Don't bother simulating rolls, just multiply the value of each possibility by the odds of reaching it, and hope you've got a converging series.

For the simple case of a chance of stopping at each integer, its pretty simple.

∑ak = 1 / (1 - a)
For reasonable values of a, of course.

Also, ∑k*ak = a / (1 - a)2

As an example, for a 50/50 flip, you'll average two flips before losing.
0.5 / (1-0.5)2 = 0.5 / (0.52) = 0.5 / 0.25 = 2

In reply to Re: Average random depth formula required by SuicideJunkie
in thread Average random depth formula required by palkia

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