American roulette crosses off two ends of the row in ordinary Labouchère after a win. European roulette in this comparison changes only the number of pockets, not the direction of the crossing off. Reverse Labouchère does the opposite: a win writes the amount staked onto the end of the row, and a loss crosses off both ends.
The bet is still equal to the sum of the two ends, and if one number is left in the row it equals that number. The even chance is the same: a color, odd or even, or half the field. On the RoulCoin wheel there are 18 winning pockets out of 38, and 20 losing ones, with 0 and 00. The payout equals the bet. The row 1, 2, 3, 4 below is for teaching, not a table limit.
An ordinary row closes at plus 10 if it is played out to empty. The reverse one, on the same numbers, grows while wins continue, and melts when losses arrive. Stopping in the middle is part of the rule, otherwise the ends that were written on are returned to the table.
Seven spins from the row on American roulette
The order: two wins, a loss, a win, two losses, and one more loss, which erases the last number. The “result” column is counted from zero.
| Spin | Row before the bet | Bet | Outcome | Result |
|---|---|---|---|---|
| 1 | 1, 2, 3, 4 | 5 | win | +5 |
| 2 | 1, 2, 3, 4, 5 | 6 | win | +11 |
| 3 | 1, 2, 3, 4, 5, 6 | 7 | loss | +4 |
| 4 | 2, 3, 4, 5 | 7 | win | +11 |
| 5 | 2, 3, 4, 5, 7 | 9 | loss | +2 |
| 6 | 3, 4, 5 | 8 | loss | −6 |
| 7 | 4 | 4 | loss | −10 |
If one stops after the second spin, the bankroll has +11, and the row is already 1, 2, 3, 4, 5, 6. If the example is played out to the end, the wins brought 5+6+7 = 18, the losses took 7+9+8+4 = 28, the result is −10, and the row is empty. The same ends that built up the plus become the bet on a loss.
Where the reverse row parts from the ordinary one
On the ordinary row 1, 2, 3, 4 the first loss writes 5 onto the end, and the minus piles up until wins arrive. Here the first win does the same thing with the end: it writes it on. So the dangerous side changes. For an ordinary row a streak of losses grows expensive. For the reverse one, continuing after wins grows expensive if the losses arrive already on a large bet.
| Event | Ordinary row | Reverse row |
|---|---|---|
| A win | crosses off two ends | writes the bet onto the end |
| A loss | writes the bet onto the end | crosses off two ends |
| The aim, if one does not stop earlier | an empty row and plus 10 | an empty row after a run of losses |
| In the example after the first two wins | the row is shorter | a result of +11, a longer row |
Plus 10 of the ordinary row is the sum of the starting numbers, and only if the row was played out. Plus 11 in this example is not an aim, but a mark at which the player can still stand up. The rule does not stop there by itself.
The share of a spin does not look at which way the end is written
Each bet remains a color. Per 100 staked an American wheel takes 5.26, and a European wheel takes 2.70. The direction of the writing changes whether the bet grows or falls after a win, and it does not change the 18 winning pockets out of 38. Two wins in a row at the start of the example are (18/38)², 22.44%. That is the frequency of a short plus, not a promise that the row will keep +11 further on.
| Wheel | A win of the color | Two wins in a row | Per 100 staked |
|---|---|---|---|
| 38 pockets | 18/38 | 22.44% | 5.26 |
| 37 pockets | 18/37 | 23.67% | 2.70 |
For a player in England, 0 and 00 do not cross off the ends by half. Both take the whole stake and erase two ends of the row, like any other loss of the color.
After two wins in the example one can take +11. If play continues by the table, the same ends bring the result to −10.
How not to mix up an end if you play online
The row is written down before the spin and is not corrected from memory. A mistake on one end changes both the bet and what will remain after a loss. You can play online without signup on a virtual balance: guest chips do not turn into a withdrawal, and the growth of the row after a win is visible on them without a deposit.
- A win writes onto the end exactly the amount staked, not one unit “to even the count.”
- A loss takes off both ends. The one number left is the next bet.
- A plus that was decided to be taken is taken. After that the row does not keep growing in the same series.
- 0 and 00 are a full loss and a full crossing off of two ends.
Why an empty row here does not equal plus 10
Emptiness in ordinary Labouchère means the starting numbers were crossed off by wins. Emptiness in the reverse example above means the losses erased both the starting numbers and what had been written on. The result of the seventh spin is −10 precisely because the row emptied from the other side.
If the example is stopped after two wins, how much is in the bankroll?
+11. Bets of 5 and 6 both won. By this moment the row is already 1, 2, 3, 4, 5, 6, and the next bet would have been 7.
The last spin stakes 4. Where does this four come from?
After the sixth spin one number is left in the row, 4. The bet equals it. A loss erases this number, the result becomes −10, and the row is empty.
Does a win on the one remaining number close the row in the plus?
No, it writes this bet onto the end. A row of a single 4 after a win becomes 4, 4, and the plus of the series grows by 4. A loss makes the row empty, not a win.
Does zero cross off only one end?
No. On a wheel of 38 pockets, 0 and 00 take the whole stake. Both ends are crossed off, as after the other color.
The reverse row moves the risk onto continuing after wins. Neighboring playing strategies either cross off the ends right after a win, or do not keep a row at all. The mark at which the plus is taken is better written down before the first five.