How Much Extra Edge Are You Giving the House in Blackjack?

Many blackjack players know what "the book" says to do in adverse situations. But they sometimes honor their intuition over the laws of the universe anyway. For instance, they'll stand rather than hit 12 versus two- or three-up. Certain solid citizens flout the rules of Basic Strategy under favorable conditions as well. An illustration is hitting in lieu of doubling 11 versus 10-up, thinking the dealer too strong to put extra money on the line.

Hands on which blackjack buffs tend to go their own ways are typically close calls. The chances of one such option "working" better than another in a specific instance don't differ much. The "cost" of breaching Basic Strategy in these cases is also usually low. And it's not even a real loss, but a theoretical forfeiture.

Pretend you bet $10 and get 12 versus a two-up. You're the underdog no matter what you do. Hitting, the statistically projected damage is around $2.50. Standing, it's about $2.90. Basic Strategy says hit, to save 40 hypothetical cents. No big deal. If the butterflies in your stomach are less agitated by doing so, you may be better off standing and letting the dealer's hand decide your fate, instead of drawing and sweating an instant bust or reaching 17 through 20 and still being clobbered.

Minimizing expected loss, as opposed to personal anxiety level, on a particular round is one take on the question. Another is selecting a strategy, and adhering to it, by considering its bearing on the edge the casino gets over a period of time.

With a $10 initial bet the statistical penalty for violating Basic Strategy by standing on 12 versus two-up, standing on 13 versus three-up, and hitting 11 versus 10 up is roughly $0.40, $0.20, and $0.60, respectively. When you make these decisions consistently, their effect on the overall edge in the game goes further and involves how often the hands are expected to occur. Players see 12 versus two- or three-up on the average of 7.5 per 1,000 playable hands each; it's 13.6 out of 1,000 for 11 versus 10-up. The corresponding increases in edge are the sizes of the penalties multiplied by their probabilities of occurrence. The products are 0.030 percent for 12 versus two-up, 0.015 percent for 12 versus three-up, and 0.082 percent for 11 versus 10-up.

The drop dead edge a casino gets in a six deck blackjack game with doubling allowed on any two cards, resplitting pairs, and doubling after splitting is about 0.46 percent. The three indicated departures from Basic Strategy add 0.127 percent to this value, bringing it to 0.587 percent. Assume that in a representative session, you make 200 bets averaging $10 each. Were you to follow Basic Strategy to the letter, the casino would expect to earn $9.20 from your action. The theoretical "take" with the three departures would be $11.74, an additional $2.54.

On an absolute scale, the 0.127 percent gift you're giving the house, the $2.54 for the 200-round session with $10 average bets, is hardly a bankroll buster, dollar-wise. It also barely alters your ultimate session prospects. For instance, on a $100 buy-in, the likelihood you'll still be in action after 200 rounds with perfect Basic Strategy is 44.9 percent. These three frequently encountered deviations only cut that chance to 44.4 percent.

For all practical purposes, in the limited number of rounds a person plays in a casino visit of reasonable duration, common violations of Basic Strategy have minor impact. Still, the edge for optimal play is small and the illustrated changes represent an increase of over 27.5 percent of the advantage the bosses are willing to accept. Add a few more "errors," such as standing on soft 18 when Basic Strategy is either to double or hit, and edge increases by 50 percent. Mix in insurance whenever the dealer shows an ace and you more than double the minimum edge.

How far are you willing to go before you decide to teach those butterflies in your belly some arithmetic? Or, at least, to calm them with this couplet by the punter's poet, Sumner A Ingmark?

Though benefits lost are incremental,
The peril is not coincidental.