Blackjack: Three Subtle Questions

Blackjack is subtle because distinctions between alternatives in many situations are so fine that intuition doesn't necessarily help. In fact, statistically correct strategies were unknown until the poo-bahs programmed powerful computers to pick the proverbial nits. So, questions solid citizens ask about the game are often quite cogent. Here are three examples.

A friend and I are comfortable betting $5 per round on blackjack. What are the pros and cons of betting at separate positions in the same game for $5 each, pooling our money and wagering $10 per round on one spot, or playing at different tables for $5 a hand?

Expectation, based on edge, is identical all three ways. But the options differ in the bankroll fluctuations you can anticipate during a session. The choices let you moderate the hazards going for less win, or intensify the risks trying for larger returns.

Concentrating on a single spot creates the wildest swings. Bets in different games produce the smallest peaks and valleys. And multiple hands at the same table put you in between. To quantify the effects, I'll give the ranges over which you have a 50-50 chance of finishing 100 rounds with each approach.

Assume that the rules and your decision strategy give the house 1 percent edge. Betting $10 on one spot, the 50-50 range is from $86 down to $66 up. With two $5 spots at one table, this narrows to minus $74 to plus $54. And betting $5 per hand at separate tables, it shrinks further to a range from $64 loss to $44 win.

In some casinos, dealers check their "hole" cards when they show a 10 or ace. If they have a blackjack, the round is over, then and there. Do you adjust your strategy against 10s or aces at these tables, knowing that the dealer doesn't have blackjack?

"Peeking" speeds-up the game. Nothing more. Basic strategy, the decisions which maximize players' expected return, is the same whether or not dealers check their hole cards. The rationale is as follows. If the dealer has blackjack, you can't affect the outcome of the round. Since your decision is irrelevant in this situation, optimization rules pertain only to "playable" hands.

Think about a pair of sevens against an ace-up. If the dealer checks and finds a 10, the round is over. Say the dealer doesn't find a 10. Basic strategy says to hit. You certainly wouldn't stand or double. But, how about splitting, as you would against two-up, knowing you're weak anyhow but seven is a stronger start than 14? A 14 against a playable ace loses an expected $0.45 per dollar bet. Single sevens have theoretical losses of $0.31 versus ace; splitting elicits twice the expected penalty -- $0.62.

The "book" says hit 12 versus a dealer's two- or three-up. When I do, I often get a 10 and bust, or something less than five which doesn't help my hand. Is basic strategy right in these cases?

You're an underdog either way. Which is the lesser evil? The devil is in the details of the arithmetic.

Say you stand. You can't push, and only win if the dealer busts. What's the actual chance this will happen? Pretend, instead, that you hit. You might get 10 and bust, ace through four and become no stronger, or five through nine and improve. What are the chances here? And, what if you do improve? A 17 pushes one dealer non-bust finish and loses to the other four. An 18 beats a 17, pushes an 18, and loses to 19 through 21. Similarly for 19 and 20. Even a 21 -- which can't lose -- may push and not win. When the dust settles on your calculator, what's the bottom line?

The laws of probability say that hitting averages less loss. Per dollar bet, standing costs $0.30 and $0.25 versus two and three, respectively. Hitting cuts the damages to $0.25 and $0.23.

These points may seem picayune. But blackjack is a game of numerous nuances, aggregate mastery of which reduces your reliance on luck. As the immortal poet, Sumner A Ingmark, stated:

A cup can fill, can reach the top,
In one big gush, or drop by drop.