Two Prisoners, Two Coins

A prison guard gives two prisoners a chance at freedom. He gives them the choice to play in the following game:

The two prisoners (let's call them A and B) will be imprisoned in separate cells, each with a fair coin.

In each round of the game, a guard will come to each prisoner's cell. The guard will have the prisoner flip his coin, tell him the result, and then ask him what the other prisoner flipped.

If they both guess correctly, they will be instantly released.
If neither of them guesses correctly, they will both be executed immediately.
If one of the two prisoners correctly guesses what the other flipped, they have passed that round.
If they are able to pass 1000 rounds in a row, they will be released.

If they choose to play, they will be given a brief moment to come up with a strategy together. They are tired of living in prison, but they definitely don't want to be executed. Should they choose to play?

Source: unknown

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