The Ultimate Prisoner's Dilemma: Can You Solve It?

Problem:

Two prisoners are trapped on an island and offered a chance to gain freedom through a probability game. Each prisoner is given a fair coin. Without prior collusion, each prisoner must independently decide whether or not to use the coin. The guard will collect the coins and flip them as follows:

1. If neither prisoner uses the coin, they will remain in prison.
2. If only one prisoner uses the coin, the coin will be flipped once. If it lands heads up, both prisoners will be freed.
3. If both prisoners use the coin, both coins will be flipped. If both land heads up, both prisoners will be freed.

The prisoners are intelligent and desire freedom. They do not have the opportunity to communicate or collaborate. What is the optimal strategy for each prisoner to maximize their chance of winning the game and gaining freedom?