D'Alembert and Fibonacci in crash games

Want progression without the steep climb of Martingale? D’Alembert adds one unit after a loss, and the Fibonacci strategy in a crash game follows 1, 1, 2, 3, 5: both recover losses at a gentler pace. They’re built for even-money bets, so in crash games you pair them with a 2x auto cash out. See where they sit among the other strategies in our crash game strategy pillar.

Every worked example on this page is in Kenyan shillings. The standard setup is a KSh 5,000 session bankroll and KSh 100 base bets (2%), the same ratios as our simulations. Topping up? M-Pesa is the quickest way in for most players in Kenya.

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. At 2x you win just under half the time, so over long sessions the bet tends to drift up a little: set a cap on the unit count and you’re set.

Example (KSh 100 units): L, L, W, L, W, W gives bets of 100, 200, 300, 200, 300, 200, which means −100, −200, +300, −200, +300, +200 = +KSh 300. A run of eight losses pushes the bet to KSh 900 and KSh 3,600 down, which is why a stop loss belongs in every progression plan.

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

Both run at the game’s 97% RTP, like every strategy. What they change is the ride: instead of Martingale’s rare big drop, you get a smoother, steadier climb back after a losing run. If you want to see a progression’s behaviour, the closest model in our simulator is Martingale. Compare it with flat fixed auto cash out betting.