The sheriff's check lines and the mathematical victory

There are only two purposeful styles of playing the sheriff: play from gathering the red team and play through finding the mafia. Which is better, and what a mathematical victory is, we examine here. (In the book the notation is КК, ЧЧ, КЧ, ЧК; here R stands for red and B for black.)

Notation

So as not to overload the text, check lines are written in abbreviations (the first letter is the colour announced for the check, the second is the true colour of the checked player):

• RR a red check of a red (including a check of a killed player);
• BB a black check of a black;
• RB a red check of a black (deception);
• BR a black check of a red (deception).

The first two lines (RR, BB) are available to the real leader of the reds, all four only to the false sheriff.

Play from black checks

The line starts with finding a player of the black team on the first night. If an unchecked mafia player is found, the false sheriff, the mafia team is found, and what remains is to carry it through to victory: BB BB. But this line leaves the mafia many options: it can kill the real sheriff on the second night without a second line of play or play team against team. With a second red check you will not have the full picture and may have to spend effort on persuading the found red. After a found mafia player it is better to discover a black colour the second time (BB RR as a fallback).

A check of the mafia gives the town the greatest amount of information, so the sheriff should go for it from the very first night. A found black is certainty in the position, a lower level of aggression, voting against the mafia and a mass of advantages described in the lesson on the best check.

Play from red checks

Play from gathering civilians starts with a red check on the first night. If the sheriff is killed on the night before the critical round, on this line he leaves behind two definitely known civilians (RR RR). They will unite the town and until the guessing round (a round at seven, at five) will be able to choose candidates for removal. The influence will be with the town, as will the final decision in the rounds, and this is the advantage of the line.

Good sheriffs, having stumbled on a civilian, find the colours of two players at once through conflicting links. The one attacking our check is mafia.

Having found a second red among doubtful players on the second night, you approach a mathematical victory. This is what the mafia community calls the strategy of finding blacks by looking for reds. A second line of play in this case either does not exist or the town does not consider it. The point: you add players to the civilian team, enlarging it, so that blacks remain in the dry remainder.

When a mathematical victory arrives

1. At nine players the town has five found reds (in the remainder, the right to a mistake and three blacks, four votes).
2. At seven players four reds are known. If the round is not critical, three are enough.
3. At five, three.
4. At three, two.

With serious positional play, when people responsibly give out colours, it is not necessary to have checks equal to the number of players. For example, player No. 5 confidently names players No. 2 and No. 4 civilians. The check of No. 5 at once forms a red team of four (No. 5, No. 2, No. 4 and you). Not in all cases, but it is a powerful help in forming the red team.

The optimal line after the critical round

If the critical round has passed and the false sheriff is at the table: you removed one black, the second is known (the false sheriff) and you find the last with a check. A red check is no longer needed: RR RR BB.

If you removed the false sheriff or think you will be killed, look for a third red. In the nicest layout (all checks alive) this is a mathematical victory. In a not so good one, until the end of the game you have a live red who will make the right decision with probability of 50 percent and more. The dry probability of a civilian victory is only 25, and with a checked red a full 50 (RR RR RR).

About mixed-colour checks

Without a black check you are meat for the shooting. In the first round the blacks, understanding the sheriff will die, send each other for a check and win on mixed colours. With a red check it is better not to stick your head out (RR BB).

A sheriff with the line BB RR can be killed on the second night. This is a frequent variant: the check of the first night is revealed by the false sheriff. In both variants when the sheriff is killed the red check is shot next. In a round of five the town will have no link that gathers the town. So mixed-colour checks should be avoided by all means.

Application

1. Play from black checks.
2. If you started with a red check, gather the red team.
3. Check conflicting links.
4. You must not drop the sheriff through a balance at seven without a found team.

Questions for self-check

1. In which situations is it profitable for the false sheriff to give a black as black with the first check? What is the victory plan?
2. Under what conditions is it profitable for the false sheriff to give a red as red?
3. Which of the four checks (RR, RB, BR, BB) on the first night is the most profitable for the mafia and why?
4. What main advantage of a check of a black who will not reveal himself as the false sheriff was not named in this chapter?
5. Does the colour of the false sheriff's first check affect planning the game: three on three, two on two or a win in the guessing round? Is there a dependence?

Practice

Write down on paper the check lines of both sheriffs from three analysed games in the format RR, BB, RB, BR and determine which lines led to victory.

Typical mistakes

• Choosing mixed-colour lines.
• Leaving a red check without attention.
• Not counting reds for a mathematical victory.

Source of the idea. The chapter "The sheriff's check lines. The mathematical victory" from Dmitry Novik's book "Mafia in the Style of Zen" (2020). The percentages belong to the author.