Candy Crush have recently introduced a new "feature" where by watching an ad you can get to spin a wheel to get extra moves (you used to have to "pay" for it).
This option pops up if you fail to complete the level in the allotted moves.
You spin a wheel which has 8 possible outcomes. 4 of them give you extra moves and 4 do not. Out of the 4 that do, one gives you 15 extra moves and three give you five.
If you still fail to complete the level you will again get the same "offer" and so on.
Assuming that the probability of hitting any of the outcomes is the same and that I never manage to finish the level, what would be my expected number of extra moves on any one level?
TBH, I have no idea even where to start.
Edit:
If you do NOT win extra moves then the level is over and you have failed.
The expected number of extra moves is $7.5$. Assume that the expected value is $E(X) \in \mathbb{R}$. We then know that we either get $+5$ extra moves and then continue to achieve $E(X)$ extra moves (as expected) or we get $+15$ extra moves and then achieve $E(X)$ extra moves each with $\frac{3}{8}$ and $\frac{1}{8}$ chances respectively. Thus we have: $$E(X) = \frac{3}{8} (5+E(X)) + \frac{1}{8} (15+E(X))$$ $$\therefore E(X) = \frac{15}{2} = 7.5$$