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To reach 4000 rating, how many victories in a row...

The basic idea behind rating and Rd is that in the beginning players don't know about their rating so in order to solve this we let the players play some games. 1 game, 2 games or more and introduce Rd to define rating interval say 2000 to 2400. When the range of this interval is high 400 in this case the rating estimate of the player is not so reliable. Do that player has a rating of 2000? Or 2300? or 2250? or 2400? And so on.

High rating range indicates a high Rd. So to make a rating more reliable the rating interval should be minimized. And the best method to know the rating of players more reliably is to actually let them play more games. This is why with more games that Rd should be reduced so that the rating interval of each player is reduced thereby reducing the rating uncertainty of the players. It is the number of games that primarily governed the reduction of Rd.

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