Always pick whatever side of the coin comes up first, i.e. if heads comes up on the first toss, always choose heads thereafter.
The reasoning: There’s probably some kind of minimal bias one way or another in the coin or in the tosser’s toss. Assuming there’s no data to help you out beforehand for determining the bias, as soon as you get your first piece of data in the form of the first coin toss, chances are the bias is towards whatever side of the coin turns up.
The complication: If the probability distribution is 90% heads and 10% tails and tails happens to come up up first, well, you’re very likely to lose a best-of-three coin toss series by always choosing tails. But if no one actually knows the probability distribution beforehand, you’re better off always choosing the side of the coin that comes up first for a short coin-toss series. Larger coin-toss series, i.e. a best of twenty series, will mean that if the bias is sufficiently skewed, it is indeed better to change your coin-flip choice in light of results.