Calculating SD
Take each member of the population, square the difference between it and the mean of the population, and multiply by its probability. The sum of these values is the variance. The square root of the variance is the standard deviation.
50-1 with probability 0.01,
25-1 with probability 0.01,
10-1 with probability 0.02,
Lose with probability 0.96.
The expectation is 0.01*50 + 0.01*25 + 0.02*10 + 0.96*(-1) = -0.01.
You have 4 different results. The mean result is -.01.
[50 - .01]^2 * .01+
[25 - .01]^2 * .01+
[10 - .01]^2 * .02+
[-1 - .01]^2 * .96=
Variance
Again, the sqrt of the variance is the SD. I don't think that you will have a normal distribution here. This means the mean may not be the median, and one SD to the right may not be the 84 percentile.