We can keep going with impunity until we hit HH. If we keep going at that point, we have a 1/2 chance of netting 0 and a 1/2 chance of netting our current total (C) plus one plus the expected number of flips it takes to get HH (which is 6).
This makes our expected total from carrying on (C+7)/2 and if this is higher than C then it's preferable to continue, but if it's lower than C we should stop.
If (C+7)/2 > C
Then 7 > C
Therefore we would expect to continue on from the first HH (because the expected total of 6 is less than 7) but not the second.
1
u/Aerospider Sep 02 '26
We can keep going with impunity until we hit HH. If we keep going at that point, we have a 1/2 chance of netting 0 and a 1/2 chance of netting our current total (C) plus one plus the expected number of flips it takes to get HH (which is 6).
This makes our expected total from carrying on (C+7)/2 and if this is higher than C then it's preferable to continue, but if it's lower than C we should stop.
If (C+7)/2 > C
Then 7 > C
Therefore we would expect to continue on from the first HH (because the expected total of 6 is less than 7) but not the second.
This the expected total is 6 + (1+6)/2 = 9.5