Except, you can always use THAT logic. Quirrell always offers a safer deal on the next round anyway, so you hold off on accepting any of the deals at all, ever, and never start doubling. Quirrell eventually randomly stops and hands you a single Quirrell point, saying nothing.
At some point the cumulative probability of self-destruction drops below the probability of accidentally cashing out this round. If you’d trade off a probability of self-destruction against an equal probability of a bajillion points, you start doubling then.
Hmm. That is a good point, but there is a slight complication: You don’t know how frequently the cash out occurs. From earlier:
In all cases, you can assume that the small positive chance of Quirrell stopping is some very tiny 1/3^^^^^^^3, but as above, you don’t know this exact number.
It’s true that if you continually half the chance of destruction every round it will eventually be the right thing to do to start doubling, but if you don’t know what the cash out chance is I’m not sure how you would calculate a solid approach, (I think there IS a method though, I believe I’ve seen these kinds of things calculated before.) even though Quirrell has removed all unknowns from the problem EXCEPT the uncertain cash out chance.
It sounds like one approach I should consider is to try to run some numbers with a concrete cash-out (of a higher chance) and then run more numbers (for lower chances) and see what kind of slope develops. Then I could attempt to figure out what kind of values I should use for your attempt to determine the cash out chance (it seems tricky, since every time a cash out does not occur, you would presumably become slightly more convinced a cash out is less likely.)
If I did enough math, it does seem like it would be possible to at least get some kind of estimate for it.
At some point the cumulative probability of self-destruction drops below the probability of accidentally cashing out this round. If you’d trade off a probability of self-destruction against an equal probability of a bajillion points, you start doubling then.
Hmm. That is a good point, but there is a slight complication: You don’t know how frequently the cash out occurs. From earlier:
It’s true that if you continually half the chance of destruction every round it will eventually be the right thing to do to start doubling, but if you don’t know what the cash out chance is I’m not sure how you would calculate a solid approach, (I think there IS a method though, I believe I’ve seen these kinds of things calculated before.) even though Quirrell has removed all unknowns from the problem EXCEPT the uncertain cash out chance.
It sounds like one approach I should consider is to try to run some numbers with a concrete cash-out (of a higher chance) and then run more numbers (for lower chances) and see what kind of slope develops. Then I could attempt to figure out what kind of values I should use for your attempt to determine the cash out chance (it seems tricky, since every time a cash out does not occur, you would presumably become slightly more convinced a cash out is less likely.)
If I did enough math, it does seem like it would be possible to at least get some kind of estimate for it.
Thanks! I’ll try to look into this further.