Final-Fan said:
I want to start by applauding your appreciation of my little wordplay.
But I don't think there's much we can get from that table. As you pointed out, there are all sorts of killing roles that might also exist -- not to mention roleblockers, doctors, etc. -- that would mess up the calculations.
I don't think we ought to say we will definitely lynch today; but if an opportunity presents itself of course we can.
But I'll be very skeptical about a No Lynch later on, when we likely will have suspects to pursue, unless we have no good direction to go AND it seems very tactically sound.
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I'm not too worried about accounting for roleblockers and doctors, because those would extend the game. That is good for the town.
Extra killers or double lynches are more problematic. Really, it comes down to whether there is an even or odd number of these extra kills. That would give us the information we need to pick 'no lynch' or 'day one lynch'. Again, that is information we don't have. Let's try and think some things out though anyway.
A. Let's say we lynch someone today. Then at some point down the road, an extra kill occurs. That would normally cause the game to end Night 5 at the latest, but we could no lynch to draw the game out to end Day 6 instead. Either way the game would have 5 lynches, 5 mafia kills, 1 other kill.
(I almost finished this post but I just thought of another option:
A1. Let's say we lynch someone today. Then at some point down the road, an extra kill occurs. That would normally cause the game to end Night 5 at the latest, but we could double lynch to end the game Day 5 instead. This way the game would have 6 lynches, 4 mafia kills, 1 other kill.)
B. Let's say we lynch someone today. Then at some point down the road, two extra kills occur. The game would end Day 5 at the latest. So the game would have 5 lynches, 4 mafia kills, 2 other kills.
C. Let's say we no lynch today. Then at some point an extra kill occurs. That would cause the game to end Day 6. Again, that is 5 lynches, 5 mafia kills, 1 other kill.
D. Let's say we no lynch today. Then two extra kills occur. That would cause the game to end Night 5 at the latest. We could no lynch a second time to get us to Day 6. Either way the game would have 4 lynches, 5 mafia kills, 2 other kills.
E. Let's say we no lynch today. Then two extra kills occur. That would cause the game to end Night 5 at the latest. We could double lynch to end the game Day 5 at the latest. The game would have 5 lynches, 4 mafia kills, 2 other kills.
The way I see it, A and C are pretty much the same result. It is just that scenario A is an informed decision, while C is a blind decision. I prefer A.
Between B and D, it is a judgement call. With B, the town gets more control over who lives and dies. With D, you get an extra night action, but the mafia gets more control over who lives and dies. It's a tough call, but I'm leaning toward B. Option E gives the town more control over who lives and dies without giving up the no lynch Day One.
You could also extend this line of thinking to if there are no extra kills.
F. Lynch today, no extra kills, game ends Day 6, 6 lynches, 5 mafia kills.
G. No lynch today, no extra kills, game usually ends Night 6, no lynch a second time, game ends Day 7, 5 lynches, 6 mafia kills either way.
H. No lynch today, no extra kills, game usually ends Night 6, double lynch once, game ends Day 6, 6 lynches, 5 mafia kills.
Option F gives the town more control over who lives and dies. Option G gives you an extra night action, but gives the mafia more control over who lives and dies. Option H gives the town back control over who lives and dies while retaining a no lynch first day.
Short Version:
It seems to me like if we no lynch Today, then we need an odd number of extra kills. In that case, we can just lynch one person per day. That gives the town and mafia control over the same number of kills. If there are zero or an even number of extra kills, we need to no lynch a second time at some point, or double lynch. The former buys us an extra night action at the expense of giving the mafia more control over who lives and dies. The later gives the town more control over who lives and dies.
If we lynch today, then we need zero or an even number of extra kills. In that case, we just lynch one person per day. That gives us more control over who lives and dies than the mafia. If there is an odd number of extra kills, we need to no lynch or double lynch so that the game will not end on a night. The former gives the town and mafia control over the same number of kills, but buys an extra night action. The later gives much more control to the town concerning who lives and dies.
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