With the slow day in the thread on a Saturday, I actually had some time to think. In case I die, I wanted to get this out.
Should the baner reveal early in the day?
The wolves will be 50/50 to know the baner.
For unknown villagers like myself, random chance would make it 60% to catch a wolf. If the baner reveals, that chance leaps to 75%, assuming a wolf doesn't also claim.
For known villagers like Roland and Ichabod, there is a 50% chance at random that they lynch a wolf. With a baner reveal, that chance goes up to 60%.
So a baner reveal increases the chances a villager voting for a wolf by roughly 13% tomorrow.
The downside is of course, that the wolves will know who the baner is, which will guarantee that the game is over if we lynch a villager tomorrow (or as long as the void-wolf survives the next villager lynch).
But by my math, the wolves have a 50% chance of blocking the correct baner either way if we lynch another villager, and thus winning. And the 50% of the time the wolves block the wrong baner, the baner will have seven people left alive to block, thus a 1/7 chance of choosing the correct one, which means the wolves win roughly 93% of the time. Now, if the baner can make some accurate assumptions about who all three wolves are, then the baner's chances improve to 1/4 to block successfully, and thus the wolves only win 87.5% of the time if we lynch a villager tomorrow. Thus having an unrevealed baner improves our chances of gaining an extra day if we lynch a villager tomorrow by 7-12.5%.
I am probably missing some important piece of the mathematics here, but that was what I came up with yesterday. I am not sure which is the superior way to play it. Thoughts?
Should we trust a baner claim late in the day?
If it becomes clear who will be lynched prior to the end of the day, the lynchee may claim baner. For an unknown villager, there is a 20% chance the person is the actual baner and a 60% chance that person is the wolf. For Roland and Ichabod, there is a 17% chance that person is the baner, and a 50% chance they are a wolf. For a villager to false claim baner would be crazy I think, because if the real baner claims, either the real baner will get lynched or the villager will get lynched, and either way the wolves will know the identity of the baner and the game is over. But for a wolf, it might be a required play to claim baner because it would either a) potentially get a villager lynched instead or b) reveal the true baner so he can be night-killed assuming the void-wolf is in play.
Does this mean that we should completely ignore a late "save me" baner claim today? Am I overlooking something here?
Voting method:
Given that 37.5% of the votes "today" are going to come from wolves, I have a few thoughts on voting.
Whatever happens, the voting cannot end up 3-2-2-1, because then the wolves could all vote for the same person and win.
Roland is the trump card in this voting. Five people will have to vote against Roland for someone other than who Roland votes for to get lynched.
One option is to be very open about it all. After discussion, Roland says who he will vote for and all the villagers should line up behind him. Granted, the wolves will very likely follow along, even to lynch a wolf, so as not to stand out, so not a lot of information will be gained, but it certainly would guarantee that the wolves have minimal influence on voting.
Another option would be to wait and have everyone cast their votes in the last minute. The benefit of this is that we get a lot more information and we keep our cards close to the vest. This would almost certainly be the optimum if PMs were allowed. This has a couple of flaws in the current setup. The wolves will be free to coordinate and we won't be. Also, since everyone will be turning in their votes so late, it will be hard to react to the voting, and the wolves will be able to coordinate and shift their votes without standing out too much (assuming villagers will probably be doing the same) unless we all agree not to change our votes with the exception of Roland and Ichabod. We also risk the 3-2-2-1 scenario happening. And perhaps not everyone will be available to vote right at the end. This also prevents us from reacting to a "save me" baner claim, but that might not be much of a negative.
Those are my thoughts on voting ATM.
Should the baner reveal early in the day?
The wolves will be 50/50 to know the baner.
For unknown villagers like myself, random chance would make it 60% to catch a wolf. If the baner reveals, that chance leaps to 75%, assuming a wolf doesn't also claim.
For known villagers like Roland and Ichabod, there is a 50% chance at random that they lynch a wolf. With a baner reveal, that chance goes up to 60%.
So a baner reveal increases the chances a villager voting for a wolf by roughly 13% tomorrow.
The downside is of course, that the wolves will know who the baner is, which will guarantee that the game is over if we lynch a villager tomorrow (or as long as the void-wolf survives the next villager lynch).
But by my math, the wolves have a 50% chance of blocking the correct baner either way if we lynch another villager, and thus winning. And the 50% of the time the wolves block the wrong baner, the baner will have seven people left alive to block, thus a 1/7 chance of choosing the correct one, which means the wolves win roughly 93% of the time. Now, if the baner can make some accurate assumptions about who all three wolves are, then the baner's chances improve to 1/4 to block successfully, and thus the wolves only win 87.5% of the time if we lynch a villager tomorrow. Thus having an unrevealed baner improves our chances of gaining an extra day if we lynch a villager tomorrow by 7-12.5%.
I am probably missing some important piece of the mathematics here, but that was what I came up with yesterday. I am not sure which is the superior way to play it. Thoughts?
Should we trust a baner claim late in the day?
If it becomes clear who will be lynched prior to the end of the day, the lynchee may claim baner. For an unknown villager, there is a 20% chance the person is the actual baner and a 60% chance that person is the wolf. For Roland and Ichabod, there is a 17% chance that person is the baner, and a 50% chance they are a wolf. For a villager to false claim baner would be crazy I think, because if the real baner claims, either the real baner will get lynched or the villager will get lynched, and either way the wolves will know the identity of the baner and the game is over. But for a wolf, it might be a required play to claim baner because it would either a) potentially get a villager lynched instead or b) reveal the true baner so he can be night-killed assuming the void-wolf is in play.
Does this mean that we should completely ignore a late "save me" baner claim today? Am I overlooking something here?
Voting method:
Given that 37.5% of the votes "today" are going to come from wolves, I have a few thoughts on voting.
Whatever happens, the voting cannot end up 3-2-2-1, because then the wolves could all vote for the same person and win.
Roland is the trump card in this voting. Five people will have to vote against Roland for someone other than who Roland votes for to get lynched.
One option is to be very open about it all. After discussion, Roland says who he will vote for and all the villagers should line up behind him. Granted, the wolves will very likely follow along, even to lynch a wolf, so as not to stand out, so not a lot of information will be gained, but it certainly would guarantee that the wolves have minimal influence on voting.
Another option would be to wait and have everyone cast their votes in the last minute. The benefit of this is that we get a lot more information and we keep our cards close to the vest. This would almost certainly be the optimum if PMs were allowed. This has a couple of flaws in the current setup. The wolves will be free to coordinate and we won't be. Also, since everyone will be turning in their votes so late, it will be hard to react to the voting, and the wolves will be able to coordinate and shift their votes without standing out too much (assuming villagers will probably be doing the same) unless we all agree not to change our votes with the exception of Roland and Ichabod. We also risk the 3-2-2-1 scenario happening. And perhaps not everyone will be available to vote right at the end. This also prevents us from reacting to a "save me" baner claim, but that might not be much of a negative.
Those are my thoughts on voting ATM.
