Your explanation actually confused me until I realized we can't conflate the two different players' throws. We basically have four cases for Bob: - HH: termin

Your explanation actually confused me until I realized we can't conflate the two different players' throws. We basically have four cases for Bob: - HH: terminates for Bob. - HT: Bob restarts the sequence. - TT: Bob restarts the sequence. - TH: This is a continuation. It degenerates into the answer to a single throw. Otherwise its just a recursion. Then we have another four cases for Alice: - HH: This is a continuation. It degenerates into the answer to a single throw or else a recursion. - HT: terminates for Alice. - TT: Alice restarts the sequence. - TH: This is a continuation. It degenerates into the answer to a single throw. Otherwise its just a recursion. So with that understanding it is a bit more clear how we get this result: Alice has one win and two opportunities for a win and one for a restart. Bob has one win and one opportunity for a win and two restarts. That was a bit confusing. I wonder how the problem could be worded to ensure that people got the answer correctly every time?