American roulette ends this session on 0 or on 00. European roulette under the same rule ends it on one zero. While the ball is colored, the same chip sits on Red. The first green pocket takes it and closes the session. Nothing is staked after that.
Until green, every spin is an even chance. There are 18 each of Red and Black, and until the ball is green these 36 split in half. So the spins before the last one on average bring nothing and take nothing. The last spin is always −1. The expectation of the whole session is exactly minus 1, not “about.”
The average length is 19 spins: 18 colored and one green. Minus 1 on 19 staked is 1/19, the same 5.26 per 100. The stopping rule does not reduce the share. It gathers that share into one last chip.
Why the minus equals one unit
The number of colored spins before the first green averages 18. On them Red wins and loses equally often, because among the 36 non-green pockets red and black are equal in number. The sum of those spins averages 0. The green spin adds −1, and the betting ends there.
| Part of the session | How many spins on average | Expected result |
|---|---|---|
| Red, while there is no 0 and 00 | 18 | 0 |
| The first 0 or 00 | 1 | −1 |
| The session as a whole | 19 | −1 |
A single session almost never equals this average. Color before zero can run to +8 or to −8, and then green takes one more unit. The average over many sessions is still −1. The plus of one lucky series does not cancel the next one, which again has to end on green.
How often a session is shorter than 19 spins on American roulette
The chance of green on one spin is 2/38. A session of only one spin, immediately −1, happens in 5.26% of cases. By the 19th spin green has already appeared in about 64.20% of sessions. In the other 35.80%, neither 0 nor 00 appeared in the first 19 spins, and the bet is still going.
| What happened | Share of sessions | Result at this point |
|---|---|---|
| Green on the first spin | 5.26% | −1, there were no colored spins |
| Green no later than the 19th spin | 64.20% | the colored stretch plus −1 |
| No green in 19 spins | 35.80% | the session is not closed yet |
A long session without zero is not a sign that the rule has turned positive. It is the tail of the same share 2/38. When green does come up, it takes one chip on top of whatever the colors have won or lost.
One zero and half the stake
On 37 pockets there is one green, with a chance of 1/37. Colored spins before it average 36, and they are again zero on average: among the non-green pockets there are 18 each of red and black. The last spin is −1. The session expectation is again exactly minus 1, but the average length is already 37 spins. Minus 1 on 37 staked is 2.70 per 100.
| Wheel and the zero rule | Average length | Session expectation | Per 100 staked |
|---|---|---|---|
| 38 pockets, zero takes the chip | 19 | −1 | 5.26 |
| 37 pockets, zero takes the chip | 37 | −1 | 2.70 |
| 37 pockets, zero returns half | 37 | −0.5 | about 1.35 |
French roulette with half returned on zero would leave the last spin at −0.5, not −1. On the RoulCoin wheel there is no such return, and there are two zeros, so the average session is shorter: 19 spins, not 37. For a player in England, 00 closes the session exactly as 0 does. The city does not stretch it out to a European 37 spins.
Colors before zero on average come out at zero. A session on average loses one chip — the one the first green pocket takes.
Where to write down the end if you play online
The end is the first 0 or 00, not “one more spin, because the colored run is ahead.” If you start again after green, that is already a new session with its own expectation of −1. The cashier can accept a coin so you can play with crypto, but the exchange rate does not push the green pocket away and does not turn the last spin into zero.
- The chip neither grows nor falls before green.
- Both 0 and 00 close the session. Waiting specifically for 0 while skipping 00 is a different rule.
- A plus on the colored stretch does not cancel the stop. Green still writes off one unit.
- A new session after zero is counted separately, not as the tail of the old one.
Why a long plus before zero is not the profit of the rule
Ten reds in a row before green give +10, then −1, a result of +9. Ten blacks give −10 and another −1, a result of −11. On average such stretches cancel each other, and −1 remains. What is easy to remember is plus 9. Minus 11 arrives with the same frequency of the colored coin.
Can a session end ahead?
Yes, if colored wins before green outnumbered colored losses, and that surplus is greater than the one unit green will take. The average across sessions is still −1.
Why is the expectation exactly minus 1, and not minus 5.26?
Minus 1 is the result of one session. 5.26 is the same loss per 100 staked. The average session stakes 19 units, and 1/19 equals 5.26 per 100.
Does 00 not count as the end if you were waiting for 0?
In this rule it does count. Both green pockets close the session. Leaving the chip after 00 is no longer “until the first zero.”
On a single zero, does a session also cost minus 1?
On average yes, if zero takes the chip in full. The length is then about 37 spins, not 19. Half the stake on zero would lower the expectation to −0.5. On the RoulCoin wheel the stake burns in full.
Stopping on the first green makes the minus short and clear: one chip at the end. Neighboring playing strategies stretch the same minus into a ladder or a rare plus. Here there is nothing to cover it between the zeros, because colors before zero on average pile up nothing.