The Martingale does not work: doubling your bet after every loss never removes the house edge, it only packs your losses into rare, large hits. At a $5 to $500 single-zero roulette table, a Martingale series wins $5 in 99.06% of cases and loses $635 in the other 0.94%, and those two outcomes average out to a loss of $1.03 per series.
The figures on this page are exact calculations, not estimates, checked against two million simulated series. They show the ladder of bets, how often it breaks for every bankroll and table limit, how long a player typically lasts, and what changes in baccarat and blackjack.
- Series that hit the $500 table limit on a single-zero wheel ($5 base bet)
- 1 in 106
- Lost in that series, against +$5 for every other series
- −$635
- Chance of getting through 100 series without hitting the limit
- 38.8%
- Expected longest losing run in 1,000 even-money spins
- 9.65
Source: Our study S3, exact formulas, src/data/studies/s3-martingale.json
How the system works
The rules fit in one sentence. Bet one unit on an even-money bet such as red, double the stake after every loss, and go back to one unit after a win. A run of bets from one unit to the next win is a series.
The appeal is simple arithmetic. Lose $5, $10 and $20, then win $40, and you are $5 up: the winning bet covers all the earlier losses plus one base bet. Whatever the length of the losing run, the first win always finishes the series $5 ahead.
That only holds while you can keep doubling. Two things stop you: the money you have, and the largest bet the table accepts. When the next doubled bet is not allowed, the series is over and every bet in it is lost.
The ladder: what each loss costs
The table below shows the stake after each number of losses, what you have already lost, and how likely it is that a series gets that far. Each row is exact for a single-zero wheel, where red wins 18 of 37 spins and loses 19.
| Losses in a row | Next bet | Already lost | Chance a series gets here | About 1 series in |
|---|---|---|---|---|
| 0 | $5 | $0 | 100% | - |
| 1 | $10 | $5 | 51.4% | 2 |
| 2 | $20 | $15 | 26.4% | 4 |
| 3 | $40 | $35 | 13.5% | 7 |
| 4 | $80 | $75 | 6.95% | 14 |
| 5 | $160 | $155 | 3.57% | 28 |
| 6 | $320 | $315 | 1.83% | 55 |
| 7 | $640 | $635 | 0.94% | 106 |
| 8 | $1,280 | $1,275 | 0.48% | 207 |
| 9 | $2,560 | $2,555 | 0.25% | 403 |
| 10 | $5,120 | $5,115 | 0.13% | 784 |
| 11 | $10,240 | $10,235 | 0.07% | 1,527 |
Row 7 is where a $5 to $500 table ends the ladder: the next bet, $640, is above the maximum. A win at any earlier row nets +$5.
Source: Our study S3 (games.european-even.ladder)
The money at risk doubles with every row, while the chance of reaching that row roughly halves. That is why the two sides cancel so exactly. Each extra rung you can afford makes the failure about half as likely and twice as expensive.
Source: Our study S3 (games.european-even.ladder)
See the numbers as a table
| Lost so far | |
|---|---|
| After 1 loss | $5 |
| After 2 losses | $15 |
| After 3 losses | $35 |
| After 4 losses | $75 |
| After 5 losses | $155 |
| After 6 losses | $315 |
| After 7 losses | $635 |
| After 8 losses | $1,275 |
| After 9 losses | $2,555 |
| After 10 losses | $5,115 |
How often the ladder breaks
How far you can climb depends on two numbers: your bankroll and the table maximum. Whichever runs out first sets the number of losses you can absorb. The heatmap gives the chance that a single series fails, for every pair. Read across a row to see that raising the limit stops helping once the bankroll is the binding constraint. Read down a column to see that adding money stops helping once the limit binds.
Source: Our study S3 (games.european-even.grid)
See the numbers as a table
| Bankroll ($5 base bet) | Max $80 | Max $160 | Max $320 | Max $640 | Max $1,280 | Max $2,560 | No limit |
|---|---|---|---|---|---|---|---|
| $50 bankroll | 13.54% | 13.54% | 13.54% | 13.54% | 13.54% | 13.54% | 13.54% |
| $125 bankroll | 6.95% | 6.95% | 6.95% | 6.95% | 6.95% | 6.95% | 6.95% |
| $250 bankroll | 3.57% | 3.57% | 3.57% | 3.57% | 3.57% | 3.57% | 3.57% |
| $500 bankroll | 3.57% | 1.83% | 1.83% | 1.83% | 1.83% | 1.83% | 1.83% |
| $1,000 bankroll | 3.57% | 1.83% | 0.94% | 0.94% | 0.94% | 0.94% | 0.94% |
| $2,500 bankroll | 3.57% | 1.83% | 0.94% | 0.48% | 0.48% | 0.48% | 0.48% |
| $5,000 bankroll | 3.57% | 1.83% | 0.94% | 0.48% | 0.25% | 0.25% | 0.25% |
| $10,000 bankroll | 3.57% | 1.83% | 0.94% | 0.48% | 0.25% | 0.13% | 0.13% |
At the common $5 to $500 table, the ceiling is seven losses. A $1,000 bankroll reaches it, and so does $5,000. The extra $4,000 changes nothing: the table refuses the eighth bet either way, so the failure rate stays at 0.94% per series, about 1 in 106.
The table limit, not the bankroll, is the real wall
With a $5 base bet and a $500 maximum, the ladder has seven rungs whatever you bring. A bankroll above $635 buys nothing more. To absorb one extra loss you would need both twice the bankroll and a table that accepts a $640 bet.
One small win, one rare large loss
Here is the full trade at the $5 to $500 table with $1,000. A series ends +$5 with probability 99.06% and −$635 with probability 0.94%. On average a player wins about 105 series, collecting roughly $526, before the one that costs $635. The expected value of one series is −$1.03.
That −$1.03 is no accident. An average series puts $37.97 through the wheel (7.59 base bets), and 2.70% of that is $1.03. The Martingale moves the edge around between small wins and a big loss. It never shrinks it.
| Setup | Losses absorbed | Series wins $5 | Loss when it fails | Fails 1 series in | Average per series | No failure in 100 series |
|---|---|---|---|---|---|---|
| $200 bankroll, $5-$500 table | 5 | 96.43% | 28.0 | −$0.71 | 2.6% | |
| $1,000 bankroll, $5-$500 table | 7 | 99.06% | 106.2 | −$1.03 | 38.8% | |
| $5,000 bankroll, $5-$500 table | 7 | 99.06% | 106.2 | −$1.03 | 38.8% | |
| $5,000 bankroll, $5-$5,000 table | 9 | 99.75% | 402.7 | −$1.36 | 78.0% | |
| $20,000 bankroll, $5-$10,000 table | 11 | 99.93% | 1,527.0 | −$1.70 | 93.7% |
A bigger bankroll at a higher-limit table makes failure rarer but costlier, and the average loss per series grows because more money is wagered.
Source: Our study S3 (games.european-even.profitVsRisk)
A smaller bankroll: $200
With $200 and a $5 base bet, the bankroll is the binding limit, not the table: $5 + $10 + $20 + $40 + $80 = $155 is the most you can lose in one ladder, so the sixth bet of $160 is out of reach. That ladder has five rungs. It fails once in 28.01 series on average and loses $155 when it does. The chance of getting through 100 series without a failure falls to 2.6%. Because a series lasts about two spins, 100 series is roughly 200 spins: one ordinary session.
The average cost per series is smaller, −$0.71, only because less money is at risk in each ladder. It is still exactly 2.70% of the amount wagered.
The last two rows matter. With $5,000 at a table that accepts $5,000 bets, failure drops to 1 series in 402.7, but it costs $2,555, and the average per series gets worse, −$1.36, because more money goes through the wheel. With $20,000 and a $10,000 limit, failure is 1 in 1,527, the loss is $10,235, and the average is −$1.70 per series.
Survival over many series
A 1 in 106 chance per series sounds remote, but series are short: about two spins each on average. The survival curve shows the chance of not yet having hit a failed series after a given number of series. At the $5 to $500 table with $1,000, it is 38.8% after 100 series and 0.0078% after 1,000.
Source: Our study S3 (games.european-even.profitVsRisk); points at 100 and 1,000 series match grid[].probabilitySurvive
See the numbers as a table
| Series played | $200, $5-$500 | $1,000, $5-$500 | $5,000, $5-$5,000 | $20,000, $5-$10,000 |
|---|---|---|---|---|
| 0 | 100% | 100% | 100% | 100% |
| 20 | 48.3% | 82.8% | 95.2% | 98.7% |
| 40 | 23.4% | 68.5% | 90.5% | 97.4% |
| 60 | 11.3% | 56.7% | 86.1% | 96.2% |
| 80 | 5.45% | 46.9% | 82.0% | 94.9% |
| 100 | 2.64% | 38.8% | 78.0% | 93.7% |
| 120 | 1.27% | 32.1% | 74.2% | 92.4% |
| 140 | 0.62% | 26.6% | 70.6% | 91.2% |
| 160 | 0.30% | 22.0% | 67.2% | 90.1% |
| 180 | 0.14% | 18.2% | 63.9% | 88.9% |
| 200 | 0.07% | 15.1% | 60.8% | 87.7% |
| 220 | 0.03% | 12.5% | 57.9% | 86.6% |
| 240 | 0.02% | 10.3% | 55.1% | 85.5% |
| 260 | 0.01% | 8.55% | 52.4% | 84.3% |
| 280 | 0% | 7.07% | 49.9% | 83.2% |
| 300 | 0% | 5.85% | 47.4% | 82.2% |
| 320 | 0% | 4.84% | 45.1% | 81.1% |
| 340 | 0% | 4.01% | 43.0% | 80.0% |
| 360 | 0% | 3.32% | 40.9% | 79% |
| 380 | 0% | 2.75% | 38.9% | 78.0% |
| 400 | 0% | 2.27% | 37.0% | 77.0% |
| 420 | 0% | 1.88% | 35.2% | 76.0% |
| 440 | 0% | 1.56% | 33.5% | 75.0% |
| 460 | 0% | 1.29% | 31.9% | 74.0% |
| 480 | 0% | 1.07% | 30.3% | 73.0% |
| 500 | 0% | 0.88% | 28.9% | 72.1% |
| 520 | 0% | 0.73% | 27.5% | 71.1% |
| 540 | 0% | 0.60% | 26.1% | 70.2% |
| 560 | 0% | 0.50% | 24.9% | 69.3% |
| 580 | 0% | 0.41% | 23.7% | 68.4% |
| 600 | 0% | 0.34% | 22.5% | 67.5% |
| 620 | 0% | 0.28% | 21.4% | 66.6% |
| 640 | 0% | 0.23% | 20.4% | 65.8% |
| 660 | 0% | 0.19% | 19.4% | 64.9% |
| 680 | 0% | 0.16% | 18.4% | 64.1% |
| 700 | 0% | 0.13% | 17.6% | 63.2% |
| 720 | 0% | 0.11% | 16.7% | 62.4% |
| 740 | 0% | 0.09% | 15.9% | 61.6% |
| 760 | 0% | 0.08% | 15.1% | 60.8% |
| 780 | 0% | 0.06% | 14.4% | 60% |
| 800 | 0% | 0.05% | 13.7% | 59.2% |
| 820 | 0% | 0.04% | 13.0% | 58.5% |
| 840 | 0% | 0.04% | 12.4% | 57.7% |
| 860 | 0% | 0.03% | 11.8% | 56.9% |
| 880 | 0% | 0.02% | 11.2% | 56.2% |
| 900 | 0% | 0.02% | 10.7% | 55.5% |
| 920 | 0% | 0.02% | 10.2% | 54.7% |
| 940 | 0% | 0.01% | 9.66% | 54.0% |
| 960 | 0% | 0.01% | 9.19% | 53.3% |
| 980 | 0% | 0.01% | 8.75% | 52.6% |
| 1,000 | 0% | 0.01% | 8.32% | 52.0% |
These curves assume you keep the same bankroll and limit from series to series. A failed series does not always mean you are broke: with $1,000, a $635 loss leaves $365, which covers six rungs of a new ladder but not seven.
How many losses in a row should you expect?
Seven losses in a row can feel like a once-in-a-lifetime event. It is not. In 1,000 even-money spins on a single-zero wheel, the expected longest losing run is 9.65 spins. A run of at least 8 shows up in 90.8% of such stretches, and at least 12 in 15.0%. On average, the first run of 7 straight losses arrives after about 216 spins.
Source: Our study S3 (games.european-even.longestLosingStreakIn1000Bets)
See the numbers as a table
| Chance in 1,000 spins | |
|---|---|
| 6+ in a row | 100.0% |
| 7+ in a row | 99.1% |
| 8+ in a row | 90.8% |
| 9+ in a row | 70.3% |
| 10+ in a row | 46.2% |
| 11+ in a row | 27.2% |
| 12+ in a row | 15.0% |
| 13+ in a row | 8.0% |
| 14+ in a row | 4.2% |
| 15+ in a row | 2.2% |
| 16+ in a row | 1.1% |
The other games are no kinder. Measured in decided bets, the expected longest losing run in 1,000 is 10.0 on a double-zero wheel, 9.13 on Banker and 10.28 in our blackjack approximation. A seven-loss run arrives first, on average, after 186.6 double-zero spins, 276.08 decided Banker hands or 166.78 decided blackjack hands.
At roughly two spins per series, 1,000 spins is about 500 series. That is a few evenings at a busy table, not a lifetime. The question is never whether the long run comes, only when.
After six losses, a win is due
Each spin is independent. After six reds, black still wins only 18 of 37 times, 48.65%. The ladder does not make the next win more likely. It only makes the next bet bigger.
Roulette, baccarat and blackjack compared
The same ladder behaves differently in each game, because the chance of losing a decided bet, the payout and the edge differ. The table compares one $1,000 bankroll at a $5 to $500 table in each.
| Game | Wins a decided bet | Edge per decided bet | Series fails 1 in | Average per series | No failure in 100 series | Expected longest losing run in 1,000 decided bets |
|---|---|---|---|---|---|---|
| Roulette, single zero | 48.65% | 2.70% | −$1.03 | 38.8% | 9.65 | |
| Roulette, double zero | 47.37% | 5.26% | −$2.16 | 32.5% | 10.00 | |
| Baccarat, Banker | 50.68% | 1.17% | −$0.39 | 49.1% | 9.13 | |
| Blackjack (approx.) | 46.37% | 0.36% | −$0.16 | 27.7% | 10.28 |
Pushes (baccarat ties, blackjack pushes) are skipped: the Martingale simply re-bets. Blackjack is an approximation; see below.
Source: Our study S3 (games[].profitVsRisk[1], games[].longestLosingStreakIn1000Bets)
Double-zero roulette
The second zero raises the chance of losing an even-money bet from 51.35% to 52.63%. That shortens the time to failure from 1 in 106.2 series to 1 in 89.4 and doubles the average cost per series, from −$1.03 to −$2.16, because the edge per bet is 5.26% instead of 2.70%.
Baccarat Banker: the commission breaks the recovery
Banker wins about 50.7% of decided hands, so losing runs are a little shorter than at roulette, and the series fails only 1 in 140.9 times at this table. But a winning Banker bet pays 0.95 to 1 after the 5% commission. The ladder therefore recovers a little less each time it doubles. After five or more losses, the finally winning bet no longer even covers the earlier losses.
Source: Our study S3 (games.baccarat-banker.ladder[].netIfNextBetWinsUnits)
See the numbers as a table
| Series result | |
|---|---|
| Win after 0 losses | $4.75 |
| Win after 1 loss | $4.50 |
| Win after 2 losses | $4.00 |
| Win after 3 losses | $3.00 |
| Win after 4 losses | $1.00 |
| Win after 5 losses | −$3.00 |
| Win after 6 losses | −$11.00 |
| Win after 7 losses | −$27.00 |
A series that wins after 5 losses ends −$3. After 6 losses it ends −$11, and after 7 it would end −$27 if the table allowed the bet. The edge per decided Banker bet is 1.17%, the same 1.06% per hand that Wizard of Odds lists once ties (9.5% of hands, which push) are counted. Our baccarat systems test covers the other progressions people use there.
Blackjack: a low edge, but longer losing runs
Blackjack is the odd one out. With good rules and basic strategy, the house edge is only about 0.33% per hand, yet about 53.6% of hands that are not pushes end as net losses. Doubles, splits and 3:2 blackjacks win more on the hands you do win. So losing runs are longer than at roulette, and the ladder breaks more often: 1 in 78.3 series at this table, though each series costs only $0.16 on average.
We treated each hand as one even-money decision for this. In real play, doubles and splits put extra money on the table in the middle of a ladder, which makes the progression harder to follow and the maximum easier to hit. Basic strategy is still what keeps the edge that low; the full chart is here.
The mirror image: doubling after wins
The Paroli and the Reverse Martingale flip the ladder: double after a win, go back to one unit after a loss. Now most series lose one base bet, and a rare run of wins pays big. The distribution is the Martingale’s turned upside down, and the cost per dollar wagered is identical. In our simulation of nine systems on the same spins, the Martingale and the Reverse Martingale with $1,000 both lost the 2.70% edge on their turnover, within sampling error. The doubling-after-losses version simply hides its losses in a rarer, larger form.
A responsible takeaway
The Martingale is not a way to make money. It is a way to win small amounts most of the time while carrying a hidden, larger loss. If you use any progression for entertainment, these rules keep the cost in view:
- Count the ladder before you sit down. Keep doubling the base bet until the next step would pass the table maximum. At $5 to $500 that is seven bets ($5 up to $320), so seven losses end the ladder.
- Decide what a failed series costs before it happens. At $5 to $500 it is $635. If that is more than you would spend on an evening out, the base bet is too high.
- Judge the night by money wagered, not by series won. Expected loss is the edge times total wagered. Winning 100 series in a row does not change that.
- Prefer the lowest edge. A single-zero wheel costs about half what a double-zero wheel does. Our ranking of every casino bet by edge shows the cheaper options.
- Bonuses do not change the maths. If you are using bonus money, check what wagering requirements actually cost first. A progression only adds to the turnover the requirement demands.
What we could not verify, and our assumptions
- Independent series. Each series is treated as independent with a fixed bankroll and limit. Winnings are not used to extend the ladder. This is exact per series and only slightly overstates failure where accumulated winnings would let you afford one more doubling, which never applies when the table limit is the binding constraint.
- Survival curves. The curves assume the bankroll is not topped up or reduced between series. A failed series is counted as one of the series played.
- Blackjack is an approximation. We count a net-positive hand as a win, a net-negative hand (including surrender and lost doubles or splits) as a loss, and a net-zero hand as a push. Doubles, splits and 3:2 blackjacks are ignored when sizing the ladder. The average per series uses the engine’s house edge on the money wagered, and hands are treated as independent, with no effect from cards already dealt.
- Real table limits vary. We used $5 to $500 as the main example and show other limits in the heatmap. Check the limits posted at your table.
- Wizard of Odds figures for the house edge of each game were fetched on 9 October 2026. Our engine’s edges agree with them at the precision shown.
- Fair games only. Everything here assumes a fair wheel, shoe or random number generator.
Rerun it yourself
Run node research/studies/s3-martingale/run.mjs with plain Node 22. It rewrites the JSON file behind every chart and table on this page in about five seconds and fails loudly if any of the 511 checks does not pass.
For small-stakes roulette specifically, our survival analysis of how long $20 to $100 lasts at different bet sizes uses the same exact methods with flat bets.