why do some games use 10 and 20 when 1 and 2 would work?

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An example, lets say there's a game where you throw rings at poles, if you get a ring on the closer pole you get ten points, when you get a ring at a farther pole you get twenty, but 1 and 2 would suffice perfectly fine, why do I sometimes see this? (Or at the very least, remembered seeing this

I think it's appealing to psychology. Who wouldn't want to eat 10 cookies instead of 1 cookie?

ah

It's more or less the Whose Line Is It Anyway thing. "Welcome to Whose Line Is It Anyway?/the show(, the show) where everything is made up and the points don't matter. That's right, the points are like (insert funny fact).”

The points are just a way for the developers to nudge people to a certain type of play. Or, not. One of the things about the original Sonic games was that the point system was supposed to encourage people to play both fast and accurately to reach the end of the game with the highest score. In Super Mario Brothers, the points are more or less completely meaningless in most cases. They don't really impact anything at all.