Yesterday, someone found out they'd been playing a favourite board game wrongly / 'not according to the printed rules'. In this case, the missed rule makes a better game and the judgement involved is half the skill in something that has a lot of luck already.
But lots of people ignore rules. Few people play Monopoly without adding some variant or other, usually making it a worse game* by increasing the money supply or reducing limits on houses or.. Even the current rights owners have been guilty of that, including by adding another die to make it easier to land on squares you want to land on / easier to avoid ones you don't.
I've been taught games wrongly – the classic example was the game where the owner had missed that each turn you could do only one of four things and thought you could do all four, every turn. The game didn't last long…
Some people make a fortune out of it: Othello is Reversi with a restriction saying you have to start with one of two opening positions. Somehow, the Japanese patent office granted a patent on it anyway and the 'inventor' cleaned up.
Some games are improved by tweaks. I think one favourite has one mechanism, a favourite of the designer, too many and so do without it.
What's your missed / ignored / improved rule story?
* Feel free to substitute 'an even worse'…