July 04, 2012
The probability graphs are all linked to below or can be found in my 2012, July blog posts.
It is useful to some extent to know what to expect if you play/grind certain sized fields and so I have calculated the chances of hitting bad swings for various sized tournaments. These are very accurate for each of the roi's given in fact for the HU,6s,9s,18s they are mathematically exact (unless I have made some sloppy mistakes). I used a Markov Chain transform approach with one absorbing state and this should produce the exact values - alas as the field size went up so did the number of states (1 x downswing size x a granular factor). This got so large that I could not get the exact values for high swing in the 27 plus graphs but don't worry too much about this as these are still so accurate they are within the width of each plot on the graphs - about 3 figures of accuracy.
I used a rake size of 10% but this is really not too important as even if a different amount was chosen if the roi is the same the plot will be about the same also.
Obviously in practice nobody can sustain an exact roi/finish distribution over 10000 games but if they did these would be the swings that they should expect. The graphs are cumulative so the value shown for a 70 buyin swing is the chance of seeing a swing 70 or more so if unlucky you may still see a 140 buyin swing at that point, if you take the value away from 1.0 this is the chance of not seeing a swing as bad as 70 buyins.
If I find that any are in error I will correct them and re-post.