Edit: which turns out to be exactly the same as what RHaver said just in a different way.

Eventually the number of past events will be so small when compared to infinity that the past events doesn't matter.
^ Exactly, and that's what helps me when I think about it. Doesn't matter whether it's 1 past event or 1,000,000 past events...they're equally small when compared to infinity

I think the lure of trying to beat or anticipate the game will always be strong enough to fool some people into thinking they know what's coming next...