You Don't Have to Know the Math, Just That It's There

We're acquainted entirely from the tables, a perspective strong for look-sees and chit-chat but weak for deep discussion. I pegged him as mathematical, for several reasons. He frequently says he's a "percentage player." After a long roll, he often summarizes aloud the hits made, like "five fours, six fives, nine sixes," and so on. His bets strike a balance between keeping the house edge small and limiting risk so a series of quick miss-outs won't kill him. If he gets in a hole, he tries to work his way out gradually instead of chasing his losses with big bets, hoping for a lucky rescue in the nick of time. And, he seems to sense when to take his profit or cut his loss and walk away.

Last week, I sat down with Charlie for a cup of coffee. We got to talking craps. He not only doesn't grasp the first thing about the math behind the game, what he thinks he knows is wrong.

Here's an example. Charlie tallies what's been rolled so he can tell what hasn't hit "enough" and is therefore "due." This is a misinterpretation of the laws of probability.

The chance of rolling any number depends on only two factors:

a) how many combinations of ways two dice can land,

b) how many of these ways add up to the number in question.

Factor (a) is fixed two six-sided dice can land 36 different ways. Factor (b) depends on the selected number. A five, for instance, can appear four different ways (1-4, 2-3, 3-2, 4-1). The probability is factor (b) divided by factor (a). For a five, this is 4 ÷ 36 or 11.11 percent. Previous rolls don't change dice geometry, so they don't alter the chance of rolling five.

Oh, yes. The likelihood of getting a particular number at least once in a roll of a certain length increases with more throws. For instance, the chance of getting a five in one roll is 11.11 percent. In ten rolls, it's 69.2 percent. In twenty rolls, 90.5 percent. But, this doesn't mean that after nineteen something elses, five has a 90.5 percent probability on the next throw. The chances are still four out of thirty-six or 11.11 percent.

I could cite other myths Charlie mentioned during our talk. But, that misses the point entirely. Charlie's a good player without the theoretical background. He learned what experience was teaching him, not the superstitions many players want it to prove.

Like Charlie, most craps players won't get to know precisely why some bets offer greater long-term profit potential than others, or whether higher payoffs on center bets are outweighed by the greater risks. Similarly, most blackjack players won't know exactly why it's wise to follow rules like splitting pairs of nines against dealer six or eight but not against seven. Unlike Charlie, though, few of these solid citizens will gain the intuition to gamble like winners.

That's where the math becomes important. Not to calculate or memorize percentages. Not to realize that the odds against winning $18 with $10 placed on the four at craps are 2-to-1. Not to recognize that the probability a blackjack dealer will break with an upcard of nine is 23 percent. But to have confidence that legitimate reasons underlie winning strategies. And, having this confidence, not to do the foolish things done so often at the tables and machines. By people who throw money away on an expensive activity they don't understand. Or who remember the times when pure guesses paid off, presume dumb luck separates winners from losers, and think their premonitions are more reliable than the laws Mother Nature laid down to govern the entire universe.

As Sumner A Ingmark, personal poet to proficient punters, prudently postulated:

The gamblers who believe canards,
That hunches rule wheels, dice, and cards,
Get hoisted with their own petards.