1. Buy a book on probability. Work through the practice exercises.
2. Time travel back to a time before the laws of probability were invented or taken seriously. Pre-1600's would be a good guess.
3. Become a gambler.
4. With the riches that will soon be pouring into your pockets, acquire resources and transform history.
Even in today's professional gambling establishments (financial markets) big winners are often cut off in the name of stability.
Actually, any kind of money hoarding - moreso than anyone else - will draw the attention. Which might be OK, of course, but if you make waves that are too big, you'll affect global policy and the course of (economic) history, and all your predictions may be off.
But, getting significant but non-controlling stakes in various successful stocks might work. You'd be like Warren Buffet, who I consider to be rich, but otherwise anonymous.
To get really rich you need to aquire people, their time and productivity. Instead of probability you need means to get people's minds so with them you can conquer territories and establish kingdom to be really rich.
Only real possibilities to avoid exile/asylum/imprisonment/execution for most of history would seem to hinge on predicting celestial events and making gunpowder, as Twain observed.
Buy two large pizzas, cheese and 'supreme'.
Be earlier than that guy.
Credits.
It's like being a gambler, but you get to stack the odds in your favour, deliberately, tell people you've done so, and have everyone be fine with that. If you use any knowledge of future events to stack a few odds a little more in your favor, no-one's going to know any different, and they'll attribute any weird variances in your income to the punters who all made poor bets, rather than to your mad odds-setting skills.
If you're going to gamble, always be the house. Only a complete moron can lose money that way.
Maybe they learn roulette strategy and show up right after Pascal invented the roulette wheel while he was trying to produce a perpetual motion machine (which could play a role in the time machine's tech itself too, which could resemble a "grande roue," visually akin to a g-force centrifuge or particle accelerator).
Might be a time traveller.
No news so far of alien visit or time traveller … but it might be hard if they tried to avoid us … except for selling something like enterprise Vulcan did to help education fund which is more physical and hence possible.
Protagonist travels to 1991 and tries to convince scientist to help him. When asked for a proof, shows Gray C90 Wristwatch. "Our real computers are different, but I show you this because it does not pollute the timeline."