Does the browser have magic prophecy powers, or just your specific installation? Because the first would mean that it's unique, and others have given pretty good answers about how you could use that.
If you can just download it to any and as many machines as you want, you end up in a vastly different universe, and I'd like to go open up that angle a bit, because I think you need to either consider this or come up with a very good reason as to why it's not used by everyone. This thing will spread, because it's far too useful, too interesting, and too good of an opportunity to make money for it to stay secret for very long.
In that scenario, it's only a matter of time until many, most, and all other people use it and have the same advantage, resulting in nobody having a real advantage anymore, but being forced to use this browser. Race betting etc. would break down, because nobody would offer these bets if they know that betters know the winner. In stock trading, you'd end up in a similar state to reality, where people fight about microseconds again after everyone has that 5 second advantage.
I'd go so far as to say that in this scenario, you actually could not make much money with this, unless you are one of the early adopters, or you get very, very creative. I could imagine scammers using this in some convoluted "bet on a coin toss while secretly glancing at the browser that shows me a webcam image of the result" scheme, but other than that there's not much room for getting rich quick. Except for one: you have control over the browser's functionality somehow, and can charge people for using it - provided nobody can reverse engineer it and create an open source version or something.