One strategy is to always bet "red". what is p (red) ? define x=#red in 38 spins. what is the probability you'll break even by betting on red-only in 38 spins? that is, what is p (19 red in 38 spins) ?

Either you get "red" or you don't. That's binomial. The probability of getting "red" is 1/2, same as the probability of getting "black."

So we have a binomial probability distribution with n=38, p=1/2 and x = 19.

Using the binompdf (function built into my TI-83 calculator, I get

binompdf (38, 1/2, 19) = 0.129 (answer)