I'm not a mathematician, so my question may be not so clear, sorry.

Let's say we toss up an ideal coin and win 1 dollar on heads and lose 1 dollar on tails. So, expected value is M = 1×0.5 − 1×0.5 = 0. It may be interpreted as: we will gain/lose nothing playing a game for a long time. It is pretty clear.

Now, let's consider bankroll size. It will be changed on every coin flip. For *Heads Tails Tails Tails Heads* sequence, bankroll size will be 1, 0, -1, -2, -1 dollar. As I understand, bankroll size is a random variable. Is it even possible to evaluate this random variable somehow? How to calculate expected value and variance? May I evaluate minimum and maximum of bankroll size?

Thanks