Here’s the rules: You have a time machine. You can’t use it to visit the past, defined as any time earlier than your starting point. You can visit the future – but the future remains indeterminate. You will visit a possible future – in this case, the future that likeliest would happen if you never came back from the trip. But you can come back, and you can use whatever you learn about the future to make changes.
Forget about looking up winning lottery numbers. Once you come back to the present (defined as your starting point), the universe resets from zero. Anything subject to random chance remains so. Old newspapers might say the winning Florida lottery for July 5, 2006, is 1-7-8-11-14-52 (which it was); but if you start from July 4 and return, that number remains no likelier to come up than any other.
OTOH, WRT outcomes depending on other factors than, or in addition to, random chance – e.g., horse races or stock market fluctuations – your knowledge of the future might help you place bets more accurately. But there are no guarantees.
Suppose you visit future dates at five-year intervals. (You won’t meet yourself at any of these stops, because this is a possible future where you mysteriously vanished back in 2006.) At each stop, you head for a library and research the history of the past five years. If you come across anything really astonishingly horrible, like the 9/11 attacks or the Holocaust, you might feel obliged to do something to prevent it. OTOH, that also means that many people living in the “possible” future you visit will never be born, owing to the “butterfly effect” – change something small and their parents might never meet; and to make any desirable difference in the future, you’ll have to change something big.
What would you do?