Martingale calculator

How the Martingale strategy works

Start with a base bet on a roughly 50/50 outcome paying 2×. After a loss, double the bet. After a win, go back to the base bet. Every completed sequence ends with a profit of one base bet, because the winning bet of base × 2^k returns more than the sum of the k losing bets before it (base × (2^k − 1)).

The catch is the size of the bets. With a $1 base, ten losses in a row means the eleventh bet is $1,024 and you have already lost $1,023. Your bankroll sets a hard limit on the streak you can absorb.

Losses survivable and bust probability

If you can afford A bets in a row, the chance a single sequence busts is q^A, where q is the loss probability. A $1,000 bankroll at $1 base covers 1 + 2 + 4 + … + 256 = $511, but not the next $512 bet, so it survives 8 losses and busts on 9. At 49.5% win chance, q = 0.505 and q^9 ≈ 0.21% per sequence.

That looks small, but sequences are short and you play many of them. The calculator computes the chance of busting within N bets with a Markov model that tracks both your current losing streak and your growing balance, since every completed sequence adds a base bet and can extend the streak you can afford by one step. For 1,000 bets at these settings it is a little over 40%, and the 1,000-session simulation lands in the same place.

Why Martingale cannot beat the house edge

Each bet still has the same expected value: −1% of the stake at a 1% edge. Martingale only changes the shape of the outcome distribution. Most sessions end slightly up, and a few end with a large loss that wipes out many sessions of gains. The average across all sessions equals total amount wagered × edge, and because Martingale wagers much more per session than flat betting, the expected loss is usually larger, not smaller.

The histogram shows this. Green bars cluster just above zero; red bars sit far to the left. The observed RTP stays close to the game's theoretical 99%.

• Raising the payout (for example 3× with a 1.5× bet increase) lowers bet growth but also the win chance per bet.
• A table or max-bet limit caps the sequence the same way a smaller bankroll does.
• Reverse Martingale (doubling after wins) has the same expected value with the opposite shape.