Let's get some math up in here...

[img]https://vincentarisato.files.wordpress.com/2013/09/5258.png[/img]

The killer has about a 14% chance of getting punished the first round (1 out of 7 outcomes)

The second round the killer has a 20% chance of getting punished. (1 out of 5 outcomes) If we look at their chances of being punished both rounds, it's closer to 31% (11 out of 35 outcomes)

The third round the killer has a 25% chance of getting punished in the final round. This has to do with how things are run. barring that and going by pure statistics (33%, 1 out of 3), there is just under a 46% chance the killer will be punished. (37 out of 85 outcomes)

So there you have it, things are slightly stacked in the killer's favor. Isn't that sad? It makes me sad...

[img]http://66.media.tumblr.com/cbbba96b2a96fde64a9f2d5e6806bb57/tumblr_inline_nx9e9y0IO91t9w8cf_500.gif[/img]

But the stats only apply for a pure entropy play style. 

For anyone wondering how I crunched the numbers for multiple rounds, you have to figure that if they were punished in the first round, they were also punished in every outcome of the second round, ETC.

EDIT: interestingly, if there were only 2 rounds starting with 5 people, the odds of the killer being punished is just a little under 47% (7 out of 15 outcomes) so that just goes to show you how meaningless that first round really is.