Does doubling your bet after every loss beat the house?
The martingale system has been tempting gamblers since 18th-century France, and the sums show why it fails.
Guess first
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Which one is it?
No. Doubling your bet after every loss feels like a way to guarantee a win, but it only works if you have unlimited money and the casino accepts unlimited bets, and nobody has either.
The idea is old. A is a class of betting strategies that originated from and were popular in 18th-century France. The simplest version has the gambler double the bet after every loss, so that the first win recovers all previous losses plus a profit equal to the original stake. Bet 1 and lose, bet 2 and lose, bet 4 and win: you have lost 3 and won 4, so you are 1 ahead. After n losses in a row, the next bet is 2 to the power n times the first. On a game close to a coin flip, such as red or black at roulette, it looks like a machine for winning one unit at a time.
The flaw is in the maths. All -type systems fail because no amount of information about past bets can be used to predict a future bet with accuracy better than chance. In most casino games, the of any individual bet is negative, so the sum of many negative numbers is negative too, however you size the bets. The system also hides a danger: the strategy fails as long as there is a limit on earnings or on the bets, which is also true in practice. A losing run makes the bets grow very fast. Ten consecutive losses mean a loss of 1,023 times the original bet.
Try it
How fast the martingale bet grows
y = 1 · 2ˣ
Challenge · Suppose the table caps any single bet at 512 units. With a first bet of 1 unit, after how many losses in a row does the next bet reach the cap?
And long losing runs are not rare. Losing 6 times in a row is unlikely in 6 plays, 1.8% on a single-zero wheel, but over a string of 200 plays a streak of 6 losses somewhere is about 84% likely. People assume the short odds apply to the long run, which is a mistake.
Quiz me
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Recap
No betting system can turn a negative expected value into a positive one, because past results do not predict the next bet.
💡 A trick to remember it · Doubling down is a staircase that gets steeper with every step, while your legs only get shorter.
Surprising fact · A streak of 6 losses somewhere in 200 roulette plays is about 84% likely, even though 6 in a row in 6 plays is about 1.8%.
Sources (2)
No source, no claim. Every fact in this lesson (14 claims) cites at least one of these.