200 people in 2 days is impossible without luck.
It's also pretty simple to understand that a game of Dominion between two equally skilled players will be decided by luck 100% of the time, otherwise they wouldn't be of equal skill, get it?
This is true because luck plays an inherent factor in Dominion. There is shuffling, hence luck.
It's not true in chess where I'm pretty sure there is no luck. Well, you could be lucky to be white but you can just play 2 games to solve that.
If there is a 1% skill difference between 2 players, the part that luck plays is still close to 100%.
So you really can't throw luck out of the equation no matter how hard you try. This means you have to accept that it's a factor and by the end of two days you're not really crowning the luckiest overall, but you are crowning the luckiest of the best players.
Chess has luck.
You can argue this from two angles
1) How else do you explain best of 7 sets between players of different strengths being anything but 4 straight wins?
2) The future possibilities of a game are too many to be analyzed and calculated. Thus, the chess player skips some analyses, and at some point, just guesses that the knight takes bishop retaken by bishop pawn push pawn push pawn push rook e4 rook f6 queen g6 is good for him. Neither player actually looked at that chain of possibilities, but one player chooses to take the first step. He bases that first step on other reasons, he probably analyzed some other equally long chains, and liked them, but neither player looked at this one.
The line of reasoning makes sense to me and I buy it. At some point there are decisionmaking criteria that are, in actuality, arbitrary to successful victory in the game. If they are arbitrary to victory they function randomly.
Think of it this way. What if in a contest, I gave you a square grid of 100 division problems. The divisors are all primes between 17 and 31 and you only have to produce the remainder, and your pencil writes quickly. The numerators are all ten digit numbers. Prize is five hundred dollars, you have to beat ftl. I give you 40% as much time as it takes an intelligent person to solve all the division problems correctly.
Both you and ftl will solve 40% of the problems, probably the first 40%, because why not. Then in a negligible amount of time you will guess the other 60% because each remainder you right gives you roughly a 4% chance of another right answer. This game clearly has luck, you didn't really work all the problems. The problems you two had time to work will be a brute contest of mathematical skill, and the best man will probably win, but one player may luck out.
Now if I instead rename half the problems "shuffle luck", and hide the numerators with black highlighter, leaving functionally random numerators, have I changed how much luck this game has? No, not really, you're still going to guess on 60% of the problems.
Outcomes that can't be foreseen exactly are indistinguishable from outcomes that we don't have the time to analyze and then foretell is what I'm getting at. It makes sense to me. It's hard though.
This is why chess requires some sample size. Not much but some.