Iowa primaries

The Highly Improbable Iowa Coin Tosses

Hillary Clinton “won” the Iowa caucuses, in part because of 6 coin tosses all of which she won! Six precincts, at least, ended up with a dead tie between the two candidates. The tie was broken and a winner declared based on a coin toss in each case.
What are the odds of one of two candidates winning all six coin tosses if the outcomes are random, that is, if the tosses are fair, unbiased and with honest coins?