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What Makes "Stiffs" So Dangerous in Blackjack?23 January 2007
Player "stiffs" in blackjack are totals from 12 through 16. Anything lower can be hit without risking an immediate loss by exceeding 21. Standing on a stiff means losing unless the dealer busts, a roughly 28 percent chance across all upcards.
Totals of 17 or above likewise win if the dealer busts, but can also make money or at least push when the dealer reaches a safe harbor. Not that 17 is especially strong. Across all upcards, chances are 28 percent for a win – the same as for a stiff, 14.5 percent for a push, and 57.5 percent for a loss. That's an average of just over two losses for every win.
When individual upcards are considered, all stiffs are more apt to lose than win. A 17 has a slight edge against a six and is at a disadvantage otherwise. An 18 is favored facing two through eight but has an uphill battle when the dealer sports a nine, 10, or ace. And 19 through 21 are all net theoretical winners.
Although 17s aren't much better than 16s, proficient play distinguishes sharply between them. Basic Strategy for 17 is to stand against all upcards. With 16, standing is decreed against two through six and hitting against seven and above.
Fortunately, solid citizens don't have to do all the arithmetic to play blackjack proficiently. Still, some intuitive grasp on the situation may be helpful when money is up for grabs. It can instill confidence that "expert" decisions are those which offer the best ultimate shot at a profit, even though they seem risky.
Consider hitting the totals from 12 through 20. For each case, out of 13 ranks, how many will improve a hand, how many are neutral, and how many will cause the player to bust?
For all stiffs, five ranks out of 13 enhance a player's position. As illustrations, 5, 6, 7, 8, or 9 will improve a 12 while ace, 2, 3, 4, or 5 will help a 16. The remaining eight ranks will be don't-cares or lead to busts. The best prospects on stiffs are with 12s, where four ranks (A, 2, 3, or 4) are irrelevant and only four (the 10-values) are wipe-outs. The worst cases are with 16s, where no cards are neutral and all eight are breakers.
This, incidentally, helps explain why 12 is best hit against dealer two or three, where 13s to 16s stand. A 12 improves more often than it busts with a draw, by odds of 5-to-4. With the 13, the chances of improving or busting are equal at 5-to-5. On the 14, they reverse with five ways to improve versus six to lose.
A 16 still has five ways to win but eight ranks lead to losses. Above 16, ways to lose go up. But all the neutral ranks are gone so losses are at the expense of wins. The impact on the relative chances of improving or busting is therefore a double whammy. Incrementing from 12 to 16, good ranks stay the same while bad ranks worsen. Going up from 17, both good and bad ranks worsen.
The proportions become four to improve and nine to lose on 17, three to improve and 10 to lose on 18, and so forth. The accompanying table shows this effect in terms of the probability of improving relative to that of breaking with a draw, for each starting total, expressed as a percentage.
Probability that a draw will improve rather than bust a hand, for each starting total.
starting chance of improving total relative to busting 12 55.6% 13 50.0% 14 45.5% 15 41.7% 16 38.5% 17 30.8% 18 23.1% 19 15.4% 20 7.7% 21 0.0%
If you're afraid to hit a 12 versus a two or three because you remember how often you break when you do, look again at the data. That 55.6 percent chance of improving relative to busting may give you some insight about choosing the lesser of two evils. A puzzle thus posed by the punter's poet, Sumner A Ingmark:
When you've two alternatives, both dire,
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