Pennies

I challenge you to a game. we each get one penny and we flip them at the same time. (so on turn 1, we each flip our respective pennies - turn 2, we flip them again, and so on until someone wins). i am looking to get heads then tails. you are looking to get heads then heads. so if you flip heads on any flip and then heads on the next flip, you win. if i flip heads on any flip and then tails on the next flip, i win. (its not a speed race, we both flip at the same time, except i'm only concerned with what appears on my coin, and you are only concerned with whats on your coin). are the odds fair? (obviously not, otherwise this wouldn't be a question). who has the advantage and why?

Solution:

In a 3 turn game:

O needs HH, X needs HT

HHH O

HHT OX

HTH X

HTT X

THH O

THT X

TTH

TTT

X wins 4 times out of 8, O wins 3 times out of 8

Its because in the event X loses there is a 50% chance of starting out on another H where O has to start on a T 75% of the time. (or something like that...)