A fair coin is being tossed. Whenever a tail follows a head, Rick wins the game and whenever a tail follows a tail, Tick wins. Who has more probability to win?
Let's say the coin has been tossed more than twice. For Tick to win, the last three tosses should be HTT, but Rick will have won it already. So if the first two flips are not TT, Tick has no chance of winning the game.
I do not know how to proceed from here. I initially planned to brute force since we can obviously compute the probability for $n$ tosses (using a simple recursion). But then this observation above kind of made this computation a bit meaningless.