Bets · Inside bet · plein
Roulette Straight Up Bet
A roulette straight up bet puts a chip on a single number. The rarest win on the table and the largest payout, with the same 2.70% house edge as everything else.
covers
1 / 37
probability
2.70%
pays
35:1
house edge
2.70%
EV per $1
−$0.027
SD per $1
5.84
On the table · example: 17
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
2:1
2:1
2:1
1st 12
2nd 12
3rd 12
1–18
Even
Red
Black
Odd
19–36
On the wheel · between 25 and 34
Roulette straight up payout and probability
One pocket out of 37 wins: 1/37, or 2.70%. The casino pays 35:1. A fair payout on 37 pockets would be 36:1; the one missing unit is the house edge.
p(win) = 1/37 = 0.0270
EV per $1 = (1/37)(35) − (36/37)(1) = −1/37 = −$0.0270
EV per $1 = (1/37)(35) − (36/37)(1) = −1/37 = −$0.0270
Example stake
stake$10 on 17
if 17 hits (1/37)+$350 won, stake returned
if anything else (36/37)−$10
expected result per spin−$0.27
Variance
The expected loss is the same as on red, but the spread of outcomes is not. Per dollar staked, a straight-up bet has a standard deviation of about 5.84 against 1.00 for an even-money bet. Over 100 spins at $10, a red player is typically within ±$100 of expectation; a straight-up player is typically within ±$584.
straight up
5.84
corner (4)
2.84
red (18)
1.00
Characteristics
- Median session result is a steady loss; the mean is pulled up by rare 35:1 hits.
- The expected wait for a hit is 37 spins, and waits run longer than most people guess: after 37 spins there is still a 36% chance of no win.
- Table minimums for inside bets are usually lower per chip, but a minimum total across inside bets often applies.
- A straight up bet in roulette is called plein in French-style casinos.
Comic relief
The same expected loss as red, with a much wider spread.