American roulette pays 5 to 1 for a Line of six numbers. European roulette pays the same for the same Line: six numbers do not become more profitable because the wheel has one zero. Only the number of empty pockets changes, 32 out of 38 against 31 out of 37.
A Line on the table is two neighboring rows of three numbers each. For example, 1–6 or 13–18. A Line holds six pockets. A hit on any of them returns a profit of 5 and the chip itself. A miss, including 0 and 00, takes the chip in full. One Line wins in 6 spins out of 38, which is 15.79%, about one spin out of six.
Two Lines that do not share numbers cover 12 pockets. Below, that is 1–6 and 19–24, one unit on each. A hit on one gives a profit of 5 and takes the second chip: +4 net. A miss on both gives −2.
One Line and two on American roulette
The chips equal 1. Net is the difference from what was sitting on the Lines before the spin.
| Layout | Stake | Pockets | If one Line hits | If it misses |
|---|---|---|---|---|
| Only 1–6 | 1 | 6 | +5 | −1 |
| 1–6 and 19–24 | 2 | 12 | +4 | −2 |
Two Lines win in 12 pockets out of 38. The expectation of a spin with a stake of 2: 12/38 × (+4) + 26/38 × (−2) = −4/38, about −0.11. Per unit staked that is 5.26 per 100. One Line gives 6/38 × (+5) + 32/38 × (−1) = −2/38. The same share, a different chip.
A full pass of the pockets
If over 38 spins each pocket came up exactly once, one Line at one unit would give 6 wins of +5 and 32 losses of −1: 30 − 32 = −2. Two Lines would give 12 times +4 and 26 times −2: 48 − 52 = −4 with 76 staked. Minus 4 out of 76 equals minus 2 out of 38.
| Layout | Staked over 38 spins | Wins | Losses | Result |
|---|---|---|---|---|
| One Line at 1 | 38 | 6 × 5 = 30 | 32 × 1 = 32 | −2 |
| Two Lines at 1 | 76 | 12 × 4 = 48 | 26 × 2 = 52 | −4 |
Such a pass is a ruler. A live stretch of 38 spins almost never visits each pocket once, and a short stretch easily ends in a plus. The expectation of one Line is still −2 units per 38 staked, that is 5.26 per 100. On 37 pockets, one Line has 31 empty pockets, not 32, and the share falls to 2.70. The RoulCoin wheel does not remove 00.
Where a Line crosses itself
Lines 1–6 and 4–9 share the numbers 4, 5 and 6. That is no longer two independent fields. If 5 lands, both chips play, and the result will not be +4. Such pairs are not in the tables above. For a clean +4, the numbers of the two Lines must not repeat. On the table there are pairs that do not cross: 1–6 with 13–18, 1–6 with 19–24, 7–12 with 25–30, and others one block apart.
| Pair | Shared numbers | Pockets covered | A hit on one number of the pair |
|---|---|---|---|
| 1–6 and 19–24 | none | 12 | +4 net |
| 1–6 and 4–9 | 4, 5, 6 | 9 | not +4; both chips play |
In England, 0 and 00 do not belong to any Line of the numbers 1–36. Both remain a miss for one Line and for two. A time zone does not add a green pocket to six numbers.
Six numbers pay 5 to 1. Over 38 different pockets one such chip gives −2, not zero and not a plus.
How not to take a Line for a Dozen if you play online
A Dozen is 12 numbers and a payout of 2 to 1. A Line is 6 numbers and a payout of 5 to 1. On the layout they sit next to each other, and it is easy to place the chip on the wrong edge. Playing online for free, the cell can be checked on a virtual balance, without an account. Guest chips do not turn into a withdrawal.
- Before the spin, count the numbers. A Line has six of them, not twelve.
- Two Lines, for a result of +4, must not share a single number.
- 0 and 00 are a loss of the whole Line stake, with no half returned.
- After a miss the Line is not doubled, unless doubling is written down as a separate rule.
Why 5 to 1 is not more profitable than a color
A color over 38 different pockets also gives −2 on 38 units staked. A Line shows the same minus through a rarer plus of +5. The large payout offsets the empty spins exactly enough for the share per 100 staked to stay 5.26, and not enough for the minus to disappear.
Do two Lines that do not cross bring plus 5?
No, plus 4. A profit of 5 on the successful Line is reduced by the one unit lost on the second. The stake was 2.
Do Lines 1–6 and 4–9 cover 12 numbers?
No, nine. The numbers 4, 5 and 6 belong to both. If one of them lands, two chips play, and that is no longer the clean +4 from the table.
How often does one Line win?
In 6 pockets out of 38, which is 15.79%, about one spin out of six. 0 and 00 are not among these six.
On a European wheel, does a Line pay more?
No, the same 5 to 1. There is one fewer empty pocket, and the share per 100 staked equals 2.70, not 5.26. The RoulCoin wheel is 38 pockets.
Six numbers with a payout of 5 to 1 are easy to compare with a Dozen and to misjudge the plus. Neighboring playing strategies cover either 12 numbers at a payout of 2 to 1, or a color. Before the chip, it is worth naming the six numbers of the Line out loud, not the row that merely happened to be at hand.