With flat bets on a single-zero wheel, a small bankroll lasts exactly 37 spins per betting unit on average: $20 at $1 lasts 740 spins, $50 at $2 lasts 925, and $100 at $5 lasts 740. The bet you choose does not change that average, but it changes everything else: on red or black half of all $20 bankrolls at $1 are still playing after 394 spins, while on a single number half are gone within 20.
This page uses exact figures from our study S2, which models every combination of a $20, $50 or $100 bankroll with $1, $2 or $5 flat bets, on even-money bets and on single numbers. It answers three questions: how long the money lasts, how likely you are to double it first, and what the time at the table costs. It does not offer a way to win, because there is none.
- Average spins until bust, any bet (exact)
- 37 x units
- Median spins for $20 at $1: red/black vs a single number
- 394 vs 20
- Chance $20 doubles first at $1 on red/black
- 25.3%
- Expected cost at $1 a spin, 40 spins an hour
- $1.08/hr
Source: Study S2 (exact Markov chain); pace assumption from study S4
Average spins until bust: exactly 37 per unit
Divide your bankroll by your stake to get your number of betting units. $50 at $2 is 25 units. Multiply by 37 and you have the average number of spins before the money runs out: 925. That is not an approximation. It is the exact result in study S2, and it holds for even-money bets and single numbers alike.
The reason is that on a single-zero wheel both bets lose, on average, exactly one stake every 37 spins. The diagram plays one idealised cycle in which each pocket comes up once.
Even-money bet (e.g. red)
18 pockets win +119 lose -1Net over 37 spins: -1 unit
Single number (straight up)
1 pocket wins +3536 lose -1Net over 37 spins: -1 unit
So a bankroll of n units lasts 37 x n spins on average with either bet. $20 at $1 is 20 units, so 740 spins on average.
Because each spin costs 1/37 of a stake on average, a bankroll of n units takes 37 x n spins on average to be used up. Mathematicians call this Wald’s identity; for you it means the average session length is fixed by just two things, your budget and your stake.
How we know: the average is exact, the median is the useful number
The mean (average) counts every possible session, including the rare one that survives thousands of spins. The median is the spin by which half of all sessions have gone broke. For single numbers the two differ hugely, because a few lucky sessions pull the average up. If you want to know what a typical evening looks like, read the median.
How long the money really lasts: the median
Here is every configuration in the study. “Still playing after 100 spins” is the share of sessions that have not gone broke by spin 100.
| Bankroll and stake | Units | Median spins to bust | Mean spins to bust | Still playing at 100 spins | Still playing at 500 | Doubles before bust |
|---|---|---|---|---|---|---|
| $20 at $1 | 20 | 394 | 740 | 41.6% | 25.3% | |
| $20 at $2 | 10 | 136 | 370 | 18.6% | 36.8% | |
| $20 at $5 | 4 | 28 | 148 | 6.6% | 44.6% | |
| $50 at $1 | 50 | 1,364 | 1,850 | 91.5% | 6.3% | |
| $50 at $2 | 25 | 543 | 925 | 53.2% | 20.6% | |
| $50 at $5 | 10 | 136 | 370 | 18.6% | 36.8% | |
| $100 at $1 | 100 | 3,134 | 3,700 | 100.0% | 0.4% | |
| $100 at $2 | 50 | 1,364 | 1,850 | 91.5% | 6.3% | |
| $100 at $5 | 20 | 394 | 740 | 41.6% | 25.3% |
Source: Study S2, exact. Mean = 37 x units.
| Bankroll and stake | Units | Median spins to bust | Mean spins to bust | Still playing at 100 spins | Still playing at 500 | Doubles before bust |
|---|---|---|---|---|---|---|
| $20 at $1 | 20 | 20 | 740 | 10.7% | 39.7% | |
| $20 at $2 | 10 | 10 | 370 | 5.4% | 24.0% | |
| $20 at $5 | 4 | 4 | 148 | 2.1% | 10.4% | |
| $50 at $1 | 50 | 158 | 1,850 | 27.2% | 42.9% | |
| $50 at $2 | 25 | 25 | 925 | 13.3% | 41.0% | |
| $50 at $5 | 10 | 10 | 370 | 5.4% | 24.0% | |
| $100 at $1 | 100 | 568 | 3,700 | 52.4% | 43.2% | |
| $100 at $2 | 50 | 158 | 1,850 | 27.2% | 42.9% | |
| $100 at $5 | 20 | 20 | 740 | 10.7% | 39.7% |
Source: Study S2, exact. Mean = 37 x units, the same as for even-money bets.
Read the two tables side by side and the pattern is clear:
- Even-money bets: the median sits below the mean, but not far below. $20 at $1 has a median of 394 spins against a mean of 740; $50 at $1 has 1,364 against 1,850. Most sessions grind down slowly.
- Single numbers: up to 25 units, the median equals the number of units. $20 at $1 has a median of 20 spins, because 57.8% of the time none of the first 20 spins hits your number and the money is gone. The mean is still 740, carried by the minority of sessions that hit early and run for a long time: 10.7% are still going after 500 spins. With more units the median rises above the unit count ($50 at $1: 158 spins; $100 at $1: 568), because a first win becomes likely before the money runs out.
- Units matter more than dollars. $20 at $1 and $100 at $5 are both 20 units, and their rows are identical. $20 at $5 is only 4 units: a median of 28 spins on even-money bets and 4 spins on a single number.
The survival curves
A survival curve shows, spin by spin, the share of bankrolls still in play. The first chart holds the budget at $50 and changes the stake.
Source: Study S2, exact Markov chain (survivalCurve)
See the numbers as a table
| Spins | $1 a spin (50 units) | $2 a spin (25 units) | $5 a spin (10 units) |
|---|---|---|---|
| 0 | 100% | 100% | 100% |
| 10 | 100% | 100% | 100% |
| 20 | 100% | 100% | 97% |
| 30 | 100% | 100% | 91% |
| 40 | 100% | 100% | 85% |
| 50 | 100% | 100% | 79% |
| 60 | 100% | 100% | 74% |
| 70 | 100% | 100% | 70% |
| 80 | 100% | 99% | 66% |
| 90 | 100% | 99% | 62% |
| 100 | 100% | 98% | 59% |
| 110 | 100% | 97% | 56% |
| 120 | 100% | 96% | 53% |
| 130 | 100% | 95% | 51% |
| 140 | 100% | 94% | 49% |
| 150 | 100% | 92% | 47% |
| 160 | 100% | 91% | 45% |
| 170 | 100% | 90% | 43% |
| 180 | 100% | 88% | 42% |
| 190 | 100% | 87% | 40% |
| 200 | 100% | 86% | 39% |
| 210 | 100% | 84% | 38% |
| 220 | 100% | 83% | 36% |
| 230 | 100% | 82% | 35% |
| 240 | 100% | 80% | 34% |
| 250 | 99% | 79% | 33% |
| 260 | 99% | 78% | 32% |
| 270 | 99% | 76% | 31% |
| 280 | 99% | 75% | 31% |
| 290 | 99% | 74% | 30% |
| 300 | 99% | 73% | 29% |
| 310 | 98% | 72% | 28% |
| 320 | 98% | 70% | 27% |
| 330 | 98% | 69% | 27% |
| 340 | 98% | 68% | 26% |
| 350 | 97% | 67% | 26% |
| 360 | 97% | 66% | 25% |
| 370 | 97% | 65% | 24% |
| 380 | 96% | 64% | 24% |
| 390 | 96% | 63% | 23% |
| 400 | 96% | 62% | 23% |
| 410 | 95% | 61% | 22% |
| 420 | 95% | 60% | 22% |
| 430 | 95% | 59% | 21% |
| 440 | 94% | 58% | 21% |
| 450 | 94% | 57% | 21% |
| 460 | 93% | 57% | 20% |
| 470 | 93% | 56% | 20% |
| 480 | 92% | 55% | 19% |
| 490 | 92% | 54% | 19% |
| 500 | 92% | 53% | 19% |
At $1 a spin, 91.5% of $50 bankrolls are still alive after 500 spins. At $5, only 18.6% are. Cutting the stake is by far the strongest lever you have over playing time.
The second chart holds budget and stake fixed at $20 and $1, and compares the two kinds of bet.
Source: Study S2, exact Markov chain (survivalCurve)
See the numbers as a table
| Spins | Even-money bet | Single number |
|---|---|---|
| 0 | 100% | 100% |
| 10 | 100% | 100% |
| 20 | 100% | 42% |
| 30 | 100% | 42% |
| 40 | 100% | 42% |
| 50 | 99% | 42% |
| 60 | 98% | 30% |
| 70 | 97% | 30% |
| 80 | 96% | 30% |
| 90 | 94% | 30% |
| 100 | 92% | 25% |
| 110 | 91% | 25% |
| 120 | 89% | 25% |
| 130 | 87% | 21% |
| 140 | 85% | 21% |
| 150 | 83% | 21% |
| 160 | 81% | 21% |
| 170 | 79% | 19% |
| 180 | 78% | 19% |
| 190 | 76% | 19% |
| 200 | 74% | 17% |
| 210 | 73% | 17% |
| 220 | 71% | 17% |
| 230 | 69% | 17% |
| 240 | 68% | 16% |
| 250 | 66% | 16% |
| 260 | 65% | 16% |
| 270 | 64% | 16% |
| 280 | 62% | 15% |
| 290 | 61% | 15% |
| 300 | 60% | 15% |
| 310 | 59% | 14% |
| 320 | 58% | 14% |
| 330 | 56% | 14% |
| 340 | 55% | 14% |
| 350 | 54% | 13% |
| 360 | 53% | 13% |
| 370 | 52% | 13% |
| 380 | 51% | 12% |
| 390 | 50% | 12% |
| 400 | 49% | 12% |
| 410 | 49% | 12% |
| 420 | 48% | 12% |
| 430 | 47% | 12% |
| 440 | 46% | 12% |
| 450 | 45% | 12% |
| 460 | 45% | 11% |
| 470 | 44% | 11% |
| 480 | 43% | 11% |
| 490 | 42% | 11% |
| 500 | 42% | 11% |
After 100 spins, 92.3% of the even-money bankrolls are still playing, against 24.6% of the single-number ones. Both groups lose the same amount on average per spin while they are playing.
The chance of doubling first
Many small-bankroll players have a target: turn $20 into $40, then stop. The study gives the exact probability of reaching double the starting amount before going broke, with a flat stake and no change of bet.
Source: Study S2, exact absorbing-chain solve
See the numbers as a table
| $1 even-money | $1 single number | $2 even-money | $2 single number | $5 even-money | $5 single number | |
|---|---|---|---|---|---|---|
| $20 | 25.3% | 39.7% | 36.8% | 24.0% | 44.6% | 10.4% |
| $50 | 6.3% | 42.9% | 20.6% | 41.0% | 36.8% | 24.0% |
| $100 | 0.4% | 43.2% | 6.3% | 42.9% | 25.3% | 39.7% |
0.45%
the chance that $100 doubles before it is gone, betting $1 at a time on red or black. Small stakes make your money last, which also means the 2.70% edge has hundreds of extra spins to grind.
Source: Study S2
What the grid shows:
- With 20 or more units, single numbers double the bankroll far more often. $50 at $1 doubles first 42.9% of the time on single numbers against 6.3% on even-money bets. Fewer, bigger swings give the edge less time to work.
- With very few units it flips. $20 at $5 (4 units) doubles 44.6% of the time on even-money bets against 10.4% on a single number, because four losing spins end a single-number session before a hit is likely.
- No plan reaches 50%. On a game with no zero, an even-money plan would double exactly half the time. The zero takes that away in every cell.
Myth: a higher chance of doubling means a better strategy
The plans with the best doubling odds do not lose less. Every plan in the grid loses $2.70 per $100 wagered. A higher doubling chance is paid for with a higher chance of losing everything quickly, as the single-number survival curve shows.
What it costs per 100 spins and per hour
While the bankroll lasts, the expected loss per 100 spins is 100 x stake / 37: $2.70 at $1, $5.41 at $2 and $13.51 at $5, on either kind of bet. To turn that into an hourly price we need a pace. Our cost-per-hour study (S4) assumes 40 spins an hour as a central figure, with a range of 25 at a crowded land-based table to 60 at an online live table; automated games can be much faster.
At 40 spins an hour the expected cost of playing is about $1.08 an hour at $1, $2.16 at $2 and $5.41 at $5. That is the number to compare with other ways to spend an evening. How roulette’s hourly cost compares with other table games is in our ranking of what each casino game costs.
What a $20, $50 or $100 budget buys you
This is the decision table. Time is the median time until the budget is gone at 40 spins an hour, so half of sessions last longer and half shorter. Cost per hour is the expected loss while playing. All rows use even-money bets; the last two columns show the single-number alternative.
| Budget and stake | Median hours to bust | Expected cost per hour | Still playing at 100 spins | Doubles first | Single number: median hours | Single number: doubles first |
|---|---|---|---|---|---|---|
| $20 at $1 | $1.08 | 92.3% | 25.3% | 0.5 | 39.7% | |
| $20 at $2 | $2.16 | 58.9% | 36.8% | 0.3 | 24.0% | |
| $20 at $5 | $5.41 | 23.8% | 44.6% | 0.1 | 10.4% | |
| $50 at $1 | $1.08 | 100.0% | 6.3% | 4.0 | 42.9% | |
| $50 at $2 | $2.16 | 97.7% | 20.6% | 0.6 | 41.0% | |
| $50 at $5 | $5.41 | 58.9% | 36.8% | 0.3 | 24.0% | |
| $100 at $1 | $1.08 | 100.0% | 0.4% | 14.2 | 43.2% | |
| $100 at $2 | $2.16 | 100.0% | 6.3% | 4.0 | 42.9% | |
| $100 at $5 | $5.41 | 92.3% | 25.3% | 0.5 | 39.7% |
Source: Study S2 (median spins, survival, doubling) and study S4 (pace of 40 spins an hour, an assumption). At 25 spins an hour times are 1.6 times longer; at 60, a third shorter.
How to read it in practice:
- $20: at $1 a spin, the typical $20 lasts about 9.9 hours of play at 40 spins an hour, longer than most people sit at a table, and costs about $1.08 an hour. At $5 it typically lasts about 0.7 hours (28 spins).
- $50: $2 a spin is a reasonable middle: a median of 13.6 hours and about $2.16 an hour. At $5 the typical session lasts 3.4 hours.
- $100: at $1 or $2 the budget will very likely outlast your evening; the hourly cost is what you are really paying. At $5 the median is 9.9 hours, the same as $20 at $1, because both are 20 units.
Planning a small-bankroll session honestly
What you can control is the stake, the kind of bet, the wheel and when you stop. Here is what each one does, and does not do.
- Set a loss budget before you start, and treat it as spent. The money you bring is the price of the evening. If the evening costs less, that is a bonus.
- Pick the stake from the time you want. Use the table above: units = budget / stake, average spins = 37 x units. If you want three hours at 40 spins an hour, that is 120 spins; aim for a median comfortably above it.
- Play single zero. A double-zero wheel costs 5.26% per spin instead of 2.70%, so money lasts roughly half as long on average. See single-zero versus double-zero wheels for the full comparison.
- Choose the ride, not a “better” bet. Even-money bets for a long, steady session; single numbers for a short session with a real chance of a big swing. The payout for each bet changes the shape, never the price.
- Use a time limit as well as a money limit. At $1 a spin, $100 almost never runs out in one evening, so a stop time is what actually ends the session.
- A win target is fine, as long as you know what it is. Stopping at double changes how a session ends, not what it costs per spin. It is a way to leave on a high, not an edge.
What not to expect: there is no staking pattern that turns these numbers in your favour. Doubling after losses, raising after wins and cancellation lines all redistribute the same losses into different shapes. When we put nine popular staking systems to the test over 100,000 simulated sessions each, none of them changed the cost of play. The page on what doubling after a loss does to a small bankroll shows why the most popular one is especially risky with $20 to $100.
Fact: the cheapest even-money bet is on a French table
If you can find a single-zero table that applies La Partage (half your even-money stake back on zero), the cost per spin halves to 1.35%. Every figure in this study assumes the standard 2.70% and no such rule, so on such a table your money would last longer on average.
What we could not verify, and our assumptions
- Your pace. We have no measured spins-per-hour figure for any specific table. The 40-spin central figure and the 25 to 60 range are assumptions; automated games can run several times faster, which makes hourly costs higher.
- Double-zero wheels and French rules. The study is single-zero only. On a double-zero wheel average survival is roughly halved; we have not computed the exact medians and doubling odds for it.
- Other bets and mixed play. Splits, streets, dozens and combinations of bets were not modelled. Their average spins to bust follow the same 37 x units rule, but we did not compute their medians or doubling odds.
- Table minimums. We cannot verify that $1 or $2 tables are available where you play; minimums vary widely.
- Assumptions: a fair single-zero wheel, the same flat stake every spin, winnings kept in the bankroll, and play stopping at zero or (for doubling) at twice the starting bankroll.