American roulette holds an even chance on 18 pockets out of 38. European roulette leaves 18 out of 37 for the same color. Contra d’Alembert steps the other way from the rule “a loss is plus one”: a win raises the bet by one unit, and a loss lowers it by one unit. The bet does not fall below one unit.
There is no aim here of “closing the cycle at plus 1.” There is no doubling either. The bet creeps one step per spin, and the direction of the step matches the last outcome. After a win there are more chips on the table, and after a loss fewer, until the bet has hit one unit.
This is not Oscar’s system. There a loss does not lower the bet, and a win does not raise it above what is still missing to plus 1. Here a loss really does lower the bet, and the plus has no ceiling.
One stretch of eight spins
The start is 5. The order of spins: loss, loss, win, loss, three wins, loss. The column “next” is the bet of the following spin.
| Spin | Bet | Outcome | Result of the stretch | Next |
|---|---|---|---|---|
| 1 | 5 | loss | −5 | 4 |
| 2 | 4 | loss | −9 | 3 |
| 3 | 3 | win | −6 | 4 |
| 4 | 4 | loss | −10 | 3 |
| 5 | 3 | win | −7 | 4 |
| 6 | 4 | win | −3 | 5 |
| 7 | 5 | win | +2 | 6 |
| 8 | 6 | loss | −4 | 5 |
Adding spin by spin: −5−4+3−4+3+4+5−6 = −4. Four wins and four losses did not give zero, because the wins and the losses stood on different bets. By the end of the stretch the bet is 5 again, and the bankroll of the stretch is in the minus by 4.
Eight identical outcomes in a row
If the loss is not interrupted, the bet melts down to one unit and then stays put. If the win is not interrupted, the bet grows the same way an ordinary step of one chip grows after losses. From a start of 5 the two rows below match number for number, but they sit on different outcomes.
| Streak from a start of 5 | Bets | Sum | How often on 38 pockets |
|---|---|---|---|
| Eight losses | 5, 4, 3, 2, 1, 1, 1, 1 | 18 | about 0.59% |
| Eight wins | 5, 6, 7, 8, 9, 10, 11, 12 | 68 | about 0.25% |
Eight losses in a row on a color are (20/38)⁸, about 1 streak out of 170. Eight wins are (18/38)⁸, about 0.25%, roughly 1 out of 395. Under d’Alembert the same eight losses from a start of 5 take 68, because there the bet grows after a loss. Here 68 is gathered only by a winning streak.
The share of American roulette does not depend on the direction of the step
Per 100 staked, a color on 38 pockets on average gives the table 5.26. On 37 pockets it is 2.70. A step up after a win stakes more where the chip has already won, and less where it has lost. The expected minus on each unit staked does not change because of that. French roulette with half returned on zero does not apply to the RoulCoin wheel: 0 and 00 take the stake in full and lower the next chip by one step, not by half.
| Wheel | A loss of the color | Per 100 staked | What zero does to the bet |
|---|---|---|---|
| 38 pockets | 20/38 | 5.26 | minus one step, not below 1 |
| 37 pockets | 19/37 | 2.70 | the same minus of one step |
For a player in England a floor of one chip does not depend on the time zone. Two green pockets remain two extra losses of an even chance.
A loss reduces the bet, so a long black streak costs 18, not 68. A winning streak of the same length gathers exactly 68.
How not to mix up the direction if you play online
Three numbers are written down before the spin: the start, the floor, and the ceiling above which one’s own bet is no longer raised. The account ceiling may not match this player’s ceiling. You can play online for money after an account is created. A live balance does not add a single cell to the 18 winning pockets.
- A win: plus one unit to the bet.
- A loss: minus one unit, but not below 1.
- 0 and 00 count as a loss, not as a reason to stay on the previous bet.
- The plus of one spin is not declared the aim of the evening. The next spin again stakes the chip that has already grown.
Why four wins in the example did not close the minus
The wins arrived on bets of 3, 3, 4 and 5, summing to 15. The losses stood on 5, 4, 4 and 6, summing to 19. The difference is −4 with an equal number of outcomes. Spins cannot be counted here without the size of the bet.
After a loss, is the bet left as it was?
No. It is reduced by 1, until it has become one unit. A different rule keeps the previous bet after a loss, with an aim of plus 1 per cycle.
Do eight losses from a start of 5 take 68?
No, 18. The bets are 5, 4, 3, 2 and then four times 1. The sum of 68 is gathered here by eight wins: 5, 6, 7, 8, 9, 10, 11 and 12.
Can the bet be lowered below one chip?
No. One unit is the floor. A second loss on one unit stakes one unit again and adds one more to the minus, not zero.
How often do eight wins in a row arrive?
On 38 pockets, about 0.25%, roughly 1 streak out of 395. On 37 pockets there are 18 winning pockets out of 37, so each next win again multiplies a share that is already less than half.
A step toward the last outcome makes a losing streak cheaper, and a winning streak more expensive in the bet. Neighboring playing strategies point this step the other way, or cut it with the aim of a cycle. The direction is better written above the bet, otherwise plus and minus are easy to swap in the middle of a stretch.