title: With the trueskill algorithm, given two players' ratings, how can I calculate the win/loss probability?
body: <p>I see this question come up a lot in discussions of trueskill, but I've yet to come across a conclusive answer.</p>
  
  <p>I'm using the Python implementation here:</p>
  
  <p><a href="https://github.com/sublee/trueskill" rel="nofollow">https://github.com/sublee/trueskill</a></p>
  
  <p>I've put together a simple simulation using that library here:</p>
  
  <p><a href="https://gist.github.com/klenwell/3a15eca6b83ce575d0ca" rel="nofollow">https://gist.github.com/klenwell/3a15eca6b83ce575d0ca</a></p>
  
  <p>The question is submitted as the <a href="https://github.com/sublee/trueskill/issues/1" rel="nofollow">first issue</a> for the Python library. In the <a href="http://www.moserware.com/2010/03/computing-your-skill.html" rel="nofollow">Jeff Moser blog post</a> which most trueskill discussions lead back to, the question comes up several times in the comments.</p>
  
  <p>Can someone provide a function compatible with the Python library implementation that accurately returns a player's predicted win probability against another player based on the two players ratings?</p>