Gambling theories and other fairy tales

Jan 15, 2002 4:35 AM

The philosopher, George Santayana (1863-1952), is often quoted as having said, “Those who cannot remember the past are condemned to repeat it.” A counterpart may pertain to gambling. Something like “Those who cannot comprehend the math are convinced they can defeat it.”

Santayana also said, “History is a pack of lies about events that never happened told by people who weren’t there.” An even better nominee for a gambling analogy! Make one up yourself.

This came to mind recently when Jimmy, the popular bartender at the posh Celebrity Club in Atlantic City’s Claridge Casino, asked me about splitting nines rather than standing against seven-up at blackjack. He thought splitting was good aggressive play, despite “the book” saying to stand. Besides, he saw a wallet-sized Basic Strategy card with an asterisk next to the “stand” symbol and a notation that “some authorities claim it’s better to split.” As a clincher, Jimmy added that since Basic Strategy comes from assuming the “unseen” card is a 10 ”” it makes sense to go for two winning 19s instead of one 18 against a dealer’s final 17. Fortunately, Jim’s mixology is much better than his mathematics.

Jimmy’s belief that Basic Strategy for any hand presupposes the unseen card to be a 10 is widespread but wrong. The decisions are actually those giving the greatest statistically expected profit or least corresponding theoretical loss, when the chances of all possible results of every alternate option are calculated. It’s therefore not a matter of one guru’s opinion over another’s, but of calculations based on the laws of probability. To picture how this works, think just about a dealer’s seven-up. The dealer has 36.8 percent chance of finishing with 17. This can come from a 10 in the hole (chances are roughly 30.8 percent). But there’s also six percent chance of getting 17 with combinations like nine plus ace, six plus four, six plus three plus ace, and so on. Too, the dealer has 26.2 percent chance of breaking and 37.0 percent chance of wrapping up with 18 through 21. All go into the stew.

On the other hand, Jim’s right in not holding those wallet-sized cards in quite the same reverence as the stone tablets Moses got from a burning bush and brought down the mountain. Players may opt to follow Basic Strategy rigorously, understanding that by doing so they’re maximizing their statistical expectation. But, solid citizens who accept the rules entirely as a matter of faith (and who tend to be the most vocal critics of anyone who deviates even slightly from the strait and narrow), fail to realize that individuals may have valid gambling criteria for which decisions violating Basic Strategy are optimum. As an example, pretend you start with a $10 bet and pull a five-six vs a dealer’s nine. Basic Strategy is to double rather than hit, because long-term earnings are projected to average $2.30 with the former and $1.57 with the latter. But chances of winning are greater by hitting, since you may draw a seven or under and can then get yet another card rather than stop below 17. Who’s to fault you for picking more chance at less win, over the converse?

That’s not the whole story. Certain Basic Strategy plays are so close to the next-best choice, expectation-wise, that statistical penalties for being aggressive or conservative are negligible. In “Blackjack Attack,” Don Schlesinger gives the following as hands where straying from the gospel has a calculated long-term average cost under a penny per dollar bet: nine vs two-up, 12 vs four-up, 16 vs 10-up, ace-four vs four-up, ace-six vs two-up, ace-seven vs two-up, two-two vs three- or four-up, and three-three vs four-up.

As for nine-nine vs seven, here’s the skinny for one of those $100 bets Jim’s sportsman status demands. Stand and your expected profit is $40. Split and your expected profit is $37. Should you grab the better shot at $100? Or is it worth sacrificing $3 “on paper” to go for a real $200 return ”” more if you happen to pull another nine, or draw a deuce to one or more sides ”” knowing you’re strongly favored either way? The only expert qualified to answer is the person who knows you best, the one you see in the mirror every morning when you’re brushing those pearly whites. For, as everybody’s favorite poet, Sumner A Ingmark, wrote:

Ask the masters, read the references,
You, alone, can state your preferences.