Editing Roulette (section)

==Bet odds table==
The expected value of a $1 bet (except for the special case of top line bets), for American and European roulette, can be calculated as

:<math>\text{expected value} = \frac{1}{n} (36 - n) = \frac{36}{n} - 1,</math>

where ''n'' is the number of pockets in the wheel.

The initial bet is returned in addition to the mentioned payout: it can be easily demonstrated that this payout formula would lead to a zero [[expected value]] of profit if there were only 36 numbers (that is, the casino would break even). Having 37 or more numbers gives the casino its edge.

{| class="wikitable"
|-
! rowspan=2 | Bet name
! rowspan=2 | Winning spaces
! rowspan=2 | Payout
! colspan=2 | French
! colspan=2 | American
|-
! [[Odds]] against winning
! Expected value<br />(on $1 bet)
! [[Odds]] against winning
! Expected value<br />(on $1 bet)
|-
| 0
| 0
| 35 to 1
| 36 to 1
| −$0.027
| 37 to 1
| −$0.053
|-
| 00
| 00
| 35 to 1
|
|
| 37 to 1
| −$0.053
|-
| Straight up
| Any single number
| 35 to 1
| 36 to 1
| −$0.027
| 37 to 1
| −$0.053
|-
| Row
| 0, 00
| 17 to 1
|
|
| 18 to 1
| −$0.053
|-
| Split
| Any two adjoining numbers vertical or horizontal
| 17 to 1
| {{frac|17|1|2}} to 1
| −$0.027
| 18 to 1
| −$0.053
|-
| Street
| Any three numbers horizontal (1, 2, 3 or 4, 5, 6, etc.)
| 11 to 1
| {{frac|11|1|3}} to 1
| −$0.027
| {{frac|11|2|3}} to 1
| −$0.053
|-
| Corner
| Any four adjoining numbers in a block (1, 2, 4, 5 or 17, 18, 20, 21, etc.)
| 8 to 1
| {{frac|8|1|4}} to 1
| −$0.027
| {{frac|8|1|2}} to 1
| −$0.053
|-
| Top line (US)
| 0, 00, 1, 2, 3
| 6 to 1
|
|
| {{frac|6|3|5}} to 1
| −$0.079
|-
| Top line (European)
| 0, 1, 2, 3
| 8 to 1
| {{frac|8|1|4}} to 1
| −$0.027
| 
|
|-
| Double street
| Any six numbers from two horizontal rows (1, 2, 3, 4, 5, 6 or 28, 29, 30, 31, 32, 33 etc.)
| 5 to 1
| {{frac|5|1|6}} to 1
| −$0.027
| {{frac|5|1|3}} to 1
| −$0.053
|-
| 1st column
| 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34
| 2 to 1
| {{frac|2|1|12}} to 1
| −$0.027
| {{frac|2|1|6}} to 1
| −$0.053
|-
| 2nd column
| 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35
| 2 to 1
| {{frac|2|1|12}} to 1
| −$0.027
| {{frac|2|1|6}} to 1
| −$0.053
|-
| 3rd column
| 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36
| 2 to 1
| {{frac|2|1|12}} to 1
| −$0.027
| {{frac|2|1|6}} to 1
| −$0.053
|-
| 1st dozen
| 1 through 12
| 2 to 1
| {{frac|2|1|12}} to 1
| −$0.027
| {{frac|2|1|6}} to 1
| −$0.053
|-
| 2nd dozen
| 13 through 24
| 2 to 1
| {{frac|2|1|12}} to 1
| −$0.027
| {{frac|2|1|6}} to 1
| −$0.053
|-
| 3rd dozen
| 25 through 36
| 2 to 1
| {{frac|2|1|12}} to 1
| −$0.027
| {{frac|2|1|6}} to 1
| −$0.053
|-
| Odd
| 1, 3, 5, ..., 35
| 1 to 1
| {{frac|1|1|18}} to 1
| −$0.027
| {{frac|1|1|9}} to 1
| −$0.053
|-
| Even
| 2, 4, 6, ..., 36
| 1 to 1
| {{frac|1|1|18}} to 1
| −$0.027
| {{frac|1|1|9}} to 1
| −$0.053
|-
| Red
| 32, 19, 21, 25, 34, 27, 36, 30, 23, 5, 16, 1, 14, 9, 18, 7, 12, 3
| 1 to 1
| {{frac|1|1|18}} to 1
| −$0.027
| {{frac|1|1|9}} to 1
| −$0.053
|-
| Black
| 15, 4, 2, 17, 6, 13, 11, 8, 10, 24, 33, 20, 31, 22, 29, 28, 35, 26
| 1 to 1
| {{frac|1|1|18}} to 1
| −$0.027
| {{frac|1|1|9}} to 1
| −$0.053
|-
| 1 to 18
| 1, 2, 3, ..., 18
| 1 to 1
| {{frac|1|1|18}} to 1
| −$0.027
| {{frac|1|1|9}} to 1
| −$0.053
|-
| 19 to 36
| 19, 20, 21, ..., 36
| 1 to 1
| {{frac|1|1|18}} to 1
| −$0.027
| {{frac|1|1|9}} to 1
| −$0.053
|}

Top line (0, 00, 1, 2, 3) has a different expected value because of [[approximation]] of the correct {{frac|6|1|5}}-to-1 payout obtained by the formula to 6-to-1.

If ''[[en prison]]'' rules are used, the house edge on the 1:1 bets is reduced to 1.35%-1.38% on a single-zero wheel,<ref>{{cite web|first=Michael|last=Shackleford|publisher=wizardofodds.com|title=Roulette -- The Basics|url=https://wizardofodds.com/games/roulette/basics/|accessdate=2025-02-22}}</ref> and to 2.63% on a double-zero wheel.<ref>{{cite web|url=https://atlanticcityweekly.com/attheshore/nightlife/can-00-roulette-top-single-zero-it-depends-on-the-half-back-rule/article_30c020aa-c1ac-11ed-bc9a-57166a11fb0e.html|title=Can 00 roulette top single-zero? It depends on the half-back rule|first=John|last=Grochowski|publisher=Atlantic City Weekly|accessdate=2025-02-22}}</ref>