You could turn it around and say, assuming I eventually succeed, what's the distribution of failures I'd have to
endure? You might get lucky, but it's definitely possible to quantify how long it would most probably take to succeed.
If you have a bunch of people tossing dice and stopping when they roll a 1, only ~1/6 will succeed immediately. Most people will take a few tries; a few will take many tries; there's a nonzero chance you will wait forever without a success.
That's not to say that a success gets more likely with time (the Gambler's Fallacy) but on the whole, you'd expect most successes to have some prior failures, unless the dice are rigged.
> it’s definitely possible to quantify how long it would most probably take to succeed
yes.
if success means to roll a 1, and anything else is a failure, you will on average roll the die 6 times before you succeed. E(x) = 1/p for a geometric with p = 1/6. your variance is q/p^2, so 30.
so then, my rational decision as an investor is to quit rolling the die after 17 rolls ( mu + 2 sd = 6 + 2*sqrt(30) = 17 ). I wouldn’t wait until heat death of universe.
If you have a bunch of people tossing dice and stopping when they roll a 1, only ~1/6 will succeed immediately. Most people will take a few tries; a few will take many tries; there's a nonzero chance you will wait forever without a success.
That's not to say that a success gets more likely with time (the Gambler's Fallacy) but on the whole, you'd expect most successes to have some prior failures, unless the dice are rigged.