Basic Strategy in blackjack is the set of decisions yielding the most expected gain or least expected loss for each player hand and dealer up-card. Some of the rules reflect fine distinctions. That is, "expectations" for the alternatives are nearly equal.
These close calls are precisely the circumstances under which even seasoned solid citizens are likeliest to defy the dogma. Not usually because good players actually know the numbers -- few do -- but because bettors get what seem like mixed signals from the gurus on the one hand, and experience and intuition on the other.
As an example, say you've wagered $10 in an eight-deck game and get sandbagged with 9-7 vs. 10-up. Standing in this situation, statistical analysis predicts a theoretical loss slightly under $5.38; hitting, it's just over $5.36. When you can't surrender, the "book" ordains hitting because its expectation is less costly by roughly a penny. Will a cent difference on a $10 bet make or break your day? Hardly. So you're not exactly giving away the family jewels by standing and simply hoping the dealer busts.
When expectations on two choices split hairs, prospects of a loss versus a win or push may unconsciously affect bettors' thinking. Standing on 9-7 vs. 10, chances are about 23 percent of winning and 77 percent of losing -- you can't push since dealers must draw to totals under 17. Hitting, chances are around 20.5 percent of a win, 5.5 percent of a push, and 74 percent of a loss.
You can gain two relevant insights from these figures. 1) Hitting cuts your risk of a loss relative to standing from 77 to 74 percent, bolstering incentives to play by the book -- but only modestly. 2) Losses by hitting are still three times as likely as wins -- and high failure rates cause even the most trusting to question whether Basic Strategy is really a map to Easy Street.
Many soft doubles also represent close calls with respect to expectation. But, on these, the odds of winning and losing might justify flouting the rules and sacrificing a bit of expected profit in favor of other rational goals. The tightest soft double decision involves A-2 vs. 5-up. In an eight-deck game, expected profit on an initial bet of $1,000 is $136.33 by hitting and $136.36 by doubling. The difference, $0.03 per $1,000 bet, while clearly insignificant, is why Basic Strategy says to double.
However, what if you pull an ace, two, or three to the A-2? And that's gonna occur 23 percent of the time. You'd be at or below soft 16. Had you hit, you could draw again with an upside but no downside because you can improve or stay the same but not get worse. Doubling, you're stuck below 16 and can only win if the dealer breaks. And pulling a four to A-3 would give you soft 17, which it would also be beneficial to hit again if you could.
When the electrons settle in the computer, doubling is found to have chances of 50.9 percent of winning two units, 5.1 percent of pushing, and 44.0 percent of losing two units. Hitting upgrades the chances to 54.6 percent of winning one unit, 4.5 percent of pushing, and 40.9 percent of losing one unit. The margins of wins over losses are 6.9 percent doubling and 13.7 percent hitting.
Personal predilection, or conditions current at some stage of a game, may make probability of winning or losing a more desirable criterion than expectation for some decisions. Hitting or standing, as appropriate, may then be justified on soft totals when doubling is customary. The opposite is never true. For instance, expectation differs by a mere $0.03 on a $10 bet with A-7 vs 2-up, but is greater hitting than doubling so Basic Strategy prescribes the former. And odds of winning are superior as well. Similarly for A-8 vs 6-up, where standing offers higher expectation than doubling by only $0.03 per dollar, while also affording more likelihood of a success than a failure.
The acclaimed composer of classic casino canto, Sumner A Ingmark, commented
cogently on the common confusion of close calls:
As lines between alternatives get narrowed,
The making of decisions waxes harrowed.