Quality decisions: weight of rounds, critical points

An experienced player differs from a beginner not by the number of tricks but by deciding consciously and being able to explain why he chose as he did. This lesson collects the tools of quality decisions from "Mafia in the Style of Zen": the awareness practice, three control questions, a scale of how much each round matters, judging whole trios, the critical point and a formula for a weighed choice.

The awareness practice

The idea that most people live in a mode of mere existence is not new. A tinned way of living does not let you feel the moment, create or think clearly. The state of "here and now" is productive, and here is why.

One of a civilian's key skills is the ability to take in and remember information. When we are not "here and now", an inner dialogue or a daze switches on. Both block the perception and processing of incoming information. You cannot make sense of the incoming data, so you cannot draw a quality conclusion. Scattered attention usually comes with boredom, and when there are many "sleepers" the game stops being intellectual and slides into gloom. A person's resource is not unlimited, and one gloomy character can infect those around him with his mood. When there are six or more of them, it is a disaster.

Three control questions

To understand that you are thinking well, ask yourself:

a) On what basis am I making my choice? A check of the intellectual side. If after the game you cannot clearly explain why you chose as you did, you dropped out of reality. Phrases such as "he spoke badly, I did not like the waking up", "the emotion was bad", "the voted-out player played terribly" do not count: they mean nothing and are not verifiable information. If you can explain what the choice rests on, you were doing intellectual work.

b) On what basis and why am I voting? A mini-controller for every round. Voting without the head switched on is one of the surest signs of dropping out of the game. The scatter of hands and mixed colours are almost key parameters for choosing a line of play. If you slept through the vote, you did not remember who put a hand where, so in the next round there is nothing to think about. And the scatter of hands is one of the most informative and precise indicators of position.

c) If I freeze the game and start the vote, how will the hands scatter and who will leave the game? This item is one of the most important skills for the mafia. Depending on who the vote will be between, you need to build your speech: redirect attention away from your black, develop a conflict among the civilians or keep the course of the game. If you are the last speaking black and the team is under threat, ignoring this item sharply lowers your chances. You can sacrifice one of your own while killing the sheriff, but this requires a plan for victory, an assessment through "here and now" and active steps. On the black who speaks last lies the responsibility for the viability of the whole team.

The weight of events

On what basis should decisions be made? What matters more and leads to the right conclusion? The author names this order of significance of the round's events, in descending order:

The round at nine players.
Round zero.
The critical round at seven or eight players.
The guessing round.
The critical round at five or six players.

Consequences: a player's position in a non-critical round matters more than the round at five; the moves of round zero matter more than those made at seven; the argumentation and speech of the round at nine matter more than the same in the guessing round; actions in early rounds matter more than later ones. (The order of significance is the author's opinion, not a calculation.)

The weight of a black who has left or is sitting at the table

Most players choose the line of the whole team by the sheriff. But both the sheriff and the don are under the pressure of the role and stress, so the leader of the reds is often mistaken for the mafia. Choosing by the sheriff is good, but such a view is narrow. It is better to look at all three blacks together, even if some have already left.

The don can play very well while the sheriff sags under an opponent's pressure. Before the final choice, assess all the players of the trio under both versions. Two players who have shown themselves well and one not-so-good sheriff against two villains and one decent leader of the reds? The author would vote against the team in the second variant.

In games with one line (or when the town has correctly chosen between two sheriffs with the shot at the real one), the main reference point is the position of the black who did not expect to be checked. The one against whom a player of the black team gathered votes in round zero and round one is a civilian.

The importance of each team member, in descending order in the author's opinion:

The sheriff (gives the most information, the leader of the team).
The player found black last (the least vulnerable in terms of stress, level of play and position).
The player voted out at nine or who became the victim of the balance. The weakest link of any team. He is most likely red, if only because at the moment of the vote there are twice as many civilians as blacks.

The critical point

One of the worst enemies of the town is paranoia. It sets in when the town has chosen the line of play correctly and decided on the red team, it is roughly clear that the mafia will lose, but suddenly someone remembers an insignificant fact and starts going through all the versions, outplaying himself. To stand firmly on your feet, remember the critical points: the turning moments of the game.

A critical point is of two kinds.

An event after which the choice is made. In a game with two sheriffs, one of them removed a player with the deciding hand both at nine and at seven. The game did not end, so this sheriff is the real leader of the reds. The town has decided: there can be no paranoia and no other versions. Another example: two lines of play and a black check, nine players, the sheriff was removed.
An action or move after which the player cannot be removed. When you hear "if he is mafia, we have already lost", something has happened after which one cannot vote for removal. In practice this is often simply a way of handing victory to a well-speaking strong player, ignoring his moves, on one speech alone. That must not be done. But if a player could have won together with the mafia by buying a vote (a critical round, one bought red hand, two black hands, he does not put his own) and did not win, that is the critical point. Such a player is a civilian.

A balanced decision and probability theory

Mathematics is not exhausted by the ability to count to ten; it helps to draw well-founded conclusions and to keep a distance from impulsive decisions. For this an arithmetic mean and a little everyday probability theory are enough.

From round zero it is more effective to gather the reds and look for the blacks by the method of the remainder: there are far more red signs that give away a civilian card, and the chance of losing by standing in a meaningless counterweight is smaller.

We compare two players by the formula X = (Xa + Xb + Xc + ...) / N and Y = (Ya + Yb + Yc + ...) / N, where X is the probability that the first player is a civilian; Y is the same for the second; Xa, Xb, Xc are the first player's observed actions and the assessment of how red they are; Ya, Yb, Yc are the same for the second; N is the number of parameters. For a balanced decision N is at least three. If X is greater than Y, we vote against the second; if Y is greater than X, against the first.

The probability of being a civilian by an action is calculated like this: take a move and count how many times only a red or only a black made it. For example, breaking the table in round zero is done only by a black in eight games out of ten: so there is an 80 percent chance he is mafia and a 20 percent chance he is a civilian. The formula takes 0.2.

Correct application (the guessing round of an experienced player)

Player no. 1 (probability of red X): in round zero, on the fifth slot, did not take a black into the team (0.8 red); proposed voting between two civilians in the first round (0.1, because it is a black move, so we invert); sent the mafia for a check on the night the sheriff was killed (0.5, a grey action). X = (0.8 + 0.1 + 0.5) / 3 = 0.47.

Player no. 2: hands were gathered against him and two blacks voted at nine (0.95 civilian); mixed up colours in his speech (0.3); at nine voted against the real sheriff (0.4). Y = (0.95 + 0.3 + 0.4) / 3 = 0.55.

We put a hand for removing the first player: 0.47 is less than 0.55.

Incorrect application (the guessing round of a weak player)

Player 1 woke up well (0.9) and took me into the red team when he could have flooded me (0.8). Player 2 voted against me at nine (mafia 0.95). After the game: "He is just a passenger, I protected the table from a break in round zero, how could he vote against me? He should not have won." "What is there to count? The second is mafia and that is it!" The author: it would be funny if it were not sad. This is thinking on wrong inferences, without switching on analytics and without assessing even three parameters. An impulsive choice on emotions that takes into account neither the trio of blacks formed over the game nor the significant actions.

Where do the numbers come from? There will be no list: you must develop, through your own experience, a sense of which action means redness or blackness and with what probability. In the example above all the numbers are taken from the author's observations of his own tables, and at yours they may be almost the opposite.

For the black

The same tools show which of your actions will colour you in the eyes of such a calculation. Think about the "critical point" in advance: you can let a chance to win slip for the sake of a long game and a red colour only if you have a plan.

Application

Awareness makes the game intellectual.
Track which players are at risk of leaving and build your strategy as mafia on that.
The earlier the event, the more important it is for the decision.
Consider events at the table in their interconnection.
Count the votes and remember who puts hands against whom.
Paranoia is removed by the critical point.
Make weighed, quality decisions.

Self-check questions

The vote will definitely be between your mafia, whatever you do. How do you win the game and what must you not do?
Why are the events of the rounds at five and six the least important at the stage of the final decision?
How is the weight of schools distributed for you personally? On which techniques do you build your play and analysis?
In a game with two sheriffs one removed a player with the deciding hand both at nine and at seven. The game did not end, so this sheriff is a civilian. How can the black team get around (break) this rule?
What other critical points do you know? At least one.
Removed and voted out: what is the difference?
What corrections must be made to the formula to decide more precisely?
A checked black persuades no. 1 to put a hand for removing you, the real sheriff. What is the probability in this case that no. 1 is a civilian?

Practice

Take a recording of a game and mark the critical points: where a player could have won as mafia and did not. Then make a table of three parameters for two players of your group and compare the calculation with the result of the game.

Typical mistakes

Explaining a choice with the words "he spoke badly".
Forgetting the trio of blacks as a whole.
Using the formula with someone else's numbers.
Allowing paranoia after a critical point.

Source of the idea. The chapters "Quality decisions" from Dmitry Novik's book "Mafia in the Style of Zen" (2020). The numbers in the examples belong to the author and are given as teaching figures.