Let me dispense with numbers to get to my point.

Lets say there are red and black marbles and randomly (coin flip, whatever) that red or black is chosen as the winning marble. Player A knows this and player B does not. If black wins and B picks it (meaning B is left with red) and there is a ante/fold betting system like in poker, wouldn't a good "head game" player B in person with visual cues be able to win?

Even having a 55% chance of winning is a massive "win".