Does the Martingale work in roulette? Why doubling feels like it works
No: doubling after each loss does not beat the house edge, it only delays the loss. In 10,000 simulated sessions of Martingale on red from $5,000, the typical session stayed ahead until spin 290 and then fell; after 500 spins the average result was -$898.23, the typical session -$5,000, and 51.2% of sessions had gone broke.
Doubling after each loss keeps the typical session ahead for a few hundred spins, until one long losing streak empties the ladder and the typical session falls to a loss.
Chapter 2 of the spinner roulette research (chapters 0 to 9): Why doubling feels like it works.
Martingale on red starts at $25 and doubles after each loss, up to $3,200: eight bets. Every win ends a cycle $25 up, and the ladder is lost only when red misses eight times running, about once in 207 cycles. So most sessions climb: the typical session is up $2,100 at spin 220.
Every session keeps facing that streak, though. Once more than half have hit it, the typical session drops: +$475 at spin 290, −$2,400 at spin 300, −$5,000 at spin 500, with 51.2 % of sessions bust. Fibonacci grows more slowly and is still ahead at spin 500 (+$1,675), yet its average is worse than flat betting (−$783.73) because it bets $30,397 a session.
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The numbers
| Strategy | Typical session ahead until | Typical session peak | Typical at the end | Average | Ended broke | Wagered per session |
|---|---|---|---|---|---|---|
| Flat $25 on red | never ahead | $0.00 at spin 0 | -$350 | -$338.21 | 0.0% | $12,500 |
| Martingale | spin 290 | +$2,100 at spin 220 | -$5,000 | -$898.23 | 51.2% | $35,056.28 |
| Fibonacci | still ahead at spin 500 | +$1,675 at spin 500 | +$1,675 | -$783.73 | 39.1% | $30,397.41 |
| Spin | Flat typical | Martingale typical | Martingale 10th pct | Martingale 90th pct | Fibonacci typical |
|---|---|---|---|---|---|
| spin 0 | $0.00 | $0.00 | $0.00 | $0.00 | $0.00 |
| spin 8 | $0.00 | +$75 | -$100 | +$150 | +$25 |
| spin 17 | -$25 | +$175 | -$175 | +$275 | +$50 |
| spin 25 | -$25 | +$275 | -$602.50 | +$375 | +$75 |
| spin 33 | -$25 | +$375 | -$925 | +$475 | +$125 |
| spin 42 | -$50 | +$475 | -$1,000 | +$600 | +$150 |
| spin 50 | -$50 | +$550 | -$2,930 | +$700 | +$175 |
| spin 60 | -$50 | +$675 | -$5,000 | +$825 | +$225 |
| spin 80 | -$50 | +$900 | -$5,000 | +$1,100 | +$300 |
| spin 100 | -$50 | +$1,100 | -$5,000 | +$1,350 | +$375 |
| spin 120 | -$100 | +$1,325 | -$5,000 | +$1,600 | +$450 |
| spin 140 | -$100 | +$1,525 | -$5,000 | +$1,850 | +$525 |
| spin 160 | -$100 | +$1,725 | -$5,000 | +$2,100 | +$600 |
| spin 180 | -$150 | +$1,900 | -$5,000 | +$2,350 | +$675 |
| spin 200 | -$150 | +$2,000 | -$5,000 | +$2,600 | +$750 |
| spin 220 | -$150 | +$2,100 | -$5,000 | +$2,850 | +$825 |
| spin 240 | -$150 | +$2,025 | -$5,000 | +$3,100 | +$900 |
| spin 260 | -$200 | +$2,000 | -$5,000 | +$3,350 | +$975 |
| spin 280 | -$200 | +$1,775 | -$5,000 | +$3,575 | +$1,050 |
| spin 300 | -$200 | -$2,400 | -$5,000 | +$3,825 | +$1,100 |
| spin 320 | -$200 | -$2,400 | -$5,000 | +$4,075 | +$1,175 |
| spin 340 | -$250 | -$2,275 | -$5,000 | +$4,325 | +$1,250 |
| spin 360 | -$250 | -$2,175 | -$5,000 | +$4,550 | +$1,300 |
| spin 380 | -$250 | -$2,050 | -$5,000 | +$4,800 | +$1,375 |
| spin 400 | -$250 | -$2,025 | -$5,000 | +$5,025 | +$1,425 |
| spin 420 | -$300 | -$2,100 | -$5,000 | +$5,275 | +$1,500 |
| spin 440 | -$300 | -$2,537.50 | -$5,000 | +$5,500 | +$1,525 |
| spin 460 | -$300 | -$3,250 | -$5,000 | +$5,750 | +$1,575 |
| spin 480 | -$350 | -$5,000 | -$5,000 | +$5,975 | +$1,625 |
| spin 500 | -$350 | -$5,000 | -$5,000 | +$6,225 | +$1,675 |
Takeaways
- The rising typical session is real, and it has a deadline: about 290 spins for Martingale on red at $25.
- The fall is sudden because a losing session loses the whole ladder at once.
- A strategy that bets more loses more on average: Fibonacci bets 2.4 times what flat betting does.
The math
A recovery ladder plays in cycles. With a per-spin win probability p and L levels, a cycle caps with probability q = (1 − p)^L. Wins arrive at rate p per spin, so after n spins the chance of no cap is about e^(−q·p·n). The median path is above zero while that exceeds ½, which gives the median horizon n½ = ln 2 / (q·p).
Martingale on red: p = 18/37 = 0.486, L = 8, q = (19/37)^8 = 0.0048, n½ ≈ 295 spins. Measured: the median is above zero through spin 290 (the path is sampled every 10 spins) and peaks at $2,100 at spin 220. Mean −$898.24 against an EV of −0.027 × $35,056 = −$947 (realized edge −2.56 %); CVaR 5 % −$5,000. Fibonacci: median $1,675, mean −$783.73, bust 39.1 %. The skew is the trade: median and mean point in opposite directions.
q = (1 − p)^L = (19/37)^8 = 0.0048
P(no cap by spin n) ≈ e^(−q·p·n)
n½ = ln 2 / (q·p) = 0.693 / (0.0048 × 0.486) ≈ 295