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# Martingale losses can be spectacular

13 March 2012

The Martingale betting system, in which players double their bets after losses, has a strange hold on a segment of roulette players. I've been warning against the system since I started writing regularly about gambling in 1994, and others exposed the system as a bankroll-eater long before I joined the fray.

And yet it's a rare month when someone doesn't ask me about the Martingale, whether by e-mail or in person. To some, it's new, something they've heard from a friend. Others have read that it's a bad, costly system, but wonder if maybe those issuing the warnings have missed something.

Daryn is one of the latter. He approached me in a casino to say he's been having success in the casino.

"I heard that one of the drawbacks is that sometimes you can't bet enough money to keep it going, because of the table limit," he said. "Well, I found a casino where the minimum bet is \$5 and the maximum \$1,000, so I can do an eight-step system. I bet on red or black. So tell me, what are the chances of losing eight in a row?"

I didn't know offhand -- I guessed somewhere in excess of half a percent -- but it's easy enough to calculate. There are 38 numbers on a double-zero wheel. For any bet with an even-money payoff, including red, black, odd, even, first 18 and last 18, there are 18 winners and 20 losers. The probability of eight losers in a row is 20/38 raised to the power of 8. In the wi-fi age, we could get the answer on the spot by typing "(20/38)^8" into Google. The result: a little less than 0.6%, 0.589%, to be more precise.

"See? That's practically nothing," Daryn said. "I've tried it four times now, and won every time."

In my view, that's not practically nothing. It's once per 169.84 trials -- love that calculator function. And when the losses come, they are spectactular.

One of the features of a Martingale system is that whenever you win, your profit is equal to your initial wager. If you bet \$5 to start, as in Daryn's table with the \$5 minimum, and you lose, you then double up and bet \$10. A \$5 loss followed by a \$10 win means an overall profit of \$5.

What if you lose at \$10? Then the Martingale calls for you to double up again and bet \$20. Losses of \$5 and \$10 followed by a \$20 win leave an overall profit of, yes, \$5.

So it goes with every step in the Martingale. In Daryn's eight-step progression, in a losing streak he'd bet \$5, \$10, \$20, \$40, \$80, \$160, \$320 and \$640. A win on any one of those bets would give him a \$5 profit, then he'd go back to \$5 on his next bet to start a new progression.

If he loses all eight bets, losses total \$1,275. I don't know about your bankroll, but mine can't stand many \$1,275 losses in pursuit of a series of \$5 profits.

"That's all well and good, but those losses are rare," Daryn said. "You showed me yourself, it's happens SIX-TENTHS of a percent of the time."

It doesn't have to happen often, I told him, because when it does, it wipes out all wins and then some. With 169 small wins at \$5 each for a total of \$845, and one \$1,275 losses in the average 170 trials, Daryn's Martingale is a \$430 loser.

Given enough chances, anything that can happen eventually will, and you never know when the big loss is coming.

"So you say," Daryn said. "But it's been good for me so far. I reckon I'll stay with it a little longer."

In the end, every player's decision on systems is his or own, so all I could do was wish him luck as we parted. For those a little more wary of betting systems, though, I'd add one more caution that doubling your bets after losses can be hazardous to your bankroll.

LIMITED MARTINGALE: A couple of weeks before I met Daryn, I received an e-mail from a reader who asked, "Is the Martingale OK if I limit it to three steps, such as \$5, \$10 and \$20?"

That depends on your definition of "OK." It's not as dangerous as an eight-step Martingale, because the wagers don't get anywhere near as large. However, with average luck, a single loss still loses more money than all the wins combined.

In the end, the house will keep 5.26% of your wagers -- the house edge on roulette. Because you are sometimes betting \$10 and \$20 and have more money exposed to that 5.26% house edge, your total losses will be higher than someone betting table minimum on every spin.

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Best of John Grochowski
John Grochowski

John Grochowski is the best-selling author of The Craps Answer Book, The Slot Machine Answer Book and The Video Poker Answer Book. His weekly column is syndicated to newspapers and Web sites, and he contributes to many of the major magazines and newspapers in the gaming field, including Midwest Gaming and Travel, Slot Manager, Casino Journal, Strictly Slots and Casino Player.

Listen to John Grochowski's "Casino Answer Man" tips Tuesday through Friday at 5:18 p.m. on WLS-AM (890) in Chicago. Look for John Grochowski on Facebook and Twitter @GrochowskiJ.

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John Grochowski
John Grochowski is the best-selling author of The Craps Answer Book, The Slot Machine Answer Book and The Video Poker Answer Book. His weekly column is syndicated to newspapers and Web sites, and he contributes to many of the major magazines and newspapers in the gaming field, including Midwest Gaming and Travel, Slot Manager, Casino Journal, Strictly Slots and Casino Player.

Listen to John Grochowski's "Casino Answer Man" tips Tuesday through Friday at 5:18 p.m. on WLS-AM (890) in Chicago. Look for John Grochowski on Facebook and Twitter @GrochowskiJ.