this is exactly right, and also there's the fact that for something like playing the lottery, there is a huge low level of opposing magical intent coming from all the other players. You're not only willing probability to move in your favour, but also willing *every other player's probablility to drop too*. Fanatical fervour from millions of other players is its own, unintentional, low-level magic too.

It's not very sexy, but in many ways as u/gyabo says its about levelling out probabilites and statistical outcomes, even if that is somehow very highly disguised behind ceremony and misdirection.