You have a unfair coin with $70\%$ chance of getting a head($H$). You toss it and it returns a tail($T$). You will then toss until there is equal number of heads and tails. What is the expected number of tosses before you stop? Do not count the first toss where the result is tail.
I ran a simulation and it requires 2.5 additional toss on average. Yet I do not have an approach to arrive at the answer.