In post 2, Kerset wrote:Did you include the fact that commuted player can't NK? If last scum happen to be baton holder then he can't kill (it might decrease scum winrate).
I didn't consider that, no. Without exhaustive searching, I think there are probably more cases where ScumRemaining = 1 and TownRemaining >= 3 (in which case scumLose has a 2/N Probability instead of a 1/N Probability) than there are cases where TownRemaining = ScumRemaining + (1 OR 2) which is the case where the additional scumwin chance matters.
Whether that translates into a higher or lower scumwin EV would be better solved using iterative casing and coding (not my forte) so I'll leave that for someone else if they want to work it out, but it DOES mean that as long as your desperation day is at 3/2 presumptive the Desperation Day bit doesn't come into play.
My suggestion to 'fix' this would be to move the Desperation Day to day 2, although I'm not sure exactly how that effects the balance of the game from a numbers perspective. If someone wanted to mock this up using coding it's actually a pretty simple set of variables to represent.