You are not logged in.
Pages: 1
Hi bobbym,
Thanks for the reply. I must admit I'm a bit confused now. Perhaps what I need to do is divide by the average stake because the -0.027 applies to the amount returned PER UNIT staked? In that case I'm unsure what the average stake is in this case.
But then, thinking about it that can't be right because the average stake would be between $1 and $2, and to get -0.027 from -0.0697 I would need to divide by about 2.5.
Hi folks,
I'm trying to solve a problem on expectation and the answer I'm getting isn't what I think it should be; can anyone see where I'm making a mistake?
The problem concerns roulette where the probability of a win on the even chances is 18/37 and a loss is 1 - 18/37 = 19/37. Roulette has a negative mathematical expectation of -1/37 and all expectations of various bets should result in this.
Suppose I bet on Red for two spins and use a betting scheme where I raise the bet from $1 to $2 after a loss. The possibilities are (W = win and L = loss):
WW probability: (18/37)^2 gain: +$2
WL probability: (18/37)*(19/37) gain: $0
LW probability: (19/37)*(18/37) gain: +$1 (-$1, then bet $2 and win)
LL probability: (19/37)^2 gain: -$3 (-$1, then bet $2 and lose)
The expectation is
E(X) = (18/37)^2*2 + (18/37)*(19/37)*0 + (19/37)*(18/37)*1 + (19/37)^2*(-3) = -0.0697
But it should be -0.027 (equivalent to -1/37)
Thanks in advance.
Pages: 1