On Player 1's turn, he tosses the coin once: if it comes up Heads, he scores one point; if it comes up Tails, he scores nothing.
On Player 2's turn, she chooses a positive integer $T$ and tosses the coin $T$ times: if it comes up all Heads, she scores $2^{T - 1}$ points; otherwise, she scores nothing.
Player 1 goes first. The winner is the first to 100 or more points.
On each turn Player 2 selects the number, $T$, of coin tosses that maximises the probability of her winning.