The Gambling Strategy That’s Guaranteed to Make Money

The martingale betting strategy sabotaged a lot of gamblers and lessened the extraordinary levels of wealth reached by the Kelly criterion.

The House Always Wins

Beneath the varnish of flashing lights and open cocktails, casinos were set up on an absolute rock-solid foundation of economics, making them bleed money from their unwary patrons ever so slowly and unnoticeably. For years, mathematically inclined minds have found ways to defeat casinos by employing probability and game theory knowledge to find loopholes and disfavor weaknesses in a rigged system.

An amusing example was when the American Physical Society held its conference in Las Vegas; a local newspaper supposedly ran the headline, "Physicists in Town, Lowest Casino Take Ever." Word gets around that the physicists knew the perfect strategy to trounce any casino game: not to play.

A Betting System Based on Probability

There may be vagueness behind the clear evil of beating a casino at its games, but probabilities are archived in betting, theoretically allowing the better to earn money in the long run-an enormous qualification.

Imagine you bet color at a roulette table: Red or Black. Yes, the payout is even. (That means while you would've won $1 if you had bet $1 and called the right color, you would end up losing $1 if you called the wrong color.) And just to make the game easier, let's assume for simplicity that you have really a 50-50 chance of calling the correct color. Actually, in real roulette tables, there are some additional green pockets on which you lose, which gives the gambling house a slight edge. Also, assume that there is no limit on how much a player can bet on the Extra-betting.com at this particular table.

The Martingale Strategy Explained

You bet an amount of $1 on either color, and if you lose, double the amount to bet again. Keep doubling ($1, $2, $4, $8, $16, and so on) until you win. If you lose the first two bets of $1 and $2 but win your third at $4, you'll probably lose a total of $3 but recoup the loss with an additional $1 profit. If you win on the fourth bet, then you lose a total of $7 ($1 + $2 + $4), but with a win of $8, you make out with a $1 profit. If you win, this continues, and each time you win, you will always gain $1. If you feel that is too little, then you can increase the stakes by recursively doing the same or starting with a bigger bankroll altogether. Starting with $1,000 will double up to winning: $2,000, and sort of keep winning; finally, at $1,000.

The “Guaranteed” Profit Fallacy

Perhaps, it may be objected that, since this strategy works only when you eventually call the right color in roulette, the guaranteed profit I promised isn't realistic. The chance of your color hitting at some point in the long run, however, is, shall we say, 100 percent. In other words, the chance of losing every bet goes to zero as the number of rounds increases. The same holds true even in a more realistic context where the house retains a constant edge. So long as there's even a small chance of winning, there will eventually come a time when you do win, simply because the ball can't land in the wrong color-all the time.

The Problem With the Martingale System

So a road trip to Reno is definitely not on the cards for us. Unfortunately, no. The martingale betting system was very much in vogue in 18th-century Europe, its simplicity and promise of easy riches continuing to draw gamblers even today-but therein lies the flaw. Among many vices practiced by the infamous womanizer Jacques Casanova de Seingalt, he wrote in his memoirs: "I still worked on the martingale but without the least success, so much so that I soon had no more sequins."

The Fatal Flaw in the Strategy

Do you see a flaw in the previously described reasoning? At this rate, you start with $7 in your pocket and attempt to make $8. You are willing to lose a series of bets: first $1, then $2, then $4. The chance that you can lose three in a row is only one in eight, though; hence, the odds of losing $7 altogether are only one in eight, or 12.5 percent. The other 7 out of 8 times, you win $1. In fact, one eighth of the time you'll lose $7 and seven eighths of the time you'll win $1. The two courses cancel each other out: −1/8 × $7 + 7/8 × $1 = $0.

The same effect is multiplied by the same amount of available capital, and there is quite a high chance to gain a little and an itsy-bitsy chance to lose everything. Consequently, many gamblers will come out ahead with the martingale system, whereas only a rare gambler will find themselves completely wiped out. All these forces sum up so that in the long-term average, there will be many players adopting the strategy with many small gains and a few huge losses summing to a net effect of $0.

The “Guaranteed” Profit Depends on Unlimited Resources

But it's not really got anything to do with $7. Generally, you continue to bet as long as you're losing. After losing three in a row, you use the ATM to press $8 on a spin. From this, the truly guaranteed profit can be made only if you're willing to raise the bar—after all, win or lose, it will happen at some point during the round.

Here, you are limited in money. Betting amounts increase astronomically every round, and you know with your next bet you'll be putting everything on the line to recover whatever you had to stake building up to that point. Therefore, the risk-to-reward ratio is highly uneven; a small but real possibility of losing one's livelihood isn't a problem if, in the end, one can surely cash out a dollar. You will be wiped out permanently before your jackpot comes in.