What happens in this multiboard scenario? You are playing 4 players at the same, you are black, white, black, white.

Player 1 makes his move, you switch to player 2 and make the same move as player 1, and so on, with player 3's first move becoming your move to player 4.

you then go back to player 1 and respond with player 2's response to your move.

if you sense a mistake, you 'go for gold' and 'play your hunch'.

does this have a name?
That's a trick once performed by Derren Brown.

This article calls it "mirroring technique" and claims it is more than 25 years old, but I don't think this is a very well known term.  If you are interested in more information about this trick you should probably google "Derren Brown Chess".