Example

set.seed(1)
mys=sample(c(-1,1),500, prob=c(20/38, 18/38), replace=T)
plot(cumsum(mys), type='l')

mys2=sample(c(-1,35), 500, prob=c(37/38, 1/38), replace=T)
plot(cumsum(mys2), type='l')