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April 24th, 2018 at 4:13:38 AM permalink
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!
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April 24th, 2018 at 6:04:54 AM permalink
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 ...
I heart Crystal Math.
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