The martingale: why doubling your bet after a loss cannot beat the casino

Miva comes back to Rono's table on Sunday night, with her system. She bets $10 on red. If she loses, she doubles the bet: $20, then $40, then $80. The first time red comes up, she wins back every loss plus $10. Then she starts again at $10.

And it works. Win. Win. Lose, lose, win. Each round ends $10 up. After an hour, Miva is $150 up, and sure she has found the trick.

Then the ball misses red seven times in a row: black, black, black, black, the zero, black, black. Miva has bet $10, $20, $40, $80, $160, $320 and $640: $1,270 gone. Her next bet should be $1,280, but this table takes no bet over $1,000. That is the table limit.

Seven misses in a row are rare: about once in 106 rounds. But Miva plays round after round, and in 100 rounds, the chance that she meets such a run is about 6 in 10. One big loss eats more than a hundred small wins.

Rono explains. A system changes the size of each bet, never its odds. Each bet still loses 2.7 cents per dollar on average, so the whole system does too. Doubling after each loss has a name, the martingale. It wins small and often, and loses big and rarely.

Miva stops for the night, $1,270 down. Then she turns the idea around: what if you lost small and often, and won big and rarely? Rono laughs. A bet on one number does just that, and it still loses 2.7 cents per dollar. At a casino table, every way of betting ends the same way.

Outside the casino, some investors use that shape on purpose. Many of the young companies they fund fail. A few giant wins, sometimes just one, pay for all the rest. Why does it work for them, and never at the roulette table? That story is here: "How venture capital funds make money".