Let's assume the odds are fair such that the odds of all horses sum up to 1. Betting on all other horses would give you 1:1.02 odds whereas they should have been 1:1.01. While there is no way to answer for sure how many races you would have to bet on to make money, we can look at the probabilities. There's a 95% likelihood that the horse will lose 5 races in a row. If you start with $100 and reinvest your winnings every time you'd earn a profit of $10 with 95% likelihood, meaning there's a positive expectation value. On the other hand, if the 1:50 odds were right, the probability of it losing 5 times in a row would be around 90%, leading to a neutral expectation value.

Except investing isn't like a horse race. Each horse has a different finish line, and those finish lines are in flux during the race. Crucially, you can change your bet in the middle of the race.