Betting Game (1)

It is fairly straightforward to calculate what the winnings might be in a simple betting game.
Let us postulate an urne containing 4 balls, three white and one black. Balls are put back into the jar after each draw. Tickets are $10 each, and the payout is as follows :

Ball 1, white a loss, -10$
Ball 2, white a loss, -10$
Ball 3, white a loss, -10$
Ball 4, black a win, +10$

If a white ball is drawn, I loose. If the black ball is drawn, I am given 20$, a 10$ win after the recovery of my ticket price. On average, I expect to loose 5$ per draw. I never actually loose 5$; this is an average.

If I bet for 20 consecutive draws, I would then expect to loose 100$.

I am a betting kind of person. Would I expect to loose precisely 100$ on 20 draws; could I bet on this. Not really. 5$ is the money average loss of the system. But the outcome choices are three white and one black. To take this into account, I need to calculate the error this introduces to my money expectations.