I am trying to calculate the probability of reaching n successes on a trial, knowing that a failure will increase success chance.
In simpler term, what is the mean number of trials before we reach $x$ successes with $p = min(y + wF, 1)$? (with $F$ being the number of failures)
This does include the fact that after a certain number of failures, success is guaranteed ($p>1$).
I've tried to inspire myself from this question, but I don't want $F$ to reset upon success.