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# Playing Roulette so that One Winning Bet Gets You Back

22 February 2005

The records of gambling history are replete with sad stories of sorry solid citizens who think they've surmised the supreme secret the bosses don't want anyone to know. It's raising their bets after every loss until the inevitable win boosts them out of the hole and over the top. This strategy for beating the casinos out of comps, if not money, is known as Martingale betting.

The failings of the Martingale system follow from the fallacy of an event becoming due, just because it hasn't transpired after more trials than an inumerate interpretation of the laws of probability seem to suggest. Say a Red number pops 17 times in 37 spins of a roulette wheel. Red is no more favored than usual on the 38th spin even though it's mathematically "expected" to occur 18 out of every 38 tries. The same is true after 37 spins during which Red hit 10, five, or no times at all. What's the chance of 38 spins without seeing Red? It's admittedly low, less than one out of 39 billion, but you could be there when it happens.

Picture how much you'd have to bet when a string of blacks occurs and you keep doubling up on Red. If you start with \$5, you'd go to \$10, \$20, \$40, \$80, \$160, and \$320 this with only six blacks in a row the chances of which are close to one out of 88. You've already run through a bankroll of \$635 and are about to put \$640 on the line. You're risking being behind by \$1,275. For what? A crummy \$5 payday! Assuming you have this much or more to burn in your belief that Red is due, you're still not home free. Another spin or two and you may reach the upper limit of the game where the casino will no longer let you raise your bet.

There's an alternate way to apply the notion of one win getting you back at roulette. Pretend you're at a \$5 table. Bet this much on a single spot. If you lose, repeat the bet. The repeat may be on the same or any other spot. Lucking out on the first attempt gets you \$175 at 35-to-1. On the second go-round, you'd net \$170, \$175 minus the \$5 lost previously. You can continue for 36 spins, with a victory on the last returning you to break-even.

The probability of winning somewhere along the line is better than 60 percent. Hardly overwhelming, but more than an even chance. Further, you've got a shot at earning \$175, then \$170, then \$165, and so on rather than just \$5. And you can go for 36 spins, about an hour's action in a typical game, on a \$180 stake.

If worse comes to worst and you lose \$180 with 36 straight misses, but have more moolah in your fanny pack, you can switch to \$10 bets and keep on trucking. For instance, were you willing to go as low as \$300, you'd get another dozen spins. A win on the first of these would bring in \$350; this, minus the \$180 you'd already donated to the dealers' pension fund would be a gain of \$170 on the bottom line. A win on your last stand, after 36 losses at \$5 and 11 at \$10 would still net you \$60. Your \$300 bankroll, bet this way, would yield roughly 70 percent chance of something between break even and a \$175 profit.

Compare these two approaches. Doubling up on even-money bets has a better chance of success over a moderate number of trials; however, you can quickly find yourself in a scary position, risking big bucks to chase a prize that's small from the get-go. And, you may be hot to trot at the outset of a series, but get cold feet when your \$5 mind-set has you putting \$320 or \$640 at risk. Although low bets on longshots with high payoff multiples will win less often, they offer greater possible proceeds, outlays with which you can feel comfortable, and extended play on budgets that seemed sensible before you left home.

Neither is much like dropping a dollar into a slot machine, hoping to grab a million. But you don't gamble because none of your other get-rich-quick brainstorms worked, and this is your last resort. You do it for the excitement, the entertainment, the joie de vivre, the coupon for the all-you-can-eat buffet? Right? You do follow this philosophy formulated by the famed poet, Sumner A Ingmark er, don't you:

Approach with utmost trepidation,
A gamble born of desperation.

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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.