By the Kelly criterion, you should bet edge/odds of your bankroll. Your edge here is 0.01 * 0.0001 = 0.000001. Your odds are 0.01. Therefore you should bet 0.0001 of your net worth. So if you had a million dollars, that $100 bet would be a sensible investment. If you've only got, say, $100k then you should only bet for entertainment value.

The investment rule that underlies Kelly is to maximize the log of your net worth. Why? Bets multiply your net worth by a random factor, take logs and you're adding a random factor. In the long run a sum of independent random factors tends to converge to the expected value, so maximizing the expected log of your net worth will result in a strategy that with 100% odds will, in the long run, beat any other.