You're probably losing more often than you're winning. The coin flips are fair, so there must be some other reason that you lose more often than you win.

Try to work out why. After you've won 10 times (or lost 20 times), the answer will appear here.

This game is unfair. But it's not the coin flips that are unfair (you can learn to play this game, and win, in real life, with a fair coin). What makes this game unfair is that I look at your prediction before I make my own prediction.

To pick the most-extreme example: if you pick "heads, heads, heads", then I will pick "tails, heads, heads". This means that so long as a tails comes up before three heads comes up, then I will win, because there's no remaining combination of flips by which you'll win.

Depending on your prediction, I will win between 2 and 7 times more often that you will.

(if you've won a few games, then you've been lucky: but keep playing and your luck will run out, sooner or later!)

This is an example of a non-transitive game. You can learn more about the game, and how to play it for yourself, from its article on Wikipedia. Or you can learn more about non-transitive games in general, and about the author of this webpage, on his blog post about it.