American roulette gives a color 18 pockets out of 38. European roulette on a single zero gives 18 out of 37. D’Alembert’s system does not double the bet. After a loss it adds one unit, and after a win it takes one away. The step is small, so a series lives longer than a martingale, but every visit to the table still costs the share of the zero pockets.
Starting from one chip is almost pointless: after the first win there is nothing left to take away. A working start is 5 units, and the floor is 1 unit. One may go below five, and one may not go below one. The payout of an even chance equals the bet, as on red and black. European roulette does not change this arithmetic of the step: only the number of unfavorable pockets changes, 19 instead of 20.
Live chips are connected after the cutoff is written down, not instead of it. You can play online on a virtual balance before that note: a guest account moves neither the floor nor the step of one unit.
One even stretch of eight spins
Below is a teaching sequence of four losses and four wins. The letter in the result column is the outcome of an even chance, not a pocket number. The bet of the next spin is already accounted for in the row below. The result accumulates from zero.
| Spin | Bet | Outcome | Result of the series | Next bet |
|---|---|---|---|---|
| 1 | 5 | loss | −5 | 6 |
| 2 | 6 | loss | −11 | 7 |
| 3 | 7 | win | −4 | 6 |
| 4 | 6 | loss | −10 | 7 |
| 5 | 7 | win | −3 | 6 |
| 6 | 6 | win | +3 | 5 |
| 7 | 5 | win | +8 | 4 |
| 8 | 4 | loss | +4 | 5 |
Four wins and four losses ended at +4. While the bet has not hit the floor, each pair of “one loss and one win” leaves plus one unit. That is a property of the step, not a property of the wheel. On 38 pockets there will be fewer wins than losses: 20 unfavorable pockets, 18 favorable ones. An even score in a long session is not the basic scenario.
What bankroll a series of eight losses asks for
Eight losses in a row from a start of 5 require bets of 5, 6, 7, 8, 9, 10, 11 and 12. The sum is 68. The next bet would have been 13. Doubling from one chip over the same eight steps stakes 128 and by this step has already lost 127. Fibonacci on the eighth step stakes 21 and accumulates 54. D’Alembert here is the quietest in the size of the chip and the longest in the number of spins needed to climb out of the hole.
| Method | Bet on the 8th losing step | Lost over 8 losses | What one next win does |
|---|---|---|---|
| A step of one unit, start 5 | 12 | 68 | returns 12, the minus becomes 56, the bet falls to 11 |
| A Fibonacci row, start 1 | 21 | 54 | erases the last two steps, not the whole minus |
| Doubling, start 1 | 128 | 255, if this loss is also staked | closes the whole cycle at +1, if the bet is still accepted by the table |
The doubling row in this table counts eight lost bets from 1 to 128, a sum of 255. One win instead of the eighth loss would have been a bet of 128 after a loss of 127 and would have closed the cycle at +1. These two outcomes must not be mixed up: in the comparison above the eighth spin has already lost.
The share of American roulette does not depend on the step
On the RoulCoin wheel a color on average gives up 5.26 units per 100 staked. On a single zero the same bet gives up 2.70. French roulette with the la partage rule lowers the loss of an even chance to about 1.35 per 100, because zero takes half, not the whole stake. A step of plus or minus one chip does not rewrite these three numbers. It only decides in what pieces the minus arrives in the bankroll.
| Condition of the even chance | Loss per 100 units of turnover | Does a step of ±1 change it |
|---|---|---|
| 18 winning pockets out of 38 | 5.26 | no |
| 18 out of 37, zero takes the stake in full | 2.70 | no |
| 18 out of 37, zero returns half | 1.35 | no |
So the limit is set not on a “handsome plus of a four,” but on depth. A reasonable cutoff for a start of 5 is a bet of 15 or a minus sum of 100, whichever comes first. After the cutoff the series closes, even if the formula asks for 16. Adding a new batch of chips into the same series cancels the cutoff.
Plus one unit per pair of spins is visible only with an equal number of wins and losses. Two extra zeros on an American wheel make losses more frequent than wins.
How not to mix up the step if you play online
In England a color on this table is counted the same way as on any other American wheel: 18 against 20. The player writes down the current bet before the spin, not after the animation. A loss is plus one unit to the next bet. A win is minus one, but not below the floor. A new series starts only when the bet has returned to the starting 5 and the previous result has been recorded separately.
A teaching run on virtual chips shows how slowly a minus of 68 crawls back. Playing online for free in guest mode is enough for such a run. Playing online for money makes sense after one fully written series up to the cutoff. Playing with crypto is possible through a deposit to the cashier: the choice of coin does not add winning pockets.
Before a series, four numbers are fixed:
- The start, in this account it is 5.
- The floor, below which the bet does not fall: 1.
- The bet ceiling, for example 15, strictly below the table maximum.
- The minus ceiling, for example 100 units, after which the series closes on that same spin.
Why frequent wins at the start spoil the expectation
Three wins from a start of 5 give bets of 5, 4 and 3 and a profit of 12, after which the bet is already 2. The next long black streak starts from a two, not from a five, and seems harmless. Up to a bet of 12 such a streak still requires tens of units. An early plus is not a cushion if it stays on the table and keeps spinning in the same series.
What to do if the bet is already 1 and a win comes up again?
Leave 1. There is nowhere to subtract, this is the floor. On this spin the series received plus one unit and did not grow. The next loss will raise the bet to 2. There is no need to pretend that the floor “resets the cycle to zero”: the previous result has not gone anywhere.
Should two units be added after zero?
No. Zero for a color is an ordinary loss, the same as the other color. A separate penalty for 0 or 00 breaks the pair “plus one / minus one” and inflates the bet without new information about the wheel.
What changes if one starts from 10 rather than from 5?
The pair still leaves plus one unit, while the bet is above the floor. Eight losses in a row now cost 10+11+…+17, that is 108, not 68. The table’s share per 100 units of turnover remains 5.26.
How much does one win return after a minus of 68?
The next bet in that example is 13. A win reduces the minus to 55 and lowers the next bet to 12. These 13 units do not bring the series to zero.
Can the floor be lowered below one chip?
No. Zero chips is a skipped spin, not a bet. On the teaching table the lower bet is the floor: 1. A win on this bet leaves it equal to 1, and does not zero out the result accumulated earlier.
D’Alembert keeps the bet near the start longer than doubling does, and that is exactly why it is easy to drag out. Next to it, it is useful to look at other playing strategies, and the step itself should first be taken to the minus ceiling on teaching chips. For that it is enough to play online without signup and write down the same eight rows as in the table above, with one’s own results.