The odds would have to be much longer for it to be effective. Sure when it's one in one hundred million there's almost no chance that *you" will win, but with millions of players playing every day there's practically a guarantee that someone will win eventually.
The SEC are the real time cops. They're a front for the Hyperextended Interval Temporal Legislation and Entropic Reduction Society (don't panic about the acronym, they started as private bodyguards and then their mission expanded as chronological abuse became more widely known). It's a lot easier to vet people buying Amazon and Apple stock at IPO. If you've got no history until 1980, then buy 10,000 shares of apple on IPO day, then do absolutely nothing else in the market for decades, then dump all 10k shares at peak that's a pretty easy to spot profile of a time traveler.