There are four possible scenarios:

1. Ava's card is red, and Bruce's is black.

2. Ava's card is red, and Bruce's is red.

3. Ava's card is black, and Bruce's is red.

4. Ava's card is black, and Bruce's is black.

To win, Ava should pick the same color as the card she sees on Bruce's forehead, and Bruce should pick the color that is different from the card he sees on Ava's forehead. (Which player chooses which strategy doesn't actually matter.)

Here is how the strategy plays out for each of the four scenarios above:

1. Ava chooses black, and Bruce chooses black. Bruce guessed correctly.

2. Ava chooses red, and Bruce chooses black. Ava guessed correctly.

3. Ava chooses red, and Bruce chooses red. Bruce guessed correctly.

4. Ava chooses black, and Bruce chooses red. Ava guessed correctly.