American roulette keeps 38 pockets on the wheel, and European roulette keeps 37. Martingale stakes an even chance and doubles the chip after every loss. A win returns one unit on top of the whole series and resets the bet to the start. The mathematics of the wheel does not shift because of that: only the shape of the loss changes.
An even chance is red or black, odd or even, 1–18 or 19–36. On the RoulCoin wheel there are 18 winning pockets out of 38. There are 20 losing ones: eighteen cells of the other color and two greens, 0 and 00. The payout for a guessed color equals the amount staked, no more. An account is needed only if you play online for money: a live balance does not add a single pocket.
French roulette on 37 pockets sometimes returns half the stake if zero comes up. In the ladder below there is no such easing. Two full losses of the color are counted: 20 pockets out of 38 and 19 out of 37.
How one cycle is counted in American roulette
The start is 1 unit. A loss doubles the next bet. A win on any step closes the cycle with a plus of 1 unit and returns the bet to 1. Below is a teaching table with a minimum of 1: the “already lost” column is the sum of the previous bets, and the “result of the step” is the result if the win arrives right now.
| Step | Bet | Already lost | Result, if the step won |
|---|---|---|---|
| 1 | 1 | 0 | +1 |
| 2 | 2 | 1 | +1 |
| 3 | 4 | 3 | +1 |
| 4 | 8 | 7 | +1 |
| 5 | 16 | 15 | +1 |
| 6 | 32 | 31 | +1 |
| 7 | 64 | 63 | +1 |
| 8 | 128 | 127 | +1 |
| 9 | 256 | 255 | +1 |
| 10 | 512 | 511 | +1 |
Nine losses in a row take 511 units. The tenth bet is 512. If the table maximum is 500, it can no longer be staked: the series breaks not by “bad luck,” but by the limit rule. In an account the ceiling can be different. It is checked before the first chip, not after the eighth loss.
How often a series reaches the ceiling
On an American wheel a loss of an even chance has probability 20/38. Nine such outcomes in a row, after which a bet of 512 is exactly what is needed, happen in (20/38)⁹ of cases. That is 0.31%, roughly 1 series out of 323. Seven losses in a row, a bet of 128, are 1.12%, about 1 out of 89.
| Losses in a row | Next bet | American wheel, 38 pockets | European wheel, 37 pockets |
|---|---|---|---|
| 7 | 128 | 1.12%, about 1 out of 89 | 0.94%, about 1 out of 106 |
| 8 | 256 | 0.59%, about 1 out of 170 | 0.48%, about 1 out of 207 |
| 9 | 512 | 0.31%, about 1 out of 323 | 0.25%, about 1 out of 403 |
A European wheel is milder only because there are 19 losing pockets, not 20. The la partage rule on the same 37 pockets returns half the stake if zero comes up. Then the expected loss on a color is about 1.35 units per 100 staked, not 2.70. On the RoulCoin table this rule is absent: 0 and 00 take the color in full.
What the table takes from a hundred units
The expected result is counted on every unit staked, not on a “successful evening.” A color on 38 pockets on average gives the table 5.26 units per 100 staked. On 37 pockets it is 2.70. Doubling does not subtract these figures. It gathers many small plus-ones and occasionally gives away the whole ladder.
| Wheel | Winning pockets of the color | Loss per 100 units of turnover |
|---|---|---|
| 38 pockets, 0 and 00 | 18 out of 38 | 5.26 |
| 37 pockets, one zero | 18 out of 37 | 2.70 |
| 37 pockets and la partage on even chances | 18 out of 37, zero cuts the stake in half | 1.35 |
From this comes a direct conclusion for the bankroll. A hundred cycles, closed on the first step, give about 100 units of profit, if not a single series has broken. One break on the ninth loss takes 511. Two such breaks over the same hundred attempts can no longer be covered. The rarity in the table above is exactly about this: 0.31% is not zero.
Plus one chip on a cycle does not cancel 511 chips on a broken ladder. What must be counted is the worst step the table still accepts.
Where to stop if you play online
For a player in England the series does not depend on the city: 18 winning pockets out of 38 and the bet ceiling in the account are the same in any time zone. It makes sense to write down three numbers in advance: the starting chip, the table maximum, and the sum one would hate to give away in full. If the next bet is larger than either of the last two, the cycle is closed by hand.
A short check on virtual chips shows the speed of growth better than any scheme on paper. Playing online for free is possible without a deposit: the guest balance is virtual and does not turn into a withdrawal. Playing online without signup is possible here only with virtual chips. Playing online for money is possible after an account is created, and then the series already uses live units. Playing with crypto is possible through the deposit cashier: the transfer network changes neither 20/38 nor the table limit.
Working limits worth keeping next to the bet:
- The starting chip is no more than 1/500 of the bankroll, if the table ceiling can hold the ninth step at all.
- The series stops a step before the maximum, not at the moment when the bet button no longer accepts the amount.
- The win of a cycle is not sent into a new ladder on the same spin: the bet is 1 again.
- The color is not changed in the middle of a series. Switching red to black does not zero out the chips already lost.
Why “I’ll win it back with the next double” breaks the count
After six losses, 63 units are already on the table, and the seventh bet is 64. Refusing it fixes a minus of 63. An attempt to “push through” makes sense only if 64, then 128 and 256, are still inside the limit and inside the sum set aside in advance. Adding chips from another pocket, or from a deposit that was not in the calculation, turns the progression into a different one, already without an upper bound.
What does one win inside a series give?
Exactly one unit above all the previous losses of this cycle. A win of the step 64 after a loss of 63 closes the cycle at +1, not at +64. The large figure on the screen is the return of the ladder, not the profit of the evening.
Does martingale make sense on a Dozen?
No, in this form. A Dozen pays 2 to 1, not 1 to 1, and it has 12 winning pockets out of 38. Doubling is calculated to return the previous bets with one payout equal to the current bet. On a Dozen the same ladder does not close the cycle at plus one chip.
Is a maximum of 100 enough for this ladder?
No, if the start equals 1. A bet of 64 still goes through, and the next one, 128, no longer does. Seven lost steps from 1 to 64 leave 127 units on the table, and the table will not accept a continuation by the doubling rule.
Must one double after a win?
No. A win of any step returns the next bet to 1. Doubling after a plus is a different progression: it hits the maximum faster and does not enter the count of this table.
Does changing the color after three losses help?
It does not help. For red and for black the same 20 pockets are unfavorable: the other color, 0 and 00. Changing the field does not reduce the 7 units already lost and does not change the next bet of 8.
Martingale is easy to check over a short distance and just as easy to overrate. Neighboring playing strategies are worth reading before the first live series. First run the ladder itself idle: play online on virtual chips up to the first artificial break, and write down the step at which the table stopped accepting the bet.