American roulette gives a color 18 pockets out of 38. European roulette, in the same comparison, gives 18 out of 37. The 1-3-2-6 system stakes four chips in turn: 1, then 3, then 2, then 6. Any loss breaks the series and returns the next bet to 1.
The bet goes on an even chance: Red or Black, Even or Odd, 1–18 or 19–36. The payout equals the amount staked. On the RoulCoin wheel there are 20 losing pockets, because 0 and 00 are added to the other color. The steps 1, 3, 2 and 6 are calculated only for that payout.
This is not doubling after a win. There, any broken step closes the series at minus 1. Here a loss on the second step costs minus 2, a loss on the third leaves plus 2, and a loss on the fourth brings the series to zero.
Five outcomes on American roulette
The “result” column is the money of the whole series, not of one spin. The shares on 38 pockets are rounded to hundredths. Beside them is the same series on 37 pockets: the shape of the result does not change, only the frequency does.
| How the series ended | Result | 38 pockets | 37 pockets |
|---|---|---|---|
| A loss on 1 | −1 | 52.63% | 51.35% |
| A win of 1, a loss of 3 | −2 | 24.93% | 24.98% |
| Then a loss on 2 | +2 | 11.81% | 12.15% |
| Then a loss on 6 | 0 | 5.59% | 5.91% |
| All four steps won | +12 | 5.03% | 5.60% |
Four wins in a row on a wheel of 38 pockets are (18/38)⁴, 5.03%, about one series out of 20. On 37 pockets, 5.60%. A check of the fourth step: +1+3+2−6 = 0. Plus 12 appears only if the bet of 6 won too.
How many of one’s own chips go into an average cycle
The first bet is placed always. The three is placed only after a win of the one, the two only after two wins, and the six only after three. On 38 pockets, about 3.51 units go onto the table per series on average. The expectation of a series is about −0.18. Over 100 such series the table takes about 18.5 units.
| Step | Bet | When it is placed | Result of the series if the step is lost |
|---|---|---|---|
| 1 | 1 | always | −1 |
| 2 | 3 | after a win on 1 | −2 |
| 3 | 2 | after wins on 1 and 3 | +2 |
| 4 | 6 | after three wins | 0 |
On 37 pockets four wins are a little more frequent, and the minus of a series is smaller. The average stake there is a little higher, because the six is reached more often.
| Wheel | Four wins | Average stake of a series | Expectation of one series | Over 100 series |
|---|---|---|---|---|
| 38 pockets | 5.03% | about 3.51 | −0.18 | about −18.5 |
| 37 pockets | 5.60% | about 3.62 | −0.10 | about −9.8 |
Per 100 staked an American wheel takes 5.26, and a European wheel takes 2.70. The series does not cancel this share: −0.18 is exactly 5.26% of the average 3.51 units. On 37 pockets the same check gives about −0.10 from an average stake of 3.62.
The worst result of one series played out is minus 2, on the second step. Plus 12 happens in about one series out of 20 and does not cover this minus.
Where to write down the reset if you play online
For a player in England the four steps do not depend on the city. 18 winning pockets out of 38 are the same in any time zone. The series is worth writing down before the spin: after a win on the two, the next bet is 6, not 2 again.
French roulette with half the stake returned on zero does not soften these results. On the RoulCoin wheel 0 and 00 take the chip in full and break the series the same way as the other color. Playing online without registration is possible on a virtual balance: guest chips do not turn into a withdrawal, and the four steps are visible on them at once.
- A loss on any step returns the bet to 1. The series is not “pushed” with the six after a loss.
- A win of the six also returns the bet to 1. Plus 12 does not become the new first chip in the same cycle.
- Step 3 equals 2, not 4. This is not a doubling ladder.
- The table ceiling almost never gets in the way of these four numbers. Another series gets in the way, if minus 1 and minus 2 have already piled up.
Why zero on the fourth step is not equal to a win
A result of 0 means that the bets 1, 3 and 2 won, and 6 lost. The bankroll has returned to the starting mark, but four spins have already been played. The next series starts from one unit again and again has an expectation of about −0.18.
Does a loss of the bet of 3 take three units from the bankroll?
No. The series closes at −2. The first bet has already given +1, and the three takes that plus together with two more units.
If the bet of 6 lost, is the series in the minus?
No, at zero: +1+3+2−6 = 0. A minus appears on the first step (−1) and on the second (−2).
Do four wins come up more often than one series out of ten?
No. On 38 pockets that is 5.03%, about one series out of 20. On 37 pockets, 5.60%. Plus 12 stands only behind this outcome.
Do the same steps suit a Dozen?
No. A Dozen pays 2 to 1 and covers 12 pockets out of 38. The steps 1, 3, 2 and 6 come out even only at a payout equal to the bet.
Four short steps are easy to take for a limit on the loss: one series does not fall below minus 2. Neighboring playing strategies limit a series differently, and the expectation of all of them sits in the table’s share, not in the order of the numbers. The steps are worth running on paper before the first live unit.