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# A Roulette Strategy That Wins Three Times More Often Than It Loses

17 May 2004

Make believe you come to a \$5 double-zero roulette table with \$360. You know this game has a usurious house advantage. But you play it because it's not intimidating, the pace is relaxed, and you use a strategy that usually gives you a few hours' action on your money and yields a small-to-modest profit most of the time with only an occasional wipeout. Although you normally don't rate a comp and haven't been invited to join the elite Croesus Club, neither matters because you pack your own mashed potato sandwiches for lunch and know lots of spots to sit and eat them.

Here's the strategy. Pick a number and bet it for \$5. Quit immediately on a win. Otherwise, bet on the same or a different single number again. And keep going. If you lose 36 in a row, you're down \$180 and start betting \$10 a spin on a single number. The worst case scenario, 18 more losses, puts you \$180 deeper in the hole for a total of \$360.

Hit within 54 spins and you'll be from break-even to \$175 ahead. Even if you're unlucky, you've had about two hours of excitement at a game featured in top-drawer, well-loved movies like Casablanca. And, of course, you only brought as much as you could afford to lose so you figure it as the price of entertainment.

What's the risk of disaster? At double-zero roulette, the chance that a bet on a single number will lose on any spin is an almost overwhelming 37 out of 38, or 97.4 percent. The chance of 54 such losses in a row is this probability multiplied by itself 54 times, or a much more tolerable 23.7 percent. The likelihood is only 37.3 percent that you'll get as far as the critical point when you lost \$180, started betting \$10 per spin, and began to doubt whether this scheme was really so brilliant after all.

On the brighter side, consider your chance of getting back after being behind, or of winning various amounts. Overall, the probability of this happy eventuality is the compliment of 54 consecutive misses, 76.3 percent.

Within the rapturous range, prospects improve for particular amounts as sizes of the wins increase. At the low end, it's 2.7 percent of breaking even or going \$5 over the top by hitting on the 35th, 36th, or 54th try. The high extreme is 6.2 percent of winning \$170 or \$175 with a score on the 1st, 2nd, or 37th attempt.

Cumulative probabilities, of winning more than some specified amount, decline as the target rises. The accompanying table shows the chances of winning at least some representative amounts -- from \$25 to \$175 in increments of \$25.

Probability of winning at least
the indicated amounts

 amount probability \$25 68.9% \$50 61.2% \$75 51.8% \$100 42.1% \$125 30.2% \$150 17.7% \$175 2.6%

This may appear unappealing if you think in terms of taking that \$360 you told yourself you could always get your hands on, and investing it in a shot at changing your life. Were this to be your goal, roulette could still be your game but an alternate approach would be appropriate. Any of many conceivable alternatives, actually. Such as running through your initial bankroll once following the \$5 and \$10 system but not stopping upon a win, or starting with the \$5 and \$10 idea and going the 54 spins while raising your bets or spreading to additional numbers using any earnings you make along the random walk to Easy Street.

But, say you're among those who gamble for recreation, hoping mainly for a free day of fun or maybe a trip home with a few more bucks in your fanny pack than you brought. This approach then offers that impressive 76.3 percent chance of success, offset by a much scantier 23.7 percent chance of a \$360 rout. Another example of how solid citizens can shape their fates within the broad limits defined by the possible and the probable. An ability reflected by rhymer, Sumner A Ingmark, when he reverently wrote: