Rating system for online games in Heroes of Might and Magic IV.

During the tournament, he received 0 points but lost 33.33 points due to the 2/3 multiplier.
By the way, he didn't quite calculate the points for the top 9 places correctly (for example, for 1st place: 2/3*100+3000*(1+100/6000)=3116.66), but it doesn't change the overall meaning.

Sage, :) Well done! I completely forgot about the rating aging. Because this system automatically ages players' ratings by 1/3. The question now is different. Let's say someone got a good rating and stopped attending tournaments altogether. In my opinion, when calculating ratings from a tournament, it seems necessary to age the ratings of all players in the database, with the exception of those who are playing in another tournament organized by someone else - or for organizers to coordinate their tournaments with each other. This will be a bit challenging. But I think a similar problem would occur in any other system (I mean, if a player played in one tournament, took 1st place, and then disappeared from the tournament scene).

Added 6 minutes ago

So, I wrote that the player at least played, so we should reward him. And those who don't show up get nothing.

Whether they show up or not is not within the scope of the rating system - the reason for not showing up may vary, and you will quickly get tired of dealing with it. What does "reward" mean? :) (Wow, what a reward! 44.20 is approximately HALF of the increase in rating points earned by the leader (100 - for 9 wins)???) Then reward ALL those who SHOWED UP, not just the one who took last place. The one who didn't show up shouldn't have a starting capital, so it will be zero. The starting capital of 100 should be awarded to a player when they register for a RATED tournament for the first time, not as you did. You just took everyone you knew from the previous tournament and immediately gave them 100 points.

So, it's good. Should I swap all the players or just player 10 and 1?

For clarity, it's better to swap ONLY players 10 and 1.

Added 12 minutes ago

By the way, he didn't quite calculate the points for the top 9 places correctly (for example, for 1st place: 2/3*100+3000*(1+100/6000)=3116.66), but it doesn't change the overall meaning.

You better explain why he made that mistake. How do you calculate it yourself? What do you take that ^ symbol in the formula for when you calculate it yourself?