roulette

Hello, first post but I have been reading for a while.

I have a roulette question to settle a bit of a friendly argument with a friend. Let me explain.

Let's say we have a sample of 100 million spins of a double zero roulette wheel betting on red or black or any other even money bet. With the house edge being 5.26% the expected loss is 5,260,000. The confidence intervals at 2 standard deviations are a loss of 5,280,000 (-5.28%) to a loss of 5,240,000 (-5.24%). For a sample of 1 million spins the confidence intervals I calculate are -5.48% to -5.06%.

I say to him that it doesn't matter from where in that 100 million sample you pick out your 1 million spins, you are still going to achieve a result of -5.06% to -5.48% 95% of the time. He argues that the result may be different or skewed if you selected it after a run of reds or blacks (or any other even money proposition). Whereas I believe I am correct in stating that it doesn't matter if you selected 1 million consecutive spins, every 10th spin, every 100th spin, every spin after you see 5 reds or 5 blacks. I argue that with a sample that large (ie 1 million) that it just doesn't matter and that believing that you'll get a better result by selecting a spin after a run of reds or blacks is something akin to gambler's fallacy.

What do you think?

I can not answer this until I know if he will be betting red or black !

As long as you do not cherry-pick spins because of their own outcome, it does not matter.

But I always bet on red, and I win every session.

Hi. Nice 1st post. Do you and your friend now agree?

Quote: vegas99

Let's say we have a sample of 100 million spins of a double zero roulette wheel betting on red or black or any other even money bet. With the house edge being 5.26% the expected loss is 5,260,000.
The confidence intervals at 2 standard deviations are a loss of 5,280,000 (-5.28%) to a loss of 5,240,000 (-5.24%).
For a sample of 1 million spins the confidence intervals I calculate are -5.48% to -5.06%.

Your math to me appears to be a little off for the 1 million.
here is what I get.
100 million (100,000,000)
HE = -2/38
EV = -5,263,158
1SD = SQRT(18/38*20/38*100million) = 4993.07
2SD = 9986.14

-5,273,144 (-5.27%)
-5,263,158
-5,253,172 (-5.25%)
OK. we close enough for the 100 million

1 million (1,000,000)
HE = -2/38
EV = -52,632
1SD = SQRT(18/38*20/38*1million) = 499.31
2SD = 998.61

-53,630 (-5.36%)
-52,632
-51,633 (-5.16%)

Quote: vegas99

I say to him that it doesn't matter from where in that 100 million sample you pick out your 1 million spins, you are still going to achieve a result of -5.06% to -5.48% 95% of the time.
What do you think?

-5.16% to -5.36%, 95.45% of the time. I now agree with you.
I also agree that is does not matter where the million spins come from.