Of course billionaires can exist without having a winning strategy. Notch didn’t set out to be a Billionaire. He just played infiniminer and thought it was cool, so he asked Zach Barth if he could make a spinoff. Facebook was started because Zuckerberg was trying to trick a chick into sleeping with him. These billionaires didn’t have some Machiavellian scheme to become billionaires. They just made a thing that happened to dominate their respective industries. It happens when someone is first to market in a field that is prone to natural monopolies.
And of course money is a zero sum game. There’s a limited amount of currency in circulation. That’s true on it’s face (ignoring government’s creating more, etc.)
But I think the issue that we are actually disagreeing on is your claim that someone can’t get more than X dollars by chance.
My counter to that is, “sure they can, by winning an X+1 dollar lottery.” And I don’t think you’ve made any sort of counter to that point other than, “yeah, but they couldn’t keep it without being unethical,” without ever providing a timeframe that you would consider sufficient to meet the definition of “keeping it.”