sd on roulette
What is the standard deviation on a round of single zero roulette, betting a single number straight up? What about betting n (n>1) numbers straight up on a single round?
What is the standard deviation on a round of single zero roulette, betting a single number straight up? What about betting n (n>1) numbers straight up on a single round?
What is the standard deviation on a round of single zero roulette, betting a single number straight up?
You will have 1 win at +35 and 36 losses at -1. The formula for SD is sqrt(sum((mean(x)-x)^2)/n).
mean(x) = (35+36*-1)/37 = -1/37
sum((mean(x)-x)^2) = 36*(-1/37-1)^2+(-1/37+35)^2 = 37.97 + 1223.11 = 1261.08.
SD = sqrt(1261.08/37) = 5.84
What about betting n (n>1) numbers straight up on a single round?
The general formula for n bets:
mean(x)=-n/37
SD = sqrt(((37-n)*(-n/37-n)^2+n*(-n/37+36-n)^2)/37)
Plugging that into a spread sheet, I get the following values:
1: 5.84
2: 8.14
3: 9.83
4: 11.18
5: 12.31
6: 13.27
7: 14.10
8: 14.83
9: 15.45
10: 16.00
11: 16.47
12: 16.86
13: 17.20
14: 17.48
15: 17.69
16: 17.86
17: 17.96
18: 18.02
19: 18.02
20: 17.97
21: 17.87
22: 17.71
23: 17.50
24: 17.24
25: 16.91
26: 16.51
27: 16.05
28: 15.52
29: 14.90
30: 14.19
31: 13.37
32: 12.43
33: 11.32
34: 10.00
35: 8.36
36: 6.15
37: 2.00
I think he is asking about making n bets in parallel, and I think that is what you answering. And it looks like your numbers are in the right ballpark, at least for small N.
But for N=37, I think your SD should be 0. If you bet 37 numbers, aren�t you guaranteed to win 1, and lose 36?
If there is a mistake in the formula, it might be where you subtracted the Mean^2?
WHen I want cover for a free drink, I bet the min, half each on red/black (or odd/even) on Roulette. Most of the time the drink is free, once in a while it costs a min bet. I get very strange looks, but this seems to be the best choice for drinks of any game in the casino for low variance.
--Eliot
You're right, I had a error in the subtraction of the mean.
The general formula for n bets should be:
mean(x)=-n/37
SD = sqrt(((37-n)*(-n/37+n)^2+n*(-n/37-36+n)^2)/37)
1, 36: 5.84
2, 35: 8.14
3, 34: 9.83
4, 33: 11.18
5, 32: 12.31
6, 31: 13.27
7, 39: 14.10
8, 29: 14.82
9, 28: 15.45
10, 27: 15.99
11, 26: 16.45
12, 25: 16.85
13, 24: 17.19
14, 23: 17.46
15, 22: 17.67
16, 21: 17.83
17, 20: 17.94
18, 19: 17.99
37: 0.00
Come on! You have an excellent job and are afraid of the risk with minimum bets?! It costs only half as much to bet on red or black. And it costs even less to play blackjack or craps. At a $5 minimum bet it costs you around $.50 per spin, so you could easily pay $5.00 (10 spins) for your drink. You may as well buy it.
