This was one of the activities on another site I used to be a part of.

Someone would challenge someone else to a match, and if it was accepted, the two would agree on a third person to act as the moderator. Matches were usually fights, but not always; really, anything is possible. Once we had an Iron Chef competition and wrote about cooking.

A match generally consisted of eight posts, with the mod doing the first and last and each player alternately posting three times. There was a time limit on these posts, usually between one day and one week, which the players would agree on.

In their posts, the players would write the story of their contest. They could use any abilities that their characters possessed. No rolls needed to be made; for each attack or ability, the players could just decide whether it would hit or miss, and write accordingly. Unless agreed upon beforehand, causing permanent damage to an opponent's character was not allowed.

The moderator would conclude the contest in the last post and then judge the match. Scoring details and criteria were left up to the mod; when I graded a match, I usually looked for creativity, the ability to roleplay one's own and one's opponent's character consistently, and overall writing ability, with bonus points for humor.

Characters would then receive awards based on their scores, with an extra prize for the winner.

These were popular enough that we even had tournaments.

I tried finding some examples, but the site where all of this happened is long gone, and the advertising spambot that now owns the domain name has blocked it from the internet archive.