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1 March 1999

The first decision gamblers make, consciously or by default, is whether to invest their stakes in a strong chance at a modest profit or a weak shot at a huge payday. Other than in dreams of gliding up to a machine or table on a moonbeam, at what turns into the onset of a hall-of-fame hot streak, you can't have it both ways. All systems and strategies incorporate this trade-off. It's what ultimately governs which games best match individuals' personal goals and temperaments, the types and amounts of their bets, and the points at which they should quit or stay.

To see the dilemma, consider three ways to bet \$10 per spin at single-zero roulette: \$10 on red with a high 48.6 percent chance to win \$10, \$1 on each of 10 numbers with an intermediate 27.0 percent chance to collect \$26, and \$10 on a single number with a low 2.7 percent chance to grab \$350. I chose this example because the wagers have the same house advantage -- 2.63 percent. After 100 \$10 spins, the statistical expectation is to lose \$26.30 in each case. Differences arise, however, out of variations in the balance between probabilities of winning and associated payoffs. This balance influences the fluctuations characteristic of the game. And these fluctuations determine the likelihood of cresting into winnerville or descending into the land of the lost.

One key issue is the prospect of achieving some win goal at the end of a session of reasonable length. Assume you have an unlimited stake -- no danger of tapping out during a downswing. Then, the following list shows the probability of being \$100, \$250, and \$500 ahead after 100 spins with each of the bets.

 profit \$10 on red \$1 each on 10 numbers \$10 on one number \$100 10% 22% 42% \$250 -- 4% 32% \$500 -- -- 18%

It's clear from these figures that the chance of earning a large multiple of the amount bet is negligible for the high-probability low-return wager on red, but improves as the bet becomes more of a longshot. For instance, a player has less than 1 percent chance of making \$250 in 100 spins betting \$10 on red -- rising to 4 percent betting the same money as \$1 on each of 10 numbers, and 32 percent sliding the full amount onto a single number.

Unfortunately, the finger of fate points two ways. Just as the opportunity to make good money grows with the longshot, so does the hazard of hitting a loss limit. The assumption of an unlimited bankroll isn't reasonable for most players. Not only are few folks flush enough to buy-in with kilobucks, but those who belly-up to the board with \$2,500, \$5,000, or more are apt to fly proportionately higher than \$10 a try. A \$2,500 stake to the \$100 bettor is like a \$250 budget to the solid citizen who squeezes \$10 onto the layout and nervously sweats out the result.

The following list shows the perils. The figures represent the chance that \$10 bettors following the three strategies will be \$100, \$250, and \$500 or more behind after 100 spins. Actual "risk of ruin," the chance of losing this much at some point before 100 spins is completed, is roughly double these values.

 loss \$10 on red \$1 each on 10 numbers \$10 on one number \$100 23% 32% 45% \$250 1% 8% 35% \$500 -- -- 21%

Comparing the two lists shows the give-and-take. Strategies offering the best chance to bag a bundle are also most likely to deplete a bankroll. For instance, turning \$100 into \$500 in 100 spins is a feasible betting \$10 on a single number, but the approach can easily lead to ruin. And, conversely, maneuvers that minimize the risk of ruin are those least liable to yield sustantial returns. Luck enters the picture, of course, determining which way a game will swing. But looking for luck is one thing, counting on the virtually impossible is quite another. As the muse of mediation, Sumner A Ingmark, said:

Some gambles are lost, too often I fear,
By players who just can't get there
Recent Articles
Best of Alan Krigman
Alan Krigman

Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.
Alan Krigman
Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.