Originally posted by FishHead111
Here's a calculator, plug in any difference you want for the probability:
This site states:
"This form calculates the theoretical probability of winning a game based on ELO ratings".
It calculates the match probability, not the individual game probability.
A hundred games between a player rated 1200 and a player rated 900 should indeed result in a final score of 85/100, but this does not mean that the 1200 player has an 85% chance of winning any individual game, because of the possibility of draws.
There are numerous ways to get a result of 85/100.
At one extreme, the 1200 player wins 85 games, draws 0 and loses 15.
At the other extreme the 1200 player wins 70 games, draws 30 and loses 0.
To find the individual game probabilities, an average can be taken from the two extremes:
Win probability: (85+70)/2 = 77.5
Draw probability: (0+30)/2 = 15
Lose probability: (15+0)/2 = 7.5
So whilst the match probability between a 1200 and a 900 player is 85%, the actual probability of the 1200 player winning an individual game is 77.5%