[QUOTE=Idle Thoughts]
Okay, let’s think this out now. What are all the cases this could be?
It could be:
(A) The night before this one, the Night Watchman was the reason why it was a no-kill and tonight he/she is the reason it’s a no-kill again.
(B) The night before this one was a mafia recruit. That means that today probably wasn’t since they only have one (and, vica versa, if tonight was one, the night before this one wasn’t). Either way, that would be the case and that makes me feel good that something is putting a wrench in the mafia’s plans.
(C) The night before this one, the Doc had protected him/herself and the mafia tried hitting them. The case COULD be, then, (and seems to make the most sense) that the mafia, JUST TO BE SURE, tried hitting them again. If this is the case, then they are now confirmed who the either the Doc or a DoGooder is (See F), probably.
(D) It was a mixture of two pro-town things. Namely: night before last the Night Watchman was right and the mafia changed/tried other targets and this night was the Doc or night before last the Doc protected themselves and the mafia changed/tried other targets and it just so happens that the Night Watchman made the same this time.
(E) The mafia tried recruiting the night before last and the person was a DoGooder (so it failed). So they then tried someone else (and were successful)
(F) The mafia tried recruiting the night before last and the person was a DoGooder (so it failed). So they then tried the same person again (just to be sure it was probably not the Night Watchman) and found again, they could not recruit (see similiar situation in C).
and finally
G, A combo of the DoGooder recruiting attempt (night before or this night) and save by a protown role.
Now A is possible (really, they are all possible), but it just doesn’t feel right. I think the odds are pretty slim for that (however I could be wrong).
E and G also feel wrong. I doubt G would be the case because it doesn’t make sense that they’d try to recruit but, the next night, not do it again.
and E strikes me as being foolish a bit. If I were scum and I made a hit and it failed…I’d try the same hit the next night just to make sure. And if that person was, again, saved, then I’d have pretty much surity that that person was either a DoGooder or the self-protecting Doctor. So I doubt they’d change targets.
That leaves B, C, D, and F.
D, again, like A, just seems too coincidental. I mean, hey, if it’s the case, that’s great! Mean’s we’re a force to be reckoned with. But in this game I’m not going to be optimistic too much and always think the worst possible case.
C and F are both equal in stature, just with different roles. I think they make the most sense of them all. It stands to reason that they tried to kill someone off night before last and were unsuccessful, that they’d try the same target again, just to make sure.
And, of course, there’s B…which has a good chance of being the case too, although I don’t feel as strong as C or F. However, I won’t count it out and hope nobody else will either. It’s very possible a recruitment took place..especially with killing off one of their own the last day.
Dunno if that helps anyone by laying it all out there like that..but it might. So based on what I said all in here, I think either C/F or B was the case last night.
[/QUOTE]
These are out of order, but it makes more sense to me this way:
A: The probability of Watchman block is 1/6, so the probability of a Watchman block on two consecutive nights is 1/6 * 1/6 or 2.78%.
D: The probabilty of a Doctor block is 1/10 or 1/11, depending on if there were originally 4 or 5 mafia at game start. Assuming a worst-case scenario for the mafia, the probability of a WD or DW block on consecutive nights is 2*(1/6 * 1/10) or 3.33%.
C: The ratio of W/D blocks is in the neighborhood of (1/6)/(1/10) or 1.67. I.e., a Watchman block for any particular night is a little more than one and a half times more probable than a Doc block. So, assuming for a moment that the night before last was a block, the mafia going back and attempting a hit on the same individual just to determine if he was doctor wouldn’t really make sense, as no real determination could be gathered from such a sequence of events that are the least probable. It also raises the question: if the mafia actually could make a sound determination as to who the Doctor is in such a manner, would it make sense for them to waste a hit just to do so? Maybe so if they are planning to recruit the Doctor on a subsequent night. But as mentioned, the point is moot since they are likely to make the wrong conclusion than the right one here. Things are different of course if things aren’t random: if they happen to correctly guess who the doc is and then try to recruit him.
If the doc self-protects one night, and protects someone else the other night, the probability of two consecutive Doc blocks is in the neighborhood of (1/10)*(1/15) or 0.67%, since he knows the status of himself one night (~1/10) but not the second (1/15). The probability of two consecutive Doc blocks, where the doc is not self protecting, is (1/15)^2 or 0.44%
If only one attempt at a recruit is allowed regardless of the outcome of the attempt, E and F are not possible.
G: If the mafia decide to recruit, the probability of picking the Do-Gooder is 1/10 or 1/11. So, the probability of a combination of a Do-Gooder block and watchman block is in the same as B above, ie in the neighborhood of 3.33%. The probability of a combination of a Do-Gooder block and Doc block would be twice that of a self-protected Doc/Doc block, i.e. in the neighborhood of 2*(1/10)^2, or 2%
I’m not sure how you would go about trying to quantify other specific scenarios such as B above, a “no kill” decision, or other combinations of a successful recruit and some other event. But you can make an accurate estimate of the combined probabilities of all other events not quantified above: 100-(2.78+3.33+0.67+0.44+3.33+2) or 87.45%
These numbers are slightly dependant upon the number of mafia originally in the game, but the overall relative probabilties of these different events won’t change.