Why some new member start with 800, 1200 or 1800 in rating?

@rufusmod

You've forgot that conditions were: both players are equally strong (850), first player starts at 500, second player starts at 1200.

Winning 3-4 games straight against equally strong opponent is not realistic.

While you're showing links to games with different opponents, differently rated and of unknown strength.

I gave an actual example in reality of a player who was rated 500 and whose strength could be, based on the result of his first 3 or 4 games, 850.

Of course players will play different opponents of different strengths. That's how the pool works on chess.com.

@rufusmod

Well level of that grandmaster is not even close to 800 now after few more games, it's now 490.

And no, that's not how "pool works on chess.com". Mathematically and statistically it is impossible to reach your "strength" in just 3 or 4 games. And we have huge issues with rating system on chess.com especially for low-Elo players. You can't take rating on chess.com as accurate measure of strength. First of all, there are lot of isolated pools here. Secondly, ratings are highly inaccurate and distorted all over the site. Moderately strong (2000 FIDE+) player can break through all the low-Elo varying strength turbulence and reach their level by playing several hours straight. But 3-4 games? Unlikely.

About all these issues and how to deal with them you can read in a book by Arpad Elo, who initially created the Elo system for FIDE.

Ratings are not really a measure of strength in the first place. They are a measure of past performance in the pool of players. It doesn't take very many games with the Glicko rating system to get players relatively close to where they would have been had they started at a different rating to begin with. That's the point and one of the main points of Glicko's rating deviation value.

That works only in theory in a consistent pool. In reality we see that strength varies wildly in low-Elo region even if all players have played hundreds of games.