos through sixes. Dealers’ 10s and aces lower the outlook for players’ 20; this isn’t because they lose often but owing to the high incidence of pushes, 36.84 and 18.94 percent, respectively. The overall range is comparatively narrow, with profits between 55.6 and 79.2 cents per dollar. Totals of 16 follow intuition a bit more reliably. They’re worst against 10s, followed by aces, nines decreasing to sevens, then twos rising through sixes. The corresponding range is fairly wide, with losses from 15.4 to 53.9 cents per dollar.

The accompanying tables show the extent to which starting totals of 20 and 16 differ, and also indicate how dealer upcards affect your prospects for playable rounds. The data not only give expectations, but also probabilities of winning, losing, and pushing for these totals against all dealer upcards. The figures are approximations for an “infinite deck” with no allowance for cards showing on the layout. Basic Strategy is assumed – standing on all 20s and 16s against upcards from two through six, hitting 16s against seven through ace, and splitting all pairs of eights.

Prospects for hands totaling 20; stand against all upcards
Upcard  expectation   prob win   prob lose   prob push
2           63.92%      5.76%      11.84%      12.40%
3           64.93%     76.43%      11.49%      12.08%
4           65.98%     77.17%      11.19%      11.64%
5           67.23%     78.03%      10.79%      11.18%
6           70.39%     80.12%       9.73%      10.16%
7           77.37%     84.75%       7.38%       7.87%
8           79.18%     86.13%       6.95%       6.92%
9           75.79%     81.88%       6.09%      12.04%
10          55.61%     59.38%       3.77%      36.84%
ace         65.59%     73.32%       7.74%      18.94%
Prospects for hands totaling 16, excluding pairs of eights;
stand against two through six, hit seven through ace
Upcard  expectation   prob win   prob lose   prob push
2          -29.30%     35.35%      64.65%       0.00%
3          -25.16%     37.42%      62.58%       0.00%
4          -20.84%     39.58%      60.42%       0.00%
5          -16.32%     41.84%      58.16%       0.00%
6          -15.43%     42.28%      57.72%       0.00%
7          -39.19%     26.43%      65.62%       5.68%
8          -45.86%     24.16%      70.02%       5.82%
9          -50.94%     21.57%      72.51%       5.93%
10         -53.92%     20.08%      74.00%       5.92%
ace        -51.71%     20.94%      72.65%       6.41%

Among the insights you can glean from the tables are that you have a reasonable shot at winning a round when your first two cards are the weakest possible total – 16, and aren’t immune to losing when they’re the strongest – 20. The possibilities either way depend heavily on the dealer’s upcard. But even the best and the worst of the cases leave ample margin for surprise, a condition described by Sumner A Ingmark, the poet laureate of the casino scene, when he wrote:

Though chance may rise or be diminished,
You’re never sure until you’re finished.
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.