Spoiler: All possible days
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A: 10v1
  1. 45/55 it's still 10v1, and becomes 9v2 in the night.
  2. 10/55 it's 10v0. Town victory.


B: 9v2
  1. 360/550 it's still 9v2, and becomes 8v3 in the night.
  2. 162/550 it's 9v1, and becomes 8v2 in the night.
  3. 28/550 it's 9v0. Town victory.


C: 8v3
  1. 1260/2475 it's still 8v3, and becomes 7v4 in the night.
  2. 864/2475 it's 8v2, and becomes 7v3 in the night.
  3. 312/2475 it's 8v1, and becomes 7v2 in the night.
  4. 39/2475 it's 8v0. Town victory.


D: 7v4
  1. 7560/19800 it's still 7v4, and becomes 6v5 in the night.
  2. 7056/19800 it's 7v3, and becomes 6v4 in the night.
  3. 4032/19800 it's 7v2, and becomes 6v3 in the night.
  4. 1008/19800 it's 7v1, and becomes 6v2 in the night.
  5. 144/19800 it's 7v0. Town victory.


E: 6v5
  1. 18900/69300 it's still 6v5, and becomes 5v6 in the night. Thing victory.
  2. 22680/69300 it's 6v4, and becomes 5v5 in the night. Thing victory.
  3. 18480/69300 it's 6v3, and becomes 5v4 in the night.
  4. 6930/69300 it's 6v2, and becomes 5v3 in the night.
  5. 1980/69300 it's 6v1, and becomes 5v2 in the night.
  6. 330/69300 it's 6v0. Town victory.


F: 8v2
  1. 252/405 it's still 8v2, and becomes 7v3 in the night.
  2. 128/405 it's 8v1, and becomes 7v2 in the night.
  3. 25/405 it's 8v0. Town victory.


G: 7v3
  1. 1512/3240 it's still 7v3, and becomes 6v4 in the night.
  2. 1176/3240 it's 7v2, and becomes 6v3 in the night.
  3. 483/3240 it's 7v1, and becomes 6v2 in the night.
  4. 69/3240 it's 7v0. Town victory.


H: 6v4
  1. 3780/11340 it's still 6v4, and becomes 5v5 in the night. Thing victory.
  2. 4032/11340 it's 6v3, and becomes 5v4 in the night.
  3. 2625/11340 it's 6v2, and becomes 5v3 in the night.
  4. 756/11340 it's 6v1, and becomes 5v2 in the night.
  5. 126/11340 it's 6v0. Town victory.


I: 7v2
  1. 84/144 it's still 7v2, and becomes 6v3 in the night.
  2. 49/144 it's 7v1, and becomes 6v2 in the night.
  3. 11/144 it's 7v0. Town victory.


J: 6v3
  1. 210/504 it's still 6v3, and becomes 5v4 in the night.
  2. 189/504 it's 6v2, and becomes 5v3 in the night.
  3. 90/504 it's 6v1, and becomes 5v2 in the night.
  4. 15/504 it's 6v0. Town victory.


K: 5v4
  1. 140/504 it's still 5v4, and becomes 4v5 in the night. Thing victory.
  2. 175/504 it's 5v3, and becomes 4v4 in the night. Thing victory.
  3. 135/504 it's 5v2, and becomes 4v3 in the night.
  4. 45/504 it's 5v1, and becomes 4v2 in the night.
  5. 9/504 it's 5v0. Town victory.


L: 6v2
  1. 630/1176 it's still 6v2, and becomes 5v3 in the night.
  2. 432/1176 it's 6v1, and becomes 5v2 in the night.
  3. 114/1176 it's 6v0. Town victory.


M: 5v3
  1. 420/1176 it's still 5v3, and becomes 4v4 in the night. Thing victory.
  2. 450/1176 it's 5v2, and becomes 4v3 in the night.
  3. 255/1176 it's 5v1, and becomes 4v2 in the night.
  4. 51/1176 it's 5v0. Town victory.


N: 5v2
  1. 60/126 it's still 5v2, and becomes 4v3 in the night.
  2. 50/126 it's 5v1, and becomes 4v2 in the night.
  3. 16/126 it's 5v0. Town victory.


O: 4v3
  1. 30/105 it's still 4v3, and becomes 3v4 in the night. Thing victory.
  2. 40/105 it's 4v2, and becomes 3v3 in the night. Thing victory.
  3. 28/105 it's 4v1, and becomes 3v2 in the night.
  4. 7/105 it's 4v0. Town victory.


P: 4v2
  1. 30/75 it's still 4v2, and becomes 3v3 in the night. Thing victory.
  2. 32/75 it's 4v1, and becomes 3v2 in the night.
  3. 13/75 it's 4v0. Town victory.


Q: 3v2
  1. 6/20 it's still 3v2, and becomes 2v3 in the night. Thing victory.
  2. 9/20 it's 3v1, and becomes 2v2 in the night. Thing victory.
  3. 5/20 it's 3v0. Town victory.


R: Town has won.

S: Thing has won.


I've done a good deal of math today, figuring out exactly how this would go if we let the dice decide how things play out. The long and short of it is that if we started 10v1, there's a ~3/8 chance village wins through random guessing. If we started with 9v2, or we fail to find the 1 today and we're at 9v2 tomorrow, we're now at ~1/4 chance village wins. That it's so stacked against us to start out just means that we need to be really on-point with our tests, if we want a good chance at winning. The good news is that, if we do manage to pop a Thing, we've got their vote history we can analyze to figure out who might be one of their buddies, and their placement in the order. The sole benefit of the "rolling randomly to determine tests" approach is that the Things are incapable of anticipating or influencing the result, but that just means that they can't really change our chances of losing anymore than we can if we do that method, and we really shouldn't so it was kinda all just a waste of time. >.>

A few other interesting tidbits:

1) Town always has a chance, no matter how far behind, to win outright on any given day. This is fairly obvious from the basic set-up, but it's amusing to me.

2) If a new day starts, we have at least 2 Things left.

I'm gonna start analyzing arguments and figuring out my own approach to playing the game from both sides.