The martingale is the most famous betting system and the easiest to disprove. Double after each loss and the first win returns your entire outlay plus one unit, which sounds like a guarantee.
Two things break it. Each spin is independent, so no bet in the sequence has better odds than the first; you are simply making a series of negative-expectation wagers, and the sum of negative-expectation bets is negative regardless of their order or size.
And the doubling is brutal. Starting at $10, eight consecutive losses require a $2,560 bet to continue, having already staked $2,550. Eight losses in a row on an even-money roulette bet happen roughly once in 150 sequences, which arrives far sooner than most players expect. Table maximums exist to make sure the sequence cannot be completed.
What the martingale actually does is trade many small wins for rare enormous losses, leaving expectation exactly where it was. Every progression system does a version of the same thing.
Where the numbers come from
Related terms in odds & money
- House edge — The average share of each bet the casino expects to keep over the long run.
- RTP — Return to player: the mirror of house edge, quoted as what comes back rather than what is kept.
- Expected value — The average result of a bet if it could be repeated indefinitely.
- Variance — How widely results scatter around their expected value.
- Standard deviation — A measure of how far results typically stray from the average.
- Bankroll — The money set aside for gambling, kept separate from money needed for anything else.
Where an entry quotes a number, that figure comes from the computed sections of this site rather than from another glossary, so the definition and the derivation cannot drift apart. Each entry links to the page where the number is worked out.