Question about slot machine odds

Hi Everyone,

I have a question regarding slot machine odds, in particular the one posted on /games/slots/atkins-diet/ made by the Wizard himself. I was wondering if anyone could explain to me why the expected value for the free spins is calculated using 10/(1-10*0.011185).

I would like to know where that formula came from and/or how it is derived. I understand usually expectation values for discrete variables is just calculated by the weighted sums but I am sure there is something different here as there is some sort of probabilistic recursion occuring.

Thank you!

Exactly. This is an infinite series to sum the number of free games.

Each free game has the chance of re-initiating 10 new games with a probability of 0.011185. The total number of games is 10 + 10*(0.011185*10) + 10*(0.011185*10)^2 + 10*(0.011185*10)^3 ...