It looks like it isn’t quite fair:

The typical person flipping a coin varies enough in velocity, position, angle, and such to produce random-looking sequence. But when viewed this way, there is no reason for the flips to be precisely fair.
Now, with mathematician Richard Montgomery, Diaconis has shown that coin flips are in fact slightly biased to land on the same side as they started when flipped. By closely observing people flipping coins and carefully modeling the process, they estimate a bias on the order of 1�2%, dominating for example the house advantage in some casino games.

And if Diaconis is flipping they will land the way he wants them 100% of the time.
Via Marginal Revolution.