How do you decide who wins a tournament?
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Like Karjiakin-Carlsen, it makes more sense to have a playoff. Why did Magnus lose?
Based on tiebreaks, which is dependent on who you played against and how well they played in the tournament. I think though, I might be wrong.
Didn't Karjakin beat Carlsen in one of the regular blitz round and based on that named the winner?
Maybe, but ive played tournaments where that happened but i beat the guy who ended up winning the tie
Tie breaks are usually decided by weird systems like Bucholz or however it is written, and as far as I know the dude that faced opponents with better results at the end of the tournament, wins.
Also, Karjakin beat Carlsen in their personal game and I dont think you have playoffs if that happened.