Recent content by Boxcar Billy

I'm confused too. I understand the Martingale condition, but why must that imply P(S_{n+1} = 0| S_{n} = 0) = 1? If P(S_{n+1} = -1 | S_{n} = 0) = 0.5 and P(S_{n+1} = 1 | S_{n} = 0) = 0.5 then the Martingale condition still holds because the expected value is still 0. Is this right or am I...