Multiple Craps Bets Moderate Your Risk

Craps players typically have multiple complementary wagers active at the same time. It's common, for instance, to bet on the pass line then "place" several numbers after a point is established. Players spread money on place bets to increase the action and avoid the agony of watching dice hit every number but theirs.

Casinos believe it doesn't matter if money is concentrated or distributed, give or take disparities in house edge on various bets. They rate players - assess the theoretical profit on their action - the same for $24 on the six or $12 each on the six and eight. Data for billions of bets show the casinos are right.

Seasoned players believe otherwise. Maybe they're at a "nickel" table, making four $5 or $6 bets at once. If the minimum goes to $10, they look for another nickel table rather than make two $10 or $12 bets. Experience tells them the game with fewer, higher-valued bets is riskier. These solid citizens rely on intuition, not computer output, but they're right.

How can opposite conclusions be correctly drawn from the same observations? In much the way that samples of people can be fat or skinny but the population is average in weight.

Casinos confront gamblers galore over prolonged periods. Some players win, others lose. But the laws of large numbers dictate that the aggregate casino "hold" will be closely predicted by house edge, unbiased by individual bettors' peaks or valleys.

For particular players, even marathon sessions are short when measured by statistical yardsticks. Specific performances are dominated by volatility - the size and direction of swings - rather than the expected value predicted by house edge. In this respect, the same totals wagered on single or multiple numbers at craps differ in effect on each bettor.

To see what this means, consider three alternatives: a) place the nine for $30, b) place the five and nine for $15 each, and c) bet "$32 across" - $6 each on the six and eight with $5 each on the four, five, nine, and 10. The statistical expectation, a direct result of house edge - and the engine driving the casino, is the same for each case. It's $12 lost for every 36 rolls of the dice.

Upswings and downswings, however, are tempered as the same dollars are spread over more numbers. Statistical fluctuations for 36-roll cycles on the three comparison bets are: a) $112 for a $30 nine, b) $94 for $15 each on five and nine, and c) $86 for $32 across. These values can be used to calculate corresponding normal bankroll ranges. I won't snow you with the math, but just give a typical result. After 36 rolls, players have 75 percent chance of being within: a) $235 loss to $210 profit with a $30 nine, b) $200 loss to $175 profit with $15 each on five and nine, and c) $185 loss to $160 profit with $32 across.

Skewness suggests whether bankroll swings are more apt to be up or down during short play intervals, and indicates strength of the tendency in that direction. With high positive skew, numerous small losses are offset by a few big wins - favoring downswings; this reverses if skew is negative. As money migrates from one to many place bets, skew goes from a small positive to a somewhat greater negative value, raising chances of short-term upswings. For the comparison bets, skewness is: a) +0.3 for a $30 nine, b) ?0.4 for $15 each on nine and five, and c) ?1.6 for $32 across.

Because of inherent volatility, spreading money rather than concentrating the same amount on fewer numbers moderates risk but also limits profit potential. Which approach is best... aggressive or conservative? You decide. How far are you willing to swing down? What upswing will you deem high enough to quit? Can you wait long enough to outride normal short-term dips? Do you have the discipline to capitalize on brief upsurges?

As Sumner A Ingmark, a bard who believes muse can never be too thinly spread, wrote:

I followed every dollar 'til,
The game became too volatile.