The short answer is no: no roulette betting system changes how much of your money the wheel keeps. We ran nine popular systems through 100,000 identical sessions each, and every one of them lost between 2.65% and 2.81% of the money it wagered on a single-zero wheel, which is the 2.70% house edge plus sampling noise.
What the systems do change is the shape of your results. Some make a small win more likely and a wipe-out more likely at the same time. Others do the reverse. This page shows the rules of each system, what happened to a $200 and a $1,000 bankroll, and why the system that bets the most money always loses the most money.
- Loss per dollar wagered on a single-zero wheel for every system (measured 2.65% to 2.81%)
- 2.70%
- The same on a double-zero wheel (measured 5.21% to 5.40%)
- 5.26%
- Labouchere sessions that went bust from $200 within 200 spins
- 92.1%
- System variants with a positive average result, in any setup
- 0 of 10
Source: Our simulation S1: 100,000 sessions per system, bankroll, stop rule and wheel
One bet on red, counted pocket by pocket
- Pockets that win
- 18 red
- Pockets that lose
- 18 black + the zero (brass)
- Chance of winning
- 18/37 = 48.65%
- Payout
- 1 to 1
- Average cost per $100 bet
- $2.70 (single zero), $5.26 with a second zero
The size or timing of the bet does not enter this sum. That is the whole reason no staking pattern changes it.
Why no staking pattern can beat the edge
Every bet on a single-zero wheel has an expected loss of 1/37 of the stake, or 2.70%. A bet on red wins on 18 of 37 pockets and pays even money. It loses on the other 18 colours and on the zero. A straight-up bet on one number wins once in 37 and pays 35 to 1. Both work out to the same 2.70% cost. On a double-zero wheel, the extra pocket raises that to 1/19, or 5.26%, for every bet except the five-number bet, which is worse at 7.89% (all three figures are on Wizard of Odds’ roulette basics page).
A betting system only decides how much to put on each spin. It cannot change what each spin is worth. So the expected loss of a whole session is simply:
expected loss = house edge × total amount wagered
That one line is the entire result of this study. A system that puts $3,000 through the wheel expects to lose about three times as much as one that puts through $1,000, no matter how cleverly the stakes go up and down. Wizard of Odds reached the same conclusion with its own simulations and puts it bluntly: betting systems “can’t even dent” the house edge.
Source: Our simulation S1, src/data/studies/s1-roulette-systems.json
See the numbers as a table
| Loss as % of total wagered | |
|---|---|
| Flat bet | 2.73% |
| Martingale | 2.79% |
| D'Alembert | 2.77% |
| Fibonacci | 2.70% |
| Labouchere | 2.81% |
| Oscar's Grind | 2.71% |
| Paroli | 2.72% |
| Reverse Martingale | 2.74% |
| James Bond ($30) | 2.66% |
| James Bond ($100, 14:5:1) | 2.74% |
| House edge (1/37) | 2.70% |
The percentages are the same, but the dollars are not. Here is the average result of one session per system with a $1,000 bankroll. Flat betting lost $27.27 on $1,000 wagered. D’Alembert lost $179.80, because it put $6,711.58 through the wheel. Labouchere lost $283.29 on $10,491.73. Same percentage, much bigger bill.
Source: Our simulation S1
See the numbers as a table
| Average net result per session | |
|---|---|
| Flat bet | −$27.27 |
| Martingale | −$94.93 |
| D'Alembert | −$179.80 |
| Fibonacci | −$70.12 |
| Labouchere | −$283.29 |
| Oscar's Grind | −$93.10 |
| Paroli | −$46.16 |
| Reverse Martingale | −$91.41 |
| James Bond ($30) | −$159.33 |
| James Bond ($100, 14:5:1) | −$400.06 |
A progression lets you recover your losses
Every progression that raises the stake after a loss does recover earlier losses when it works. The problem is that the bigger stake carries the same 2.70% cost as the small ones. Raising the stake raises the amount exposed to the edge, so it raises the expected loss.
How we tested the systems
Each system played on a simulated single-zero wheel and a double-zero wheel with a $5 base unit, a $5 minimum and a $500 maximum bet. Even-money systems bet on red. Results on black, odd, even, high or low would be identical. We started each session with either $200 or $1,000 and used two stop rules:
- Play 200 spins. The session ends early only if the bankroll can no longer cover the minimum bet.
- Stop at target or bust. The session ends as soon as the bankroll reaches +50% (+$100 on $200, +$500 on $1,000), on bust, or after 200 spins, whichever comes first.
The important design choice is that every system played the same 100,000 sequences of 200 spins on each wheel. So when one system does better than another, it is because of its staking rules, not because it got luckier spins.
When a progression called for a stake above the $500 table maximum, or above the money left, the progression was abandoned, the loss accepted, and the system restarted at its first stake. If even the first stake was more than the money left, the player bet everything left in $5 chips. “Bust” means the bankroll can no longer cover the minimum stake: below $5 for even-money systems, and below $30 or $100 for the two James Bond spreads.
The systems, rule by rule
Flat bet
$5 on red every spin. This is the control group. With $200 and 200 spins it went bust in 1.3% of sessions, finished ahead in 32.4% and lost $27.20 on average, against an exact theoretical $26.97 for the $997.93 it wagered.
Martingale
Start at $5, double after every loss and go back to $5 after a win. It is the best-known system and it gets its own full test with exact ladder odds. In this study it behaved like every other progression: with $200 and 200 spins it went bust in 62.5% of sessions, lost 2.79% of turnover, and hit the $500 table maximum in 1.5% of sessions before it could finish a recovery.
D’Alembert
Start at one unit ($5). Add one unit after a loss and take one away after a win, never going below one unit. The progression is gentler than doubling, but it climbs steadily through a losing patch. With $200 and 200 spins it went bust in 71.1% of sessions and wagered $2,450.07 on average, more than any other loss-chasing system except Labouchere.
Fibonacci
Stakes follow the sequence 1, 1, 2, 3, 5, 8, 13 and so on, in $5 units. Move one step forward after a loss and two steps back after a win. With $200 it went bust in 43.7% of sessions. With $1,000 it finished ahead 71.0% of the time, the highest of any system, and still lost $70.12 per session on average.
Labouchere (cancellation)
Write down 1-2-3-4-5-6 (in $5 units). Each stake is the first plus the last number on the list, so the first bet is 7 units, or $35. After a win, cross off both numbers. After a loss, add the amount lost to the end of the list. Clearing the list wins 21 units ($105), and then a new list starts. The list grows faster than it shrinks during a losing patch, so stakes run away quickly. Labouchere was the worst system on survival: from $200, 92.1% of sessions went bust within 200 spins.
Oscar’s Grind
Aim for one unit ($5) of profit per cycle. Start at one unit. After a loss, keep the same stake. After a win, raise the stake by one unit, but never stake more than needed to end the cycle at exactly +1 unit. Then start a new cycle. It finishes ahead often (69.9% of sessions with $1,000) but loses $93.10 on average at that bankroll.
Paroli
The mirror image of a loss-chasing system. Start at $5 and double after a win. After three wins in a row, bank the $35 profit and go back to $5. Any loss also returns you to $5. The stake never goes above $20, so Paroli never puts a large bet at risk. With $1,000 it wagered less than any system except flat betting and never went bust within 200 spins. From $200 it went bust in 22.2% of sessions.
Reverse Martingale
Start at $5, double after every win and go back to $5 after a loss. Unlike Paroli, our version has no fixed win cap: it banks the run only when the next doubled bet would pass the $500 maximum ($5, $10 and so on up to $320, then reset). So it is looking for seven wins in a row. That rarely happens, so the typical session bleeds $5 at a time: the median $1,000 session ended at $575, while the best 5% ended above $1,810.
James Bond
A fixed spread, not a progression. Our main version bets $30 every spin: $20 on high (19 to 36, pays 1 to 1), $5 on the 13 to 18 six-line (pays 5 to 1) and $5 straight up on zero (pays 35 to 1). High numbers net +$10, zero nets +$150, a 13 to 18 result returns exactly the $30 staked, and 1 to 12 loses $30. This is the common 4:1:1 version at a $5 minimum. It is not the 14:5:1 proportions of Ian Fleming’s original $200 spread ($140, $50, $10), so we also ran a $100 version with those exact proportions ($70, $25, $5). Both carry exactly the wheel’s edge, because every bet inside them does: the $30 spread lost 2.66% of turnover and the $100 spread 2.74%.
| System | Bust | Hit +$100 target | Mean final | Median final | 5th percentile | 95th percentile | Mean wagered | Largest bet seen |
|---|---|---|---|---|---|---|---|---|
| Flat bet | 8.7% | $173.71 | $170 | $60 | $300 | $967.06 | $5 | |
| Martingale | 58.9% | $180.22 | $300 | $0 | $300 | $742.92 | $80 | |
| D'Alembert | 57.9% | $176.21 | $300 | $0 | $310 | $871.77 | $65 | |
| Fibonacci | 51.4% | $172.91 | $300 | $0 | $300 | $996.52 | $105 | |
| Labouchere | 61.6% | $188.39 | $305 | $0 | $305 | $433.66 | $145 | |
| Oscar's Grind | 54.5% | $170.37 | $300 | $0 | $300 | $1,097.34 | $95 | |
| Paroli | 35.9% | $167.28 | $170 | $0 | $310 | $1,212.58 | $20 | |
| Reverse Martingale | 50.5% | $180.32 | $300 | $0 | $430 | $720.76 | $160 | |
| James Bond ($30) | 50.6% | $178.29 | $300 | $0 | $390 | $820.09 | $30 | |
| James Bond ($100, 14:5:1) | 51.8% | $188.55 | $300 | $0 | $330 | $428.18 | $100 |
Target = stop as soon as the bankroll reaches $300, or on bust, or after 200 spins. Every system started with $200, so every mean final below $200 is an average loss. Final values can overshoot $300 when the winning bet is larger than the remaining gap.
Source: Our simulation S1 (100,000 sessions per row)
What the results look like
Four ways a session can end
The chart below splits the 200-spin sessions with $200 into four outcomes. Flat betting rarely goes bust but rarely wins either: most sessions end a little down. Every progression trades those small losses for a mix of more wins and many more busts.
Source: Our simulation S1
See the numbers as a table
| Bust | Down, not bust | Broke even | Finished ahead | Total | |
|---|---|---|---|---|---|
| Flat bet | 1.3% | 61.1% | 5.2% | 32.4% | 100.0% |
| Martingale | 62.5% | 9.3% | 0.3% | 27.9% | 100.0% |
| D'Alembert | 71.1% | 6.4% | 0.1% | 22.4% | 100.0% |
| Fibonacci | 43.7% | 18.5% | 0.4% | 37.4% | 100.0% |
| Labouchere | 92.1% | 0.5% | 0.0% | 7.4% | 100.0% |
| Oscar's Grind | 48.7% | 11.6% | 0.2% | 39.5% | 100.0% |
| Paroli | 22.2% | 41.0% | 1.3% | 35.5% | 100.0% |
| Reverse Martingale | 77.2% | 0.0% | 0.0% | 22.8% | 100.0% |
| James Bond ($30) | 76.9% | 3.3% | 0.2% | 19.6% | 100.0% |
| James Bond ($100, 14:5:1) | 94.0% | 0.1% | 0.0% | 5.9% | 100.0% |
The spread of final results
A histogram shows the full spread. Flat betting produces a bell shape centred a little below the starting $200: the median session ended at $170, the 5th percentile at $60 and the 95th at $290.
Source: Our simulation S1
See the numbers as a table
| Final bankroll | Share of sessions |
|---|---|
| $0 to $10 | 1.32% |
| $10 to $20 | 0.27% |
| $20 to $30 | 0.44% |
| $30 to $40 | 0.61% |
| $40 to $50 | 0.90% |
| $50 to $60 | 1.21% |
| $60 to $70 | 1.56% |
| $70 to $80 | 1.94% |
| $80 to $90 | 2.38% |
| $90 to $100 | 2.85% |
| $100 to $110 | 3.36% |
| $110 to $120 | 3.83% |
| $120 to $130 | 4.20% |
| $130 to $140 | 4.70% |
| $140 to $150 | 5.06% |
| $150 to $160 | 5.38% |
| $160 to $170 | 5.54% |
| $170 to $180 | 5.61% |
| $180 to $190 | 5.66% |
| $190 to $200 | 5.54% |
| $200 to $210 | 5.24% |
| $210 to $220 | 5.02% |
| $220 to $230 | 4.53% |
| $230 to $240 | 4.09% |
| $240 to $250 | 3.57% |
| $250 to $260 | 3.11% |
| $260 to $270 | 2.70% |
| $270 to $280 | 2.10% |
| $280 to $290 | 1.79% |
| $290 to $300 | 1.39% |
| $300 to $310 | 1.11% |
| $310 to $320 | 0.87% |
| $320 to $330 | 0.64% |
| $330 to $340 | 0.48% |
| $340 to $350 | 0.34% |
| $350 to $360 | 0.22% |
| $360 to $370 | 0.17% |
| $370 to $380 | 0.12% |
| $380 to $390 | 0.06% |
| $390 to $400 | 0.04% |
| $400 to $410 | 0.03% |
| $410 to $420 | 0.01% |
| $420 to $430 | 0.02% |
| $430 to $440 | 0.01% |
| $440 to $450 | 0.01% |
A progression with a target splits the same spins into two piles. Oscar’s Grind with $200 and a +$100 target reached the $300 target in 54.5% of sessions and at $0 in 40.1%, with almost nothing in between. The average of those two piles is $170.37, a loss of $29.63 per session.
Source: Our simulation S1
See the numbers as a table
| Final bankroll | Share of sessions |
|---|---|
| $0 to $10 | 40.1% |
| $10 to $20 | 0.18% |
| $20 to $30 | 0.20% |
| $30 to $40 | 0.20% |
| $40 to $50 | 0.19% |
| $50 to $60 | 0.19% |
| $60 to $70 | 0.24% |
| $70 to $80 | 0.19% |
| $80 to $90 | 0.24% |
| $90 to $100 | 0.24% |
| $100 to $110 | 0.26% |
| $110 to $120 | 0.27% |
| $120 to $130 | 0.28% |
| $130 to $140 | 0.29% |
| $140 to $150 | 0.27% |
| $150 to $160 | 0.28% |
| $160 to $170 | 0.26% |
| $170 to $180 | 0.25% |
| $180 to $190 | 0.25% |
| $190 to $200 | 0.20% |
| $200 to $210 | 0.18% |
| $210 to $220 | 0.17% |
| $220 to $230 | 0.14% |
| $230 to $240 | 0.09% |
| $240 to $250 | 0.09% |
| $250 to $260 | 0.05% |
| $260 to $270 | 0.05% |
| $270 to $280 | 0.06% |
| $280 to $290 | 0.06% |
| $290 to $300 | 0.03% |
| $300 to $310 | 54.5% |
Same 200 spins, different systems
Because every system saw the same spins, we can follow one sequence through all of them. We picked the first of the stored sessions in which the flat bettor finished close to the typical result (within $10 of the $170 median). This is session 4 of the 40 sample paths stored in the study file. The flat bettor ends at $160. On the identical spins, the loss-chasing systems all went bust, at different moments.
Source: Our simulation S1, samplePaths (session 4 of 40)
See the numbers as a table
| Spin | Flat bet | Martingale | D'Alembert | Fibonacci | Labouchere |
|---|---|---|---|---|---|
| 0 | $200 | $200 | $200 | $200 | $200 |
| 5 | $195 | $210 | $205 | $200 | $180 |
| 10 | $190 | $205 | $205 | $195 | $115 |
| 15 | $195 | $235 | $230 | $205 | $10 |
| 17 | $0 | ||||
| 20 | $200 | $250 | $250 | $210 | |
| 25 | $195 | $260 | $255 | $210 | |
| 30 | $170 | $105 | $155 | $150 | |
| 35 | $175 | $120 | $200 | $60 | |
| 40 | $170 | $125 | $180 | $55 | |
| 45 | $165 | $135 | $155 | $55 | |
| 50 | $160 | $115 | $125 | $45 | |
| 55 | $165 | $150 | $180 | $60 | |
| 60 | $180 | $180 | $290 | $80 | |
| 65 | $165 | $35 | $205 | $30 | |
| 70 | $150 | $25 | $75 | $20 | |
| 75 | $145 | $35 | $30 | $20 | |
| 80 | $140 | $20 | $35 | $10 | |
| 84 | $0 | ||||
| 85 | $135 | $20 | $20 | ||
| 90 | $160 | $45 | $45 | ||
| 95 | $185 | $70 | $70 | ||
| 100 | $170 | $35 | $45 | ||
| 105 | $175 | $50 | $75 | ||
| 110 | $170 | $30 | $70 | ||
| 115 | $165 | $25 | $60 | ||
| 120 | $180 | $60 | $125 | ||
| 125 | $175 | $70 | $125 | ||
| 130 | $160 | $0 | $70 | ||
| 135 | $155 | $50 | |||
| 140 | $150 | $25 | |||
| 145 | $165 | $40 | |||
| 150 | $160 | $40 | |||
| 155 | $165 | $20 | |||
| 160 | $170 | $35 | |||
| 165 | $155 | $5 | |||
| 170 | $150 | $0 | |||
| 175 | $165 | ||||
| 180 | $170 | ||||
| 185 | $175 | ||||
| 190 | $170 | ||||
| 195 | $155 | ||||
| 200 | $160 |
The other systems on the same spins: Paroli ends at $170, close to flat betting, because its stakes stay small. The $30 James Bond spread ends at $240. Oscar’s Grind and Reverse Martingale go bust.
Source: Our simulation S1, samplePaths (session 4 of 40)
See the numbers as a table
| Spin | Flat bet | Paroli | Oscar's Grind | Reverse Martingale | James Bond ($30) |
|---|---|---|---|---|---|
| 0 | $200 | $200 | $200 | $200 | $200 |
| 5 | $195 | $200 | $200 | $200 | $130 |
| 10 | $190 | $205 | $195 | $170 | $120 |
| 15 | $195 | $200 | $205 | $165 | $160 |
| 20 | $200 | $190 | $210 | $155 | $130 |
| 25 | $195 | $175 | $205 | $140 | $130 |
| 30 | $170 | $145 | $155 | $110 | $60 |
| 35 | $175 | $170 | $180 | $135 | $120 |
| 40 | $170 | $155 | $145 | $85 | $130 |
| 45 | $165 | $140 | $105 | $70 | $80 |
| 50 | $160 | $125 | $115 | $55 | $220 |
| 55 | $165 | $150 | $185 | $45 | $210 |
| 60 | $180 | $180 | $215 | $40 | $210 |
| 65 | $165 | $165 | $200 | $25 | $100 |
| 70 | $150 | $140 | $160 | $0 | $70 |
| 75 | $145 | $125 | $125 | $110 | |
| 80 | $140 | $110 | $95 | $180 | |
| 85 | $135 | $100 | $15 | $290 | |
| 90 | $160 | $165 | $40 | $330 | |
| 95 | $185 | $215 | $65 | $290 | |
| 100 | $170 | $180 | $45 | $240 | |
| 105 | $175 | $170 | $65 | $170 | |
| 110 | $170 | $155 | $60 | $320 | |
| 115 | $165 | $140 | $35 | $340 | |
| 120 | $180 | $175 | $80 | $270 | |
| 125 | $175 | $160 | $75 | $230 | |
| 130 | $160 | $135 | $65 | $190 | |
| 135 | $155 | $120 | $45 | $230 | |
| 140 | $150 | $105 | $10 | $240 | |
| 145 | $165 | $135 | $25 | $190 | |
| 150 | $160 | $125 | $20 | $180 | |
| 152 | $0 | ||||
| 155 | $165 | $145 | $320 | ||
| 160 | $170 | $150 | $360 | ||
| 165 | $155 | $150 | $400 | ||
| 170 | $150 | $135 | $400 | ||
| 175 | $165 | $165 | $370 | ||
| 180 | $170 | $190 | $370 | ||
| 185 | $175 | $180 | $290 | ||
| 190 | $170 | $165 | $300 | ||
| 195 | $155 | $145 | $270 | ||
| 200 | $160 | $170 | $240 |
One session proves nothing on its own, which is the point of running 100,000. In the very first stored session the spins were kind: flat betting ended at $240, D’Alembert at $580 and Martingale at $715, while Labouchere and both James Bond spreads went bust. Lucky and unlucky sequences both exist. Over all of them, the averages settle on the edge.
Two stop rules: play on, or quit at the target
Many players use a system with a goal: win a set amount, then leave. That does change your chance of walking away ahead. It does not change the cost per dollar.
With $200 and Martingale, quitting at +$100 raised the share of sessions that finished ahead from 27.9% to 59.6%. The loss per dollar wagered stayed at the edge (2.66% versus 2.79%, both within sampling error). The average loss fell from $48.28 to $19.78, but only because quitting early cut the average amount wagered from $1,733.16 to $742.92.
Labouchere shows the same thing more sharply. With a +$100 target, sessions lasted 9.85 spins on average and hit the target 61.6% of the time. The average loss was only $11.61, because only $433.66 was wagered. Playing 200 spins with the same system lost $86.90. The target did not make the system better. It made the session shorter.
Source: Our simulation S1
See the numbers as a table
| $200, play 200 spins | $200, stop at +$100 | $1,000, play 200 spins | $1,000, stop at +$500 | |
|---|---|---|---|---|
| Flat bet | 1.3% | 1.3% | 0.0% | 0.0% |
| Martingale | 62.5% | 38.7% | 11.7% | 11.7% |
| D'Alembert | 71.1% | 41.6% | 22.1% | 22.1% |
| Fibonacci | 43.7% | 36.6% | 4.3% | 4.3% |
| Labouchere | 92.1% | 38.4% | 61.4% | 41.5% |
| Oscar's Grind | 48.7% | 40.1% | 9.4% | 9.4% |
| Paroli | 22.2% | 21.8% | 0.0% | 0.0% |
| Reverse Martingale | 77.2% | 49.5% | 0.0% | 0.0% |
| James Bond ($30) | 76.9% | 49.4% | 3.7% | 3.7% |
| James Bond ($100, 14:5:1) | 94.0% | 48.2% | 51.9% | 46.2% |
A target trades one number for another
With the stop-at-target rule, the chance of reaching the target and the size of the loss when you miss are locked together by the edge. A 58.9% chance of winning $100 with Martingale came with a 38.7% chance of losing the whole $200. Roughly 0.589 × $100 − 0.387 × $200 is already negative before counting the sessions that ended in between.
A bigger bankroll: $200 versus $1,000
More money lets a progression survive longer losing runs, so the bust rate falls. It also lets the progression put more money through the wheel, so the average loss rises.
- Martingale: the bust rate fell from 62.5% to 11.7%, but the average loss rose from $48.28 to $94.93, because turnover almost doubled to $3,422.34. In 60.3% of $1,000 sessions, the $500 maximum stopped at least one doubling.
- D’Alembert: the bust rate fell from 71.1% to 22.1%, and the average loss rose from $67.81 to $179.80.
- Fibonacci: the bust rate fell from 43.7% to 4.3% and the chance of finishing ahead rose to 71.0%. The average loss still rose, from $41.02 to $70.12.
- Flat betting: with $1,000 it never went bust and never reached the +$500 target, not once in 100,000 sessions. At $5 a spin, +$500 in 200 spins is all but impossible. The average loss stayed at $27.27.
A larger bankroll does not change the price. It changes how long you can keep paying it.
One zero or two
The double-zero wheel adds a 38th pocket that loses every outside bet. That nearly doubles the edge, from 2.70% to 5.26%, and the simulation shows it in every system. With $200, flat betting lost $27.20 on a single-zero wheel and $52.37 on a double-zero wheel, and its bust rate rose from 1.3% to 3.0%. For Martingale with $1,000, the average loss went from $94.93 to $183.96. For a full comparison of the wheel types, including French rules, see how the three wheel types differ.
| System | Loss % of wagered, single zero | Loss % of wagered, double zero | Mean result, single zero | Mean result, double zero | Bust, single zero | Bust, double zero |
|---|---|---|---|---|---|---|
| Flat bet | 2.73% | 5.26% | 0.0% | 0.0% | ||
| Martingale | 2.77% | 5.23% | 11.7% | 15.9% | ||
| D'Alembert | 2.68% | 5.27% | 22.1% | 32.7% | ||
| Fibonacci | 2.65% | 5.21% | 4.3% | 6.5% | ||
| Labouchere | 2.70% | 5.25% | 61.4% | 71.3% | ||
| Oscar's Grind | 2.71% | 5.33% | 9.4% | 15.0% | ||
| Paroli | 2.73% | 5.29% | 0.0% | 0.0% | ||
| Reverse Martingale | 2.77% | 5.24% | 0.0% | 0.0% | ||
| James Bond ($30) | 2.67% | 5.27% | 3.7% | 8.5% | ||
| James Bond ($100, 14:5:1) | 2.69% | 5.29% | 51.9% | 70.8% |
French La Partage and En Prison rules are not modelled. They halve the edge on even-money bets only.
Source: Our simulation S1 (100,000 sessions per cell, seeds 1001 and 1002)
If you play at all, the choice of wheel matters far more than the choice of system. Moving from double zero to single zero cuts the expected loss of every system by nearly half. No staking pattern does anything like that.
Is there a winning roulette strategy?
No. The arithmetic above leaves no room for one, and the common arguments for one all rely on the same mistake.
The gambler’s fallacy
After five reds in a row, many players feel black is “due”. It isn’t. The wheel has no memory, and red still wins on 18 of 37 pockets, a 48.65% chance, on the next spin and every spin after it. A long run of one colour is not rare in itself. In our flat-bet sessions, the longest losing run in 200 spins averaged 7.25 spins, and 5% of sessions saw a run of 11 or more. The longest in 100,000 sessions was 24 losses in a row.
Every loss-chasing system is built on the gambler’s fallacy. Martingale, D’Alembert, Fibonacci, Labouchere and Oscar’s Grind all raise the stake after a loss, as if a win were becoming more likely. It isn’t, so the bigger stake just carries the same 2.70% cost on more money.
Hot and cold numbers
Some live and online tables show “hot” and “cold” numbers from the last few hundred spins. On a fair wheel, those lists describe the past and predict nothing. Each number has a 1 in 37 chance on every spin, whatever happened before. Over a few hundred spins, some numbers will come up far more than others by chance alone.
A number that has not appeared for a while is overdue
Spins are independent. A number that has missed 100 spins has the same 1 in 37 chance on spin 101 as on spin 1. Betting on cold numbers, or on hot ones, carries exactly the 2.70% edge.
What actually reduces your losses
Since the expected loss is the edge times the amount wagered, only two things lower it:
- A lower edge. Play a single-zero wheel rather than double zero. French rules on even-money bets halve the edge again, to 1.35%.
- Less money wagered. Smaller stakes, fewer spins, and a firm stopping point. A $5 flat bet for 200 spins is not a strategy for winning, but it is the cheapest way to play 200 spins.
For how long a small bankroll lasts at different stakes, see how long $20 to $100 lasts at the table. For every bet’s probability and payout in one table, see the payout and probability for each bet. And for how roulette compares with other games, see every casino bet ranked by its edge.
What we could not verify, and our assumptions
- Our own rules for each system. Many systems have several versions. We used one clear version of each and printed its rules above. Other versions, with different units, caps or reset rules, will give different bust and win rates. They will not give a different loss per dollar wagered, because no version can.
- Reverse Martingale has no win cap here. Our version banks a run only at the table maximum ($320 stake). Versions that stop after a fixed number of wins behave like Paroli, which we report separately.
- The target definition. “Hit target” means the bankroll reached +50% of the starting amount within 200 spins. A different target changes the hit rate and the bust rate, not the edge.
- James Bond proportions. The common $30 version (20/5/5) is not proportional to Fleming’s $200 original (140/50/10). We report both.
- Simulation error. Probabilities come from 100,000 sessions and carry sampling error of roughly ±0.3 percentage points at 50%, less near 0% or 100%. The flat-bet figures were checked against an exact calculation.
- French rules not modelled. La Partage and En Prison are not in the simulation. The 1.35% figure is from Wizard of Odds.
- Wheel bias. We looked for a reliable account of historical attempts to beat biased wheels. The sources we could fetch disagree on basic facts such as the year and the amounts involved, so we left the topic out. Nothing on this page assumes a biased wheel, and we make no claim about how common one is today.
- Biased or rigged games. All figures assume a fair wheel. We did not test any real casino’s wheel or software.
Rerun it yourself
The study script runs with plain Node 22 and no dependencies: node research/studies/s1-roulette-systems/run.mjs. It rewrites the JSON file behind every chart and table on this page and exits with an error if any validation check fails.
If you want to see how the same edge plays out in another game, our test of baccarat betting systems reaches the same result with a 1.06% edge.