Hey all. Wondering if you can help me out with the chances of winning in a round of N spins in a modified game of roulette
THE GAME
15 numbers, red/black and green
0 : GREEN
1-7 : RED
8-14 : BLACK
Chances of getting red/black = (7/15)
Chances of getting green = (1/15)
THE STATEGY
To bet one color (red/black) until you get that color, then switch to the other color
The first thing I want to calculate is the chance of getting to spin N and winning on spin N. Say for this example N = {1,2,3}.
I hope this makes sense, but I think that the chance of getting to and winning on spin N should be (the chance of getting to spin N) * (the chance of winning on spin N)
The chance of getting to spin N = (8/15)^(n-1)
The chance of winning on spin N once you are on spin N = (7/15)
So the chance of getting to and winning on spin N = (8/15)^(n-1)*(7/15)
S1 = The chance of winning on the first spin = 1*(7/15) = 0.46666667
S2 = The chance of winning on the second spin = (8/15)*(7/15) = 0.248888888
S3 = The chance of winning on the third spin = (8/15)^2*(7/15) = 0.132740741
Please correct me if this is wrong
So the next thing I'm trying to figure out is the chance of you winning in a round of N spins. So for this example N = 3. This is where I am unsure how to calculate your chance of winning. Do you simply just add up the chances?
So your chance of winning in 3 spins would simple be S1 + S2 + S3 = 0.848296291 = 84.83%
Does this all make sense?
Thanks in advance
THE GAME
15 numbers, red/black and green
0 : GREEN
1-7 : RED
8-14 : BLACK
Chances of getting red/black = (7/15)
Chances of getting green = (1/15)
THE STATEGY
To bet one color (red/black) until you get that color, then switch to the other color
The first thing I want to calculate is the chance of getting to spin N and winning on spin N. Say for this example N = {1,2,3}.
I hope this makes sense, but I think that the chance of getting to and winning on spin N should be (the chance of getting to spin N) * (the chance of winning on spin N)
The chance of getting to spin N = (8/15)^(n-1)
The chance of winning on spin N once you are on spin N = (7/15)
So the chance of getting to and winning on spin N = (8/15)^(n-1)*(7/15)
S1 = The chance of winning on the first spin = 1*(7/15) = 0.46666667
S2 = The chance of winning on the second spin = (8/15)*(7/15) = 0.248888888
S3 = The chance of winning on the third spin = (8/15)^2*(7/15) = 0.132740741
Please correct me if this is wrong
So the next thing I'm trying to figure out is the chance of you winning in a round of N spins. So for this example N = 3. This is where I am unsure how to calculate your chance of winning. Do you simply just add up the chances?
So your chance of winning in 3 spins would simple be S1 + S2 + S3 = 0.848296291 = 84.83%
Does this all make sense?
Thanks in advance
