**Roulette – An Analysis**

Roulette is played by spinning a ball around a wheel. The wheel contains 37 to 38 numbered pockets from 0 to 36 for a 37-numbered wheel and 00 and 0 to 36 for a 38-numbered wheel.

The winning number is decided by which numbered pocket the ball comes to rest on. Payment is then made based on where a player has wagered on a layout displaying all the numbers on the wheel.

This table assesses the wagers for Single-Zero (European) Roulette:

European Roulette (Single Zero) | |||||

Wager | Numbers covered | Probability (Win) | Probability (Loss) | Expectation | Break-even odds |

Straight Up | 1 | 0.02703 | 0.97297 | -0.94595 | 36.00 |

Split | 2 | 0.05405 | 0.94595 | -0.89189 | 17.50 |

Street | 3 | 0.08108 | 0.91892 | -0.83784 | 11.33 |

Corner | 4 | 0.10811 | 0.89189 | -0.78378 | 8.25 |

6-Line | 6 | 0.16216 | 0.83784 | -0.67568 | 5.17 |

Dozen | 12 | 0.32432 | 0.67568 | -0.35135 | 2.08 |

Column | 12 | 0.32432 | 0.67568 | -0.35135 | 2.08 |

Small (1-18) | 18 | 0.48649 | 0.51351 | -0.02703 | 1.06 |

Big (19-36) | 18 | 0.48649 | 0.51351 | -0.02703 | 1.06 |

Red | 18 | 0.48649 | 0.51351 | -0.02703 | 1.06 |

Black | 18 | 0.48649 | 0.51351 | -0.02703 | 1.06 |

Even | 18 | 0.48649 | 0.51351 | -0.02703 | 1.06 |

Odd | 18 | 0.48649 | 0.51351 | -0.02703 | 1.06 |

This table assesses the wagers for Double-Zero (American) Roulette:

American Roulette (Double Zero) | |||||

Wager | Numbers covered | Probability (Win) | Probability (Loss) | Expectation | Break-even odds |

Straight Up | 1 | 0.02632 | 0.97368 | -0.94737 | 37.00 |

Split | 2 | 0.05263 | 0.94737 | -0.89474 | 18.00 |

Street | 3 | 0.07895 | 0.92105 | -0.84211 | 11.67 |

Corner | 4 | 0.10526 | 0.89474 | -0.78947 | 8.50 |

6-Line | 6 | 0.15789 | 0.84211 | -0.68421 | 5.33 |

Dozen | 12 | 0.31579 | 0.68421 | -0.36842 | 2.17 |

Column | 12 | 0.31579 | 0.68421 | -0.36842 | 2.17 |

Small (1-18) | 18 | 0.47368 | 0.52632 | -0.05263 | 1.11 |

Big (19-36) | 18 | 0.47368 | 0.52632 | -0.05263 | 1.11 |

Red | 18 | 0.47368 | 0.52632 | -0.05263 | 1.11 |

Black | 18 | 0.47368 | 0.52632 | -0.05263 | 1.11 |

Even | 18 | 0.47368 | 0.52632 | -0.05263 | 1.11 |

Odd | 18 | 0.47368 | 0.52632 | -0.05263 | 1.11 |

**Wager **lists the specific wager type players can make on the layout.

**Numbers covered** indicates how many numbers the wager will be counted to be wagered on. If the ball rests on any of the numbers covered by this wager, the wager is paid.

**Probability (Win)** indicates the probability that this wager will win. This is calculated by:

**= Numbers covered/total numbers on the layout **(37 for Single-Zero and 38 for Double-Zero)

Example:

For a Corner (Single-Zero) wager, 4/37 = 0.10811

**Probability (Loss) **indicates the probability that the wager will lose. The calculation for this is 1-Probability (Win).

Example:

For a Street (Double-Zero) wager, 3/38 = 1-0.07895 = 0.92105

**Expectation **is the Probability (Win) – Probability (Loss).

Example:

For a Street (Double-Zero) wager, 0.07895 – 0.92105= -0.84211

**Break-even odds **indicates the odds at which the expectation for the house is 0. The house should ALWAYS pay BELOW these odds to maintain a positive expectation.