Re: Am I stupid? I can\'t fit these two concepts into any type of harmony.
I think this is tricky but I don't remember exactly how to handle it. It should be easy for the practicing mathematicians around here.
It's true that an event with low probabilty will occur infinitely many times given an infinte sequence of trials. However, a sequence of events whose non-zero probabilities become smaller and smaller might not occur infinitely many times given an infinite sequence of trials. Your problem has that flavor because as time goes on and you build up more winnings your element of ruin gets smaller.
PairTheBoard
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