I'm not good enough at mafia to claim that I have a framework down pat.
I think most of it is actually already intuitively used by good mafia players. A townie saying "That seems scummy" is isomorphic to "that increases the probability that voting for you leads to a win". A strong analyst will be able to pick up scumtells, and scumtells can be viewed as elements that increase the probability that a given target is scum, which in turn provides an opportunity to increase the probability of victory (by voting that target).
On the scum side, the probabilities are better-defined, because you have more information. There are still unknowns, though - obviously the general unknowns of how humans will react to things, but also mechanics-specific things like "is there a cop?", "who will protective roles target?".
I think the probability-oriented perspective is most useful when it specifically sheds light on something that would be overlooked. I think that mostly happens in the decision-making phase, where it's useful for three things:
1) Avoiding overconfidence. Viewing the game as a deterministic skill contest or pattern-matching can make one believe that, because a pattern was matched, there is certainty and the alternative doesn't need to be considered. Trying to assign probabilities can force the alternatives into view, force them to be evaluated.
2) Avoiding underconfidence / decision paralysis. This is particularly the case for things like vigs. It is natural to not want to act except on near-certainty - but often, inaction eats away at your odds of winning. A balanced game of mafia should be assumed to be 50/50; if you can push your odds even a bit higher, it's generally worth it.
3) Specifically seeking things that clarify probabilities. That means asking questions that clarify the unknowns, and probing to get info that can either confirm or contradict the current "leading probability".
Just one final question: Would you consider chess equivalent to a die roll?
Depends on who's playing, and whether you view the game as a whole or a specific subpart of the game. A chess endgame is purely deterministic. The game as a whole is theoretically deterministic, but as played by humans, it is not. It makes sense to say that a game between equally matched players is basically a coin flip.
This is basically the problem. If you watch anything as a die roll, it loses it's meaning.
Only if you choose to let it. Does it cause the world to lose meaning if you recognize that everything is made of the same subatomic particles?
What you're trying to do is minimizing skill and attributing it to chance which is not a view I can get behind.
I'm not trying to minimize skill. I am trying to appropriately attribute skill.
Skill and chance are not incompatible. Most things are both. The reason I think recognizing this improves play (or decisions in general)? Because increasing the probability of a victory takes (and, I would say, is the essence of) skill. Trying to create a deterministic algorithm to solve games is fragile - you can go back and say "if I'd seen this one thing, or done that one thing, I would have won", but that won't actually work the next time you play because circumstances will be different. Rather, if you try to see heuristics and their effect on victory probability, you can get a resilient, adaptive improvement.
Notably, this is not just for Mafia. Top-level chess players - and top-level chess AIs - approach chess exactly this way. Yes, they can think out more moves ahead - but they do not "solve the game". They are aware of the effects of different game factors on their probability of victory, and they constantly push to increase those probabilities higher. This is the point of tempo, position, initiative, and so forth. They play a fundamentally heuristic game. They play chess as an iterated series of dice rolls, where each side is trying to swap in their own loaded dice, and the side that loads the dice the most wins.
This doesn't minimize skill. The highly skilled player wins much more than the unskilled player because they can push the odds in their favor.
But the whole world is based around RNG. Elementary particles exist as probabilities, but on macro level we can't attribute our actions to chance.
Yes, we can! I find it to be a very useful approach to decisions. Thinking in terms of probabilities makes decision-making more focused and results in better choices.
It's true that you can consider every event to have an inherent probability, but that doesn't really make voting in mafia the same as throwing a die.
Voting in Mafia isn't the same thing as literally throwing a physical die - but it's a lot closer to it than most things in life. A lot of probabilities in life are 99.999+%. I can take a hundred thousand steps without tripping over my own feet (though perhaps not ten million). Voting, on the other hand, is a lot closer to being 1 in 2, or 2 in 3, or 4 in 5 kinds of chances.
Just one final question: Would you consider chess equivalent to a die roll?
Depends on who's playing, and whether you view the game as a whole or a specific subpart of the game. A chess endgame is purely deterministic. The game as a whole is theoretically deterministic, but as played by humans, it is not. It makes sense to say that a game between equally matched players is basically a coin flip.
But after all that song and dance, if I roll a 4 and “lose” I go “well it was just how the dice fell” absolving me of any reason to analyze why I lost. It stops being about my decision.
That's what I'm referring to as psychology.
You roll a 4 and "lose". You can say "that's just how the dice fell", and not change anything - or you can note that there was an opportunity to get a +1 earlier, which you missed, and which would have made that 4 a "win".
You are in LyLo and fire at the wrong person. You can say "that's just how the game goes", and not change anything - or you can note that there was an opportunity to take note of some behavior and correlate it with another thing that happened, and which would have made you more accurate with your read.
The trappings of the situation - dice vs. votes - are different, but the underlying mechanics are the same. Mafia has an element of chance - the sheer unpredictability of the other humans you're playing with. It's a more complex RNG than a die roll, but from the perspective of the decision-maker, it can be treated as an RNG.
But we are psychologically more likely to attribute a die roll to the final chance element, ignoring how we affected (or could have affected) the outcome before we even rolled; and we are psychologically more likely to attribute win/loss in a mafia game to correct/incorrect analysis, discounting the unpredictability of humans.
My counter point to this would be that making that informed decision is still inherently different than picking at random. Statistically making informed decisions isn’t always going to get the correct result, but it’s a different concept than just rolling a die.
Certainly! But you're just including additional context.
"Roll 2d6. If you get at least 5, you win." That's a pure die roll, right? But what if the process is like this:
1. The player starts with 1d8 and needs to get at least a 7 to win.
2. The player makes some decisions and takes some actions. As a result, the 1d8 upgrades to 2d6.
3. The player makes more decisions/actions. As a result, the "target number" goes down from a 7 to a 5.
4. Now the player rolls the dice - 2d6 to get at least a 5.
In this light, it was a series of informed decisions.
The difference is simply that you're looking at a larger scope. The two are not separate things - it's more that one is a subcomponent of the other.
This is not at all how mafia works. Every vote you make should be a informed decision not a random die roll.
An informed decision is a die roll. There is no difference between the two besides psychology and what you call it.
No. An die roll is by definition a uniform CDF.
I would definitely not consider that part of the definition. "Roll 2d6" has a Gaussian distribution centered around 7, not a uniform distribution; I would consider 2d6 a die roll.
And this is talking about statistics aka a multitude of events. An informed decision is a single event that has no computable probability.
You are using a frequentist approach to the terms of statistics and probability. I am using a Bayesian approach, which has no problem talking about the computable probabilities associated with unique events and decisions.
The frequentist vs. Bayesian dichotomy is a longstanding difference in views on probability, and essentially every example has a frequentist response and a Bayesian response, each of which are fairly self-consistent. For example:
Let me give you an example: You have three doors. One has molten lava behind it, one has a frozen tundra and the last one has full table. You have 33% chance of getting the door that doesn't kill you. Instead of picking randomly, you go near every door. One is much hotter than the rest while one is much colder. You pick the door that has neither of these problems. You made an informed decision that cannot be quantized as a probability, even though the probability of picking the right door is 33%.
I would respond that my decision certainly can be quantified as a probability; what I've done by sensing temperature is not removed the concept of probability, but simply changed the distribution. I have increased the chance of being correct. If I knew that my temperature sense is infallible, and there are no tricks, then I have increased my probability of success to 100%. But if I know that this whole game was set up by an infinitely powerful genie that likes to trick people, I might think I've only gone up to 50%, as the question is now "is the temperature a trick?" and I have no way of being certain about the answer to that.
• Regarding the "button you can push that gives you particular odds of winning", I agree with Shadow in 108: while there are games that rely on die rolls (either significantly or completely), I don't think I'd want to play any game where the entire kit'n'caboodle falls to the roll of a single die. Even if that single roll follows tons of analysis, it still just feels like gambling (perhaps with better odds, but still).
During the game, I was mostly using that line of questioning to gently poke at behavior. But I do think it's a useful examination outside the game, and I disagree.
I think Mafia inherently already falls to such die rolls, and the only difference is they're not explicit. When you're in LyLo, you can never know with complete certainty who the scum is; even if you have Cop results you can always worry about millers and godfathers and all that sort of thing. So you're always going to be pressing the Vote button with some odds of being right and winning, and some odds of being wrong and losing. If you really weren't willing to play a game that can come down to a gamble, you wouldn't be playing Mafia.
Rather, I think people are resistant to explicit gambles, where it feels like some outside force sets the odds - but implicit gambles ("I could be wrong about this") feel psychologically fine. Statistically, they're equivalent. If your hunches/analyses/scumreads are correct about two out of three times, and you act on that in endgame, that has the same outcome as a button that's 67% win / 33% loss.
To me, "would you press a 50/50 win/loss button" is the same as "would you place the hammer vote in a LyLo if you're half certain of your scumread".
V/LA till Sunday. Since I have no scalpels this shouldn't affect game flow much.
I am in agreement with seeking 1 more kill today. I am against it being shadow. I can see the "we get info" argument for people who aren't me, but that should still be informed by scum reads.
I also wouldn't want osie dead. Those are my two town reads.
That's exactly the wine I was talking about earlier.
Consider this scenario for example: scum is under the knife and going to die. They fire at X hoping to get another kill. X gets deflected. Scum flips. X is now townfirmed.
There is also the practical fact that they might just not have had a good window to log in and fire.
General observation: this game is extremly wine-friendly. I was just thinking through the possible reasoning for what scum would do when under a pending Strike, and there's so many WIFOM twists.
I think most of it is actually already intuitively used by good mafia players. A townie saying "That seems scummy" is isomorphic to "that increases the probability that voting for you leads to a win". A strong analyst will be able to pick up scumtells, and scumtells can be viewed as elements that increase the probability that a given target is scum, which in turn provides an opportunity to increase the probability of victory (by voting that target).
On the scum side, the probabilities are better-defined, because you have more information. There are still unknowns, though - obviously the general unknowns of how humans will react to things, but also mechanics-specific things like "is there a cop?", "who will protective roles target?".
I think the probability-oriented perspective is most useful when it specifically sheds light on something that would be overlooked. I think that mostly happens in the decision-making phase, where it's useful for three things:
1) Avoiding overconfidence. Viewing the game as a deterministic skill contest or pattern-matching can make one believe that, because a pattern was matched, there is certainty and the alternative doesn't need to be considered. Trying to assign probabilities can force the alternatives into view, force them to be evaluated.
2) Avoiding underconfidence / decision paralysis. This is particularly the case for things like vigs. It is natural to not want to act except on near-certainty - but often, inaction eats away at your odds of winning. A balanced game of mafia should be assumed to be 50/50; if you can push your odds even a bit higher, it's generally worth it.
3) Specifically seeking things that clarify probabilities. That means asking questions that clarify the unknowns, and probing to get info that can either confirm or contradict the current "leading probability".
Skill and chance are not incompatible. Most things are both. The reason I think recognizing this improves play (or decisions in general)? Because increasing the probability of a victory takes (and, I would say, is the essence of) skill. Trying to create a deterministic algorithm to solve games is fragile - you can go back and say "if I'd seen this one thing, or done that one thing, I would have won", but that won't actually work the next time you play because circumstances will be different. Rather, if you try to see heuristics and their effect on victory probability, you can get a resilient, adaptive improvement.
Notably, this is not just for Mafia. Top-level chess players - and top-level chess AIs - approach chess exactly this way. Yes, they can think out more moves ahead - but they do not "solve the game". They are aware of the effects of different game factors on their probability of victory, and they constantly push to increase those probabilities higher. This is the point of tempo, position, initiative, and so forth. They play a fundamentally heuristic game. They play chess as an iterated series of dice rolls, where each side is trying to swap in their own loaded dice, and the side that loads the dice the most wins.
This doesn't minimize skill. The highly skilled player wins much more than the unskilled player because they can push the odds in their favor.
Voting in Mafia isn't the same thing as literally throwing a physical die - but it's a lot closer to it than most things in life. A lot of probabilities in life are 99.999+%. I can take a hundred thousand steps without tripping over my own feet (though perhaps not ten million). Voting, on the other hand, is a lot closer to being 1 in 2, or 2 in 3, or 4 in 5 kinds of chances.
Depends on who's playing, and whether you view the game as a whole or a specific subpart of the game. A chess endgame is purely deterministic. The game as a whole is theoretically deterministic, but as played by humans, it is not. It makes sense to say that a game between equally matched players is basically a coin flip.
You roll a 4 and "lose". You can say "that's just how the dice fell", and not change anything - or you can note that there was an opportunity to get a +1 earlier, which you missed, and which would have made that 4 a "win".
You are in LyLo and fire at the wrong person. You can say "that's just how the game goes", and not change anything - or you can note that there was an opportunity to take note of some behavior and correlate it with another thing that happened, and which would have made you more accurate with your read.
The trappings of the situation - dice vs. votes - are different, but the underlying mechanics are the same. Mafia has an element of chance - the sheer unpredictability of the other humans you're playing with. It's a more complex RNG than a die roll, but from the perspective of the decision-maker, it can be treated as an RNG.
But we are psychologically more likely to attribute a die roll to the final chance element, ignoring how we affected (or could have affected) the outcome before we even rolled; and we are psychologically more likely to attribute win/loss in a mafia game to correct/incorrect analysis, discounting the unpredictability of humans.
"Roll 2d6. If you get at least 5, you win." That's a pure die roll, right? But what if the process is like this:
1. The player starts with 1d8 and needs to get at least a 7 to win.
2. The player makes some decisions and takes some actions. As a result, the 1d8 upgrades to 2d6.
3. The player makes more decisions/actions. As a result, the "target number" goes down from a 7 to a 5.
4. Now the player rolls the dice - 2d6 to get at least a 5.
In this light, it was a series of informed decisions.
The difference is simply that you're looking at a larger scope. The two are not separate things - it's more that one is a subcomponent of the other.
The frequentist vs. Bayesian dichotomy is a longstanding difference in views on probability, and essentially every example has a frequentist response and a Bayesian response, each of which are fairly self-consistent. For example:
I would respond that my decision certainly can be quantified as a probability; what I've done by sensing temperature is not removed the concept of probability, but simply changed the distribution. I have increased the chance of being correct. If I knew that my temperature sense is infallible, and there are no tricks, then I have increased my probability of success to 100%. But if I know that this whole game was set up by an infinitely powerful genie that likes to trick people, I might think I've only gone up to 50%, as the question is now "is the temperature a trick?" and I have no way of being certain about the answer to that.
I think Mafia inherently already falls to such die rolls, and the only difference is they're not explicit. When you're in LyLo, you can never know with complete certainty who the scum is; even if you have Cop results you can always worry about millers and godfathers and all that sort of thing. So you're always going to be pressing the Vote button with some odds of being right and winning, and some odds of being wrong and losing. If you really weren't willing to play a game that can come down to a gamble, you wouldn't be playing Mafia.
Rather, I think people are resistant to explicit gambles, where it feels like some outside force sets the odds - but implicit gambles ("I could be wrong about this") feel psychologically fine. Statistically, they're equivalent. If your hunches/analyses/scumreads are correct about two out of three times, and you act on that in endgame, that has the same outcome as a button that's 67% win / 33% loss.
To me, "would you press a 50/50 win/loss button" is the same as "would you place the hammer vote in a LyLo if you're half certain of your scumread".
I am in agreement with seeking 1 more kill today. I am against it being shadow. I can see the "we get info" argument for people who aren't me, but that should still be informed by scum reads.
I also wouldn't want osie dead. Those are my two town reads.
Consider this scenario for example: scum is under the knife and going to die. They fire at X hoping to get another kill. X gets deflected. Scum flips. X is now townfirmed.
There is also the practical fact that they might just not have had a good window to log in and fire.
First of all, FIRST BLOOD!!!
Second, what do people think of that? In particular, I want osie's take.