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.
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.