Originally Posted by cgkdisc
It's somewhat complicated and you have to know each player's standard deviation in their ratings. There's probably a direct calculation in the stats book. But I've built a simulator that generates 1000 random scores on a bell curve for 1 to 30 people using their SD values. Then just looks at the scores and figures who won. For example, a player with a 1033 rating and an SD of 23.7 will beat a player with a 1013 rating and SD of 29.5 72% of the time if they are playing head-to-head. Can't help beyond that.
The distribution of the difference in round ratings has a mean equal to the difference in ratings, and a variance equal to the sum of the variances (square of the standard deviations). So, just use the normal distribution function to get the probability of the difference being greater than zero. (Like 70.1433% in your example.)
For general interest purposes, it wouldn't be hard to make a table of probabilities (of one rating beating another) using "typical" standard deviations.