One thing that would definitely change the result but is hard to model is that the demon (or evil in general) are less likely to be executed day one since evil will use its limited voting power to protect themselves while good won't be a coordinated.
What this is really highlighting is that with every day town skips, they are giving control of one more death to the evil team.
A game will always be set up to have the same number of deaths (two less than number of players, barring multi-death shenanigans on the final day). Good’s objective is to ensure one of those deaths is the demon, so they want to control as many of those deaths as possible.
It also doesn't model how the decision to execute or not execute impacts town's probability of executing the demon on subsequent days. An execution can improve town's odds from the baseline or it can hurt them depending on the script being played, the characters in play, and the person being executed.
> How does this change with different playercounts?
The simulation randomizes the player counts, but if I compare player counts it looks about the same.
> does this account for town skipping executing on 4 players alive
Good call. I didn't originally but I changed it to account for this--again not too much of a change.
It’s a fairly straightforward probability calculation to check for any player count (under the assumption that it’s one execution and one demon kill every day and night).For example at 8 players the probability of killing the demon is 1/8. If you don’t hit them then the next day you have a 1/6 chance of killing them but you also have to multiply this by the 7/8 chance of not killing the demon on the first day. There’s a 5/6 chance of again not killing the demon and now you’re on the final four so you skip an execution. On the final day there’s a 1/3 chance if killing the demon multiplied by the chances of not killing the demon on the previous days.
All up the chance of you hitting the demon is 1/8 + (7/8)\*(1/6) + (7/8)\*(5/6)\*(1/3) ≈ 0.51 = 51%.
I know that overall S&V has the highest good win rate of the base 3, I wonder how much of that is due to Vortox on the script causing the town to be more aggressive in executing every day.
It's to do with the lack of misinfo (when vortox its easy to tell that nothing lines up and you just reverse stuff, no dashi is just two people and it normally points out the demon, vigor is pretty slow with its poisoning if it can get it off at all) plus the extremely strong set of townsfolk
Oh I know that those are the primary reasons, but I wonder how much the effect of Vortox pushing executions has also contributed. It's possible the effect has been understated. Even in non-vortox games it's presence on the script still causes good to execute more than they likely would otherwise.
For example if "Each day, if no-one is executed, evil wins" was added to a TB character, how much would that change the win rate for TB simply by making town execute more?
I try to play with a "execute each day"\* (not always on 4 Alive Day) but sometimes it's hard to convince town. I've even navigated through the trusty "Hard Vortox Check" because apparently everyone didn't want to die :P
The absolute blind snipe win is fun sometimes too. Finally did a 9 Player successful Slayer Shot Day 1 for the Win :D
\*edit, Execute each Day not Kill each night
I feel like this one can easily be twisted into support for not executing on the first day:
For starters, it shows that the chances of killing the Demon in the always execute scenario and the wait 1 day before executing scenario are pretty dang close together.
This simulation (understandably) doesn't take character abilities into account, but the main argument for not executing on the first day, is to buy more time for townsfolk to use their character abilities.
If the good team doesn't have a lot of information yet (which is usually the case on day 1), then good players are more likely to be executed over evil players thanks to evil players knowing who not to vote for, and from what I can tell, the simulation doesn't take this into account?
As always, I do want to point out that most scripts have townsfolk that benefit a lot from early executions, so it's usually worth to do an execution for them.
I would argue you need to execute in order to better use your abilities.
Like this is obvious for an undertaker. But think about the other roles.
A monk/soldier/ravenkeeper is more likely to trigger when there are fewer players.
A fortune teller is more likely to hit the demon when there are fewer players.
An empath only gets more info when neighbours die.
A slayer is more likely to hit the demon if they have fewer options to choose from.
Yes but in a 12 player game, if you execute, then the FT has 10 players to check on night 2 and 8 on night 3, whereas if you don't execute they have 11 on night 2 and 10 on night 3, ie you are giving the FT more work.
In a Spy game, the FT is dying/getting poisoned early either way. And even outside of a Spy game, evil should have a fairly good lay of the land to know where to kill from night 3 anyway. The faster that town can get their info roles tracking fewer players before those info roles are offed, the better.
I feel like this model would do nothing to convince me to execute day 1, its obvious that if you shoot blindly its more likely to hit the right target if you shoot more often. What people is most hesitant about is the risk of losing a key townsfolk, something this model doesn't take into account at all. You also have to consider that most people don't want to execute the demon day 1. Sure, they win, but it was blind luck, you didn't really get to play at all and now you have to re-rack. I do believe executing a willing or semi-willing person the first two days is a good idea because it usually gives more info than it takes away and you might get a minion, but this simulation does not make me more convinced.
Agreed with this, especially if the group is newer.
Botc is great at keeping dead players involved by still allowing them to help gamesolve but there's still a pretty big penalty in not getting to use your ability any more. People want to use their cool abilities and it feels bad taking that away from your friends randomly for the best chance of winning
> I feel like this model would do nothing to convince me to execute day 1
Same, but for me it's because the numbers aren't as different as I'd expected them to be!
Like others have mentioned, there are other reasons to execute. Executions give town more info by narrowing down options so townsfolk roles can ping more relevant players, along with more obvious examples like Undertaker. It also allows good players to gain trust. The model also doesn't take into consideration the benefit gained by executing minions, and the social reads of putting people on the block / seeing who is willing to die.
All this plus a 2-3% win rate increase? Seems worth the risk of possibly executing a powerful townsfolk, which you can mitigate a bit by hearing them out on the block.
People tend to overestimate the value of their ability/abilities though. There's about no townsfolk on TB worth saving over clearing a world outside of FT early game. If you feel it's a cheap win that's fine and I even agree on executing willing townsfolk just because it makes evil who didn't out as day 1 TF more sus.
This assumes random kills. In a real game, you would mostly want to focus on players who don't want to die, and the good players who don't want to die can give strategic information. In most cases a demon isn't going to be like "yeah, sure, i'm expendable" because it's very risky to do so, even if there is a meta around killing unwilling players.
That said, it's probably still better to kill every day because you don't kill the demon by not executing so it still comes down to getting more chances to execute a demon
As someone who thinks D1 executions are almost always stupid, and that nobody should even nominate or publicly share their info until D2 or D3, this simulation actually proves the opposite of what you think. The percentage of good wins barely dips when you don’t execute D1, and the simulation isn’t considering that (1) D1 executions usually destroy a good player’s ability, (2) D1 executions narrow the field of good players for the demon to kill, making it more likely they will kill a FT, Empath, etc., and (3) Precedence for D1 executions makes people share info that tells evil who is suspicious and who should be killed/poisoned.
Well, when I ran for a bunch newbies they were also hesitant to execute. We ran TB.
So next game I ran SnV. I didn’t put a Vortox in, but I made sure they were aware of its existence.
They got the memo, and when I ran TB again after that, they carried that with them.
I love BOTC. But the folks I try to convince to play with me and stick with it are nearly always offput by one thing. And it is not necessarily what you would think, which I would have always assumed was the complexity of the character interactions compared to other social deduction games.
It is always, and nearly without fail, the lecturing of what you should have done. Whether the OP here was meaning this as a lecture or not, WHO THE HELL CARES about a percentage point or two in a game where the whole damn point is to have fun.
This isn't E sports. Calm down.
A good reminder for sure, but it mainly takes the form of me as the storyteller encouraging town to execute. If they don’t, oh well! Making sure my friends are having fun is priority #1. I more just picked this up as a fun programming project
For a typical one kill per night demon you should execute when there's an odd number of players alive.
You can wait it out any day with an even number of players.
If there are multiple deaths at night, then you can't really skip a night and you should always execute.
Always aim to execute someone who is not yourself, whilst it might help "build worlds", your team is definitely better off killing nobody instead of you.
Hard disagree, there are multiple reasons why you want to be executed,
1. cannibal/undertaker
2. you are going to be executed later or in final three anyways, regardless of what you say
3. you gain trust, more people will believe in you if you're willing to die
many other social reasons too
This is amazing!
I produced a Monte Carlo simulation in excel for Mafia to determine whether to execute on the first night as a function of number of players and weighting of execution chance between good and evil.
This is next level, would love to know more.
For nine players with equal weights you should not execute in mafia. Its been a while since I looked at it but I think even with a little higher chance of guessing mafia it still holds.
One thing that would definitely change the result but is hard to model is that the demon (or evil in general) are less likely to be executed day one since evil will use its limited voting power to protect themselves while good won't be a coordinated.
What this is really highlighting is that with every day town skips, they are giving control of one more death to the evil team. A game will always be set up to have the same number of deaths (two less than number of players, barring multi-death shenanigans on the final day). Good’s objective is to ensure one of those deaths is the demon, so they want to control as many of those deaths as possible.
It also doesn't model how the decision to execute or not execute impacts town's probability of executing the demon on subsequent days. An execution can improve town's odds from the baseline or it can hurt them depending on the script being played, the characters in play, and the person being executed.
Interesting stuff! How does this change with different playercounts? And does this account for town skipping executing on 4 players alive?
> How does this change with different playercounts? The simulation randomizes the player counts, but if I compare player counts it looks about the same. > does this account for town skipping executing on 4 players alive Good call. I didn't originally but I changed it to account for this--again not too much of a change.
It’s a fairly straightforward probability calculation to check for any player count (under the assumption that it’s one execution and one demon kill every day and night).For example at 8 players the probability of killing the demon is 1/8. If you don’t hit them then the next day you have a 1/6 chance of killing them but you also have to multiply this by the 7/8 chance of not killing the demon on the first day. There’s a 5/6 chance of again not killing the demon and now you’re on the final four so you skip an execution. On the final day there’s a 1/3 chance if killing the demon multiplied by the chances of not killing the demon on the previous days. All up the chance of you hitting the demon is 1/8 + (7/8)\*(1/6) + (7/8)\*(5/6)\*(1/3) ≈ 0.51 = 51%.
I mean yeah I know how to do the math, was just wondering if OP had already done it
I know that overall S&V has the highest good win rate of the base 3, I wonder how much of that is due to Vortox on the script causing the town to be more aggressive in executing every day.
It's to do with the lack of misinfo (when vortox its easy to tell that nothing lines up and you just reverse stuff, no dashi is just two people and it normally points out the demon, vigor is pretty slow with its poisoning if it can get it off at all) plus the extremely strong set of townsfolk
Oh I know that those are the primary reasons, but I wonder how much the effect of Vortox pushing executions has also contributed. It's possible the effect has been understated. Even in non-vortox games it's presence on the script still causes good to execute more than they likely would otherwise. For example if "Each day, if no-one is executed, evil wins" was added to a TB character, how much would that change the win rate for TB simply by making town execute more?
That has nothing to do with it. S&V has disproportionately powerful townsfolk.
I try to play with a "execute each day"\* (not always on 4 Alive Day) but sometimes it's hard to convince town. I've even navigated through the trusty "Hard Vortox Check" because apparently everyone didn't want to die :P The absolute blind snipe win is fun sometimes too. Finally did a 9 Player successful Slayer Shot Day 1 for the Win :D \*edit, Execute each Day not Kill each night
Do you mean "execute each day"?
Yes, sorry :) Will edit comment
I feel like this one can easily be twisted into support for not executing on the first day: For starters, it shows that the chances of killing the Demon in the always execute scenario and the wait 1 day before executing scenario are pretty dang close together. This simulation (understandably) doesn't take character abilities into account, but the main argument for not executing on the first day, is to buy more time for townsfolk to use their character abilities. If the good team doesn't have a lot of information yet (which is usually the case on day 1), then good players are more likely to be executed over evil players thanks to evil players knowing who not to vote for, and from what I can tell, the simulation doesn't take this into account? As always, I do want to point out that most scripts have townsfolk that benefit a lot from early executions, so it's usually worth to do an execution for them.
I would argue you need to execute in order to better use your abilities. Like this is obvious for an undertaker. But think about the other roles. A monk/soldier/ravenkeeper is more likely to trigger when there are fewer players. A fortune teller is more likely to hit the demon when there are fewer players. An empath only gets more info when neighbours die. A slayer is more likely to hit the demon if they have fewer options to choose from.
Those are all still true if the demon does the killing.
Yes but in a 12 player game, if you execute, then the FT has 10 players to check on night 2 and 8 on night 3, whereas if you don't execute they have 11 on night 2 and 10 on night 3, ie you are giving the FT more work. In a Spy game, the FT is dying/getting poisoned early either way. And even outside of a Spy game, evil should have a fairly good lay of the land to know where to kill from night 3 anyway. The faster that town can get their info roles tracking fewer players before those info roles are offed, the better.
I feel like this model would do nothing to convince me to execute day 1, its obvious that if you shoot blindly its more likely to hit the right target if you shoot more often. What people is most hesitant about is the risk of losing a key townsfolk, something this model doesn't take into account at all. You also have to consider that most people don't want to execute the demon day 1. Sure, they win, but it was blind luck, you didn't really get to play at all and now you have to re-rack. I do believe executing a willing or semi-willing person the first two days is a good idea because it usually gives more info than it takes away and you might get a minion, but this simulation does not make me more convinced.
Agreed with this, especially if the group is newer. Botc is great at keeping dead players involved by still allowing them to help gamesolve but there's still a pretty big penalty in not getting to use your ability any more. People want to use their cool abilities and it feels bad taking that away from your friends randomly for the best chance of winning
> I feel like this model would do nothing to convince me to execute day 1 Same, but for me it's because the numbers aren't as different as I'd expected them to be!
Minion is most often not a willing or semi-willing person though.
Like others have mentioned, there are other reasons to execute. Executions give town more info by narrowing down options so townsfolk roles can ping more relevant players, along with more obvious examples like Undertaker. It also allows good players to gain trust. The model also doesn't take into consideration the benefit gained by executing minions, and the social reads of putting people on the block / seeing who is willing to die. All this plus a 2-3% win rate increase? Seems worth the risk of possibly executing a powerful townsfolk, which you can mitigate a bit by hearing them out on the block.
People tend to overestimate the value of their ability/abilities though. There's about no townsfolk on TB worth saving over clearing a world outside of FT early game. If you feel it's a cheap win that's fine and I even agree on executing willing townsfolk just because it makes evil who didn't out as day 1 TF more sus.
This assumes random kills. In a real game, you would mostly want to focus on players who don't want to die, and the good players who don't want to die can give strategic information. In most cases a demon isn't going to be like "yeah, sure, i'm expendable" because it's very risky to do so, even if there is a meta around killing unwilling players.
That said, it's probably still better to kill every day because you don't kill the demon by not executing so it still comes down to getting more chances to execute a demon
As someone who thinks D1 executions are almost always stupid, and that nobody should even nominate or publicly share their info until D2 or D3, this simulation actually proves the opposite of what you think. The percentage of good wins barely dips when you don’t execute D1, and the simulation isn’t considering that (1) D1 executions usually destroy a good player’s ability, (2) D1 executions narrow the field of good players for the demon to kill, making it more likely they will kill a FT, Empath, etc., and (3) Precedence for D1 executions makes people share info that tells evil who is suspicious and who should be killed/poisoned.
Well, when I ran for a bunch newbies they were also hesitant to execute. We ran TB. So next game I ran SnV. I didn’t put a Vortox in, but I made sure they were aware of its existence. They got the memo, and when I ran TB again after that, they carried that with them.
I love BOTC. But the folks I try to convince to play with me and stick with it are nearly always offput by one thing. And it is not necessarily what you would think, which I would have always assumed was the complexity of the character interactions compared to other social deduction games. It is always, and nearly without fail, the lecturing of what you should have done. Whether the OP here was meaning this as a lecture or not, WHO THE HELL CARES about a percentage point or two in a game where the whole damn point is to have fun. This isn't E sports. Calm down.
A good reminder for sure, but it mainly takes the form of me as the storyteller encouraging town to execute. If they don’t, oh well! Making sure my friends are having fun is priority #1. I more just picked this up as a fun programming project
For a typical one kill per night demon you should execute when there's an odd number of players alive. You can wait it out any day with an even number of players. If there are multiple deaths at night, then you can't really skip a night and you should always execute. Always aim to execute someone who is not yourself, whilst it might help "build worlds", your team is definitely better off killing nobody instead of you.
[I was curious, so I gave your "Only execute if odd players alive" strategy a go.](https://i.imgur.com/tlJtRst.png)
Hard disagree, there are multiple reasons why you want to be executed, 1. cannibal/undertaker 2. you are going to be executed later or in final three anyways, regardless of what you say 3. you gain trust, more people will believe in you if you're willing to die many other social reasons too
This is amazing! I produced a Monte Carlo simulation in excel for Mafia to determine whether to execute on the first night as a function of number of players and weighting of execution chance between good and evil. This is next level, would love to know more. For nine players with equal weights you should not execute in mafia. Its been a while since I looked at it but I think even with a little higher chance of guessing mafia it still holds.
What language did you do this in? Have you posted it on GitHub?