Puzzle: the Riddler vs Batman and Robin

This is a puzzle adapted from Max Schireson’s blog.

It is based on the trope that villains tend to use elaborate execution schemes.

Here is the problem:

The Riddler has captured Batman and Robin. He could kill the dynamic duo, but he decides to have some fun while they are hostage. So he tells them they will play a game, with their lives on the line.

Here is the game: Batman and Robin will be held captive in two separate facilities, under constant surveillance. Every day, each will flip a coin. Each person must then guess the result of the other person’s coin (Batman has to guess Robin’s toss and vice versa).

As long as one of them guesses correctly, the caped crusaders will both get to live for another day. But if ever both should guess wrong, then the Riddler will end things once and for all.

The Riddler smiles and then instructs the guards to proceed. Just as Batman and Robin are being taken away, Batman whispers something to Robin.

How long can Batman and Robin survive this game, on average? What must they do?

Can you solve it? Give it a try before reading the answer below.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
The answer to the puzzle

Batman, super-genius that he is, devised a strategy that could allow them to survive indefinitely. The trick is the two will not be trying to guess correctly individually, but they will work as a team in their guesses.

Batman told Robin the following: every day, Robin will guess the same outcome as his flip, and Batman will guess the opposite outcome as his flip. Since the two flips will either show the same face, or the opposite face, at least one of them must be right!

To see this explicitly, here are the possible outcomes:

(Batman’s flip, Robin’s flip)

(H, H) –> same outcomes, Robin guesses correctly
(T, T) –> same outcomes, Robin guesses correctly
(T, H) –> opposite outcomes, Batman guesses correctly
(H, T) –> opposite outcome, Batman guesses correctly

Batman and Robin will keep on winning, which will no doubt provide them with enough time to devise an escape plan.