If all the coins are quantum-mechanical, you should never quit, nor if all the coins are logical (digits of pi). If the first coin is logical (“what laws of physics are true?”, in the LHC dilemma), the following coins are quantum, and your utility is linear in squared amplitude of survival, again you should never quit. However, if your utility is logarithmic in squared amplitude (i.e., dying in half of your remaining branches seems equally bad no matter how many branches you have remaining), then you should quit if your first throw comes up heads.
I’m not getting the same result… let’s see if I have this right.
If you quit if the first coin is heads:
50%*75% death rate from quitting on heads, 50%*50% death rate from tails
If you never quit:
50% death rate from eventually getting tails (minus epsilon from branches where you never get tails)
These deathrates are fixed rather than a distribution, so switching to a logarithm isn’t going to change which of them is larger.
I don’t think the formula you link to is appropriate for this problem… it’s dominated by the log(2^-n) factor, which fails to account for 50% of your possible branches being immune to death by tails. Similarly, your term for quitting damage fails to account for some of your branches already being dead when you quit. I propose this formula as more applicable.
If all the coins are quantum-mechanical, you should never quit, nor if all the coins are logical (digits of pi). If the first coin is logical (“what laws of physics are true?”, in the LHC dilemma), the following coins are quantum, and your utility is linear in squared amplitude of survival, again you should never quit. However, if your utility is logarithmic in squared amplitude (i.e., dying in half of your remaining branches seems equally bad no matter how many branches you have remaining), then you should quit if your first throw comes up heads.
I’m not getting the same result… let’s see if I have this right.
If you quit if the first coin is heads: 50%*75% death rate from quitting on heads, 50%*50% death rate from tails
If you never quit: 50% death rate from eventually getting tails (minus epsilon from branches where you never get tails)
These deathrates are fixed rather than a distribution, so switching to a logarithm isn’t going to change which of them is larger.
I don’t think the formula you link to is appropriate for this problem… it’s dominated by the log(2^-n) factor, which fails to account for 50% of your possible branches being immune to death by tails. Similarly, your term for quitting damage fails to account for some of your branches already being dead when you quit. I propose this formula as more applicable.
You seem to have a deep understanding of this. Could you expand on it?