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# Gamblers Can Be Right by Being Wrong (and Conversely)

10 June 2003

Many gamblers want badly to believe in the Law of The Maturity of Chances. That is, the more often a proposition fails, the more it becomes due to succeed. The proof they cite for this pudding is that the probability of repeated losses tends toward zero as series lengthen, so chances of a win must rise toward certainty.

Only, the "law" is a fallacy. In games of independent trials, probabilities aren't determined by past events. Rather, by the subset of the universe of possibilities representing winners.

A coin, for instance, can land on Heads or Tails. So the universe comprises two possibilities; a bet, say on Heads, is a subset having one member. The probability of winning is accordingly one out of two, denoted by numero-noodniks as 1/2 or 50 percent. Similarly, a roulette wheel has 38 grooves. A wager on a single spot therefore has one way to win out of 38 possibilities, such that the probability is 1/38 or 2.63 percent. Alternately, since 18 of the grooves are Red, a bet on this color can win 18 ways out of 38 possibilities. The chance is 18/38 or 47.37 percent.

A series of 3,700 spins of a roulette wheel in which every number except the nine hits exactly 100 times doesn't alter the one groove out of 38 situation and somehow make the chance of that spot more likely on the 3,701st spin. In fact, it might more logically lead to the conclusion that something was wrong with the wheel that prevented the ball from stopping in the nine.

Although the Maturity of Chances is a misconception, solid citizens can build reasonable strategies around the decreasing probability of growing series of losses. Reasonable, provided players understand the associated positives and negatives.

The most common such strategy is the "Martingale" progression. Essentially, bet on an even-money proposition and double it after every loss. If a win comes along before you go belly-up or hit the table limit, you earn one unit of profit for the series.

For instance, start a Martingale with \$5 on Red at roulette. Say the results are four Blacks in a row and then a Red. You've bet and lost \$5 + \$10 + \$20 + \$40, a total of \$75. Your fifth bet is \$80 which you win for a net profit of \$5. If you've got a \$200 bankroll, you can only sustain five losses in a row because your total outlay would then have been \$155 and you don't have the \$160 required for the sixth bet.

Ignoring the half-back concession some casinos give on 0 or 00, the probability of five successive losses is 20/38 multiplied by itself five times, or 4 percent. This yields 96 percent chance of winning \$5, offset by 4 percent probability of losing \$155. You can have a lot of fun and plenty of action accumulating those \$5 profit increments. Or you could get a swift kick in the pants.

An alternative for roughly the same bankroll would be to bet \$5 on a single number, and repeat the wager until it won or you went broke. Then quit, or start again. This bet pays 35-to-1, so a win on the first spin, earns \$35x5 or \$175. Win on the second try and you net \$175 minus the \$5 already lost, or \$170. On the third go, the profit is \$175-\$10 or \$165. You can continue for 36 tries on a \$180 stake. Success on the 35th spin will net you \$5. On the 36th, it'll bring you to break-even. This approach has a sliding scale of probability and profit -- 2.6 percent chance of winning \$175, 5.2 percent of at least \$170, and so forth up to 61 percent of at least \$5 and 62 percent of at least breaking even. The downside is 38 percent probability of losing the entire \$180.

Neither of these strategies depends on a win magically coming due after a string of losses. Neither is a secret about surmounting the house edge that the casino bosses don't want anyone to know. Both are approaches individuals might want to take to gambling, depending on what lured them to the casino in the first place.

Ultimately, it's as the punters' poet, Sumner A Ingmark, penned:

A range of strategies enhances,
Successful gamblers' winning chances,
Confronting different circumstances.

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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.