[PairTheBoard]

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You each guess the other's coin will land the same as yours - which you know. That way, you will each guess right when your coins match, which happens half the time. As a team you are employing a strategy which produces a correlation between your two guesses. In other words, your guesses are no longer independent. You will be guessing the same when your coins are the same, which is favorable to the team.

PairTheBoard

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I would put your odds at 25% if using strategy you both decided in advance how you will answer each time or if you guess the other coin matches yours.

Consider:

Coin A Coin B
Heads Heads
Heads Tails
Tails Heads
Tails Tails

Yes, the odds of a coin being heads / tails is 50% but each has its own 50% that must be considered as well.

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When H-H you both look at your own coin, you both guess the other has heads, and you are Both Right.
When T-T you both guess the other has Tails and you are Both Right.

So you Both guess right 50% of the time. If you were both guessing independently and randomly you would each be right 50% of the time and by Independence, you would Both be right (.5)(.5) = 25% of the time. The strategy has improved your chances of "Both Being Right" from 25% to 50%.

PairTheBoard