Martingale (betting system explained)
The martingale doubles your bet after every loss. The worked numbers show why it cannot beat a 3 percent house edge and can end in one huge loss.
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The martingale is a betting system in which you double your stake after every loss and return to the starting stake after a win. The idea is that the first win recovers all earlier losses plus one starting bet. It cannot beat the house edge. It only trades many small wins for a small chance of a very large loss.
Worked example in Dice
Start at 10 coins on a 50 percent Dice bet, which pays 1.94x. Each loss doubles the next bet.
| Bet number | Stake | Total staked so far | Return if this bet wins | Net result if it wins |
|---|---|---|---|---|
| 1 | 10 | 10 | 19.4 | plus 9.4 |
| 2 | 20 | 30 | 38.8 | plus 8.8 |
| 3 | 40 | 70 | 77.6 | plus 7.6 |
| 4 | 80 | 150 | 155.2 | plus 5.2 |
| 5 | 160 | 310 | 310.4 | plus 0.4 |
| 6 | 320 | 630 | 620.8 | minus 9.2 |
Two things stand out. First, the net gain on a win shrinks every step, because the game pays 1.94x rather than the fair 2x. By the sixth bet a "winning" bet still loses coins overall. Second, the stakes grow fast. With a 1,000-coin bankroll you can place only the first six bets (630 coins in total); the seventh would need 640 coins and you have 370 left.
How likely is the bad run?
Losing six 50 percent bets in a row has a probability of 1 in 64, about 1.56 percent. That sounds rare, but the system is played many times. Over 100 starting cycles it is more likely than not that at least one such run occurs: 1 minus (63/64) to the 100th power is about 79 percent.
Why it cannot work
Every bet in the sequence has the same expected loss of 3 percent of its stake. The martingale changes how much is staked, not the percentage kept, so the expected loss is always 3 percent of everything you wager, and doubling makes the wagered total very large. Many small wins of about 9 coins are paid for by rare losses of hundreds of coins.
Real tables also set maximum bets, which stops the doubling sooner. Whatever the table rules, the practical limit is the bankroll, as the example shows.
Common misconceptions
- "A win is due, so doubling is safe." That is the Gambler's fallacy (definition and example). Every bet has the same chance.
- "I only need one win." True, but the cost of the run before it grows faster than the prize.
- "A higher win chance fixes it." At a 90 percent chance Dice pays 1.0777x, so one win on a 10-coin bet nets less than 1 coin while a loss costs the whole stake and doubling.
See Martingale and Betting Systems: Why They Fail for simulations and other systems, and Bankroll (definition and limits) for budgeting. Coins have no cash value.