D'Alembert and Fibonacci in crash games

Martingale’s problem is exponential growth. D’Alembert and Fibonacci are the two classic “gentler” progressions. They’re designed for even-money bets, so in crash games they’re usually used with a 2x auto-cashout. See where they sit among other systems in our crash game strategy pillar.

D’Alembert

• Start at 1 unit.
• After a loss, add 1 unit. After a win, subtract 1 unit (minimum 1).

The idea is that wins and losses roughly balance, and each win is worth one unit more than the loss before it. The catch is that at 2x you win slightly less than half the time, so the bet drifts upwards over long sessions.

Example ($10 units): L, L, W, L, W, W gives bets of 10, 20, 30, 20, 30, 20, which means −10, −20, +30, −20, +30, +20 = +$30. But a run of eight losses pushes the bet to $90 and leaves you $360 down.

Fibonacci

• Bet sizes follow 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 units.
• After a loss, move one step forward. After a win, move two steps back.

Losses in a row	Martingale bet	Fibonacci bet
5	32 units	8 units
8	256 units	34 units
10	1,024 units	89 units

Fibonacci escalates far more slowly, so busts are rarer. Recovery is also slower: one win doesn’t clear a losing run.

The bottom line

Neither system changes the average: every bet loses 3% of its stake at 97% RTP. Gentler progressions just move risk from “rare total loss” towards “long, slow grind”. If you want to see a progression’s behaviour, the closest model in our simulator is Martingale. Compare it with flat fixed auto-cashout betting.