Chork's Puzzle 08

Difficulty Rating: 3

Tom decides to play a coin flipping game with Mary. He bets that heads will turn up when he flips the coin.

On the first game, he starts off with a stake of $1. If he loses, he doubles his stake in the next game, and for subsequent games, he will continue to double his stake until he eventually wins. However, at any point of time should he win the bet, in his next game, his stake will return to $1 again.

Tom continues playing in this manner (ie doubling stakes for the next game if he loses, or decreasing his stake back to $1 if he wins) for 200 rounds. Tom prayed fervently for a heads to appear on each toss, but unfortunately, he is rather down on luck, and tails seem to show up more frequently than usual. In fact, on the 200th round, Tom only managed to toss his 16th heads.

"Looks like I'm not so lucky today," mutters Tom, and he decides to quit the game on the 200th round.

How much did Tom lose?
If you know the answer, post it in the comments section of this post.