Youre flipping a fair coin Initially you just flip it After

You\'re flipping a fair coin. Initially you just flip it. After that, if it was heads the previous round you turn it over to tails (so it guarantees a tails in the current round), and if it was tails you flip it again in the current round. What is the probability of a heads in the nth round? (it should converge to some value for sufficiently large n)

Solution

The answer is 50%, since the first coin flip is random, and then it alternates subsequently.