An investor in a casino is offered a choice of getting a return each time a certain game is played. The game is played by tossing $N$ times a fair coin and recording the sequence of heads (H) and tails (T). Let $h$ be the number of appearances of HH in the recorded sequence and let $t$ be the number of appearances of HT. For example, when $N=5$ and THHHT is recorded then $h=2$ and $t=1$. The investor can choose to either get $h$ cents each time the game is played, or to get $t$ cents each time the game is played. Which choice offers a better expected return?