Lifting four at eight: a pair of blacks

The author of "50 Shades of Red" opens the chapter with a joke attributed to Winston Churchill, that it is easier to govern a nation than to raise four children, and adds that this is exactly why the tradition of lifting four at eight is popular in Mafia. Lifting four at eight people is the removal of the maximum number of suspicious candidates in one vote. The author sometimes calls it a mathematical victory and writes that there are exactly two justified situations for it: this lesson covers the first (when there is certainly no black trio in the town), the second is covered in the lesson "Lifting four with found teams".

Why lift several at all

The author explains the meaning of the whole section on tie votes like this. We raise the percentage of wins of the red town and punish the mafia for a miss. Several guideposts from the book:

in a guessing round at four, lifting two players raises the town's probability of winning to 50 percent, while a vote for one candidate gives a "dry" win rate of 25 percent; if two from different teams are lifted, it is a one hundred percent win;
lifting three players at six with three found reds gives a one hundred percent win;
lifting four in a round at eight people with known teams also wins mathematically;
the threat of removing many candidates at nine provokes the mafia into a second line of play, and therefore gives additional known colours through reveals and checks;
if there is no second line, that is even better: lifting several gives the town the right to a mistake, that is, the chance to vote out a civilian without losing. For the win the blacks need to remove only two reds, so by removing several people at once we give the town invaluable help. Even if two reds were removed, the town has not lost: civilians are still the majority, and all methods of finding the mafia can be used. Besides, the sheriff's circle of checks shortens and the probability of a black check grows.

The author draws a hard conclusion: in modern conditions it is simply shameful not to know the situations where lifting several players is needed, and not understanding the point of a lift means a low level of play.

Three rules for all lifts and tie votes

Never remove the sheriff and the false sheriff from the game before the critical round.
Explain all lifts and tie votes to the participants of the vote. A person who sabotages a tie vote that is objectively beneficial for the town is either mafia or understands the game poorly (the author calls the civilians' weak understanding of the game the pain point of the section).
It is desirable to duplicate the explanation with gestures, showing on the fingers who votes where.

And the author's memorable phrase: activating, campaigning for and realising a tie vote with the removal of many suspicious candidates is a red move.

Condition of application

The device is applied when there is certainly no black trio in the town. This happens if a break was made into a mafioso and the sheriff was killed (or the other way round), or there were misses: in short, one black player left on each of the two versions. Then at eight players no more than two mafia remain. We use the same voting principle as with other tie votes: with all its wish the mafia cannot break into a civilian.

The voting scheme

The author's example: eight players (no. 9 and no. 10 absent). We remove no. 1, no. 7, no. 4 and no. 3.

For no. 1 vote no. 1 and no. 7.
For no. 7 vote no. 4 and no. 3.
For no. 4 vote no. 2 and no. 5.
For no. 3 vote no. 6 and no. 8.

What the author explains about the meaning of the scheme: in this tie vote anyone who did not add a hand (the one who breaks) "flies off" by all hands as mafia.

The default rule

For removing the player under the first hands vote he himself and the player under the second hands.
For the one nominated second vote the players nominated under the third and fourth hands.
For removing the player under the third hands two civilians put hands in ascending order of numbers.
For removing the player under the fourth (last) hands the two remaining civilians put hands in ascending order.

The one breaking the tie vote is finished off by all players.

The universal tie vote

The author advises using the universal rule in all splits in the middle and late stage of the game, because creativity (drawing up a scheme by mood for each situation) uses extra energy and time. The universal rule answers which exact civilian votes together with the suspicious candidate: the choice is given to the slot with the earliest serial number. The author notes that in a guessing round at four it is not needed, but in lifting three players at six, four at eight and three at nine it greatly simplifies thinking.

The author's example for four: at the table no. 1, no. 2, no. 3, no. 4, nominated no. 4 and no. 2. For removing no. 4 the hands are put by no. 1 and no. 2, for removing no. 2 vote no. 3 and no. 4. Another example: at the table no. 2, no. 5, no. 9, no. 10, nominated no. 9 and no. 10. For removing no. 9 no. 10 and no. 2 put hands, for removing no. 10 players no. 5 and no. 9.

Why the scheme works (explanation of the Academy)

Each candidate gets exactly two hands. Automatically nobody leaves, and two mafia cannot remove even one civilian without the help of the reds.
If the mafia did not add a hand, its break is visible to the whole table: the distribution of hands is known in advance, and the "breaker" is finished off by all.
The town itself votes only within the scheme, so there are no discrepancies and no "creativity".
Nomination goes by suspicion. The better you chose the four, the higher the chance that at least one of them is mafia.

Arithmetic (the Academy's calculation): at eight players there are two mafia and six reds. If both mafia are among the four removed, the town has won. If one, 3 reds and 1 mafia remain, the game continues with a good count. If among the four there is no mafia, 2 reds and 2 mafia remain, and the town loses. So the "mathematical victory" here refers to minimising the risk, not to a guarantee: choose the four by the best information.

The author's workshop

Saw a table of eight people (a pair of blacks at the table). The first four variants on paper, the rest in your head.

Killed no. 3, removed no. 7. Nominated no. 1, no. 2, no. 4, no. 5.
Killed no. 10, removed no. 2. Nominated no. 9, no. 3, no. 1, no. 7.
Killed no. 4, removed no. 2. Nominated no. 5, no. 1, no. 8, no. 10.
Killed no. 5, removed no. 6. Nominated no. 9, no. 1, no. 7, no. 3.
Killed no. 9, removed no. 10. Nominated no. 8, no. 7, no. 6, no. 5.
Killed no. 6, removed no. 8. Nominated no. 2, no. 9, no. 4, no. 7.
Killed no. 10, removed no. 3. Nominated no. 8, no. 2, no. 9, no. 5.
Killed no. 1, removed no. 3. Nominated no. 5, no. 6, no. 7, no. 10.

In each task first determine who sits at the table, then write the scheme "who for whom" by the default rule. Check solutions with each other: each candidate has two hands, and the mafia must have no chance to gather two hands onto a civilian.

Key

Written as "who votes: for whom". Checked against the rule and matches the answers in the appendix of the book.

No. 1 and no. 2: for no. 1; no. 4 and no. 5: for no. 2; no. 6 and no. 8: for no. 4; no. 9 and no. 10: for no. 5.
No. 9 and no. 3: for no. 9; no. 1 and no. 7: for no. 3; no. 4 and no. 5: for no. 1; no. 6 and no. 8: for no. 7.
No. 5 and no. 1: for no. 5; no. 8 and no. 10: for no. 1; no. 3 and no. 6: for no. 8; no. 7 and no. 9: for no. 10.
No. 9 and no. 1: for no. 9; no. 7 and no. 3: for no. 1; no. 2 and no. 4: for no. 7; no. 8 and no. 10: for no. 3.
No. 8 and no. 7: for no. 8; no. 6 and no. 5: for no. 7; no. 1 and no. 2: for no. 6; no. 3 and no. 4: for no. 5.
No. 2 and no. 9: for no. 2; no. 4 and no. 7: for no. 9; no. 1 and no. 3: for no. 4; no. 5 and no. 10: for no. 7.
No. 8 and no. 2: for no. 8; no. 9 and no. 5: for no. 2; no. 1 and no. 4: for no. 9; no. 6 and no. 7: for no. 5.
No. 5 and no. 6: for no. 5; no. 7 and no. 10: for no. 6; no. 2 and no. 4: for no. 7; no. 8 and no. 9: for no. 10.

For the black

For a black at eight it is clear that there are two mafia. His task is either to break the split so that the reds lose the right to a mistake, or to arrange it so that two reds end up among the four. A correct distribution of hands and a loud "we finish off the breaker" deprives him of the first chance. Against the second, information works: whom the reds nominate and for what reasons. Nominating reds into the four instead of yourself is possible if it agrees with your line, but every break will give you away.

Example (compiled for the Academy)

Eight players, no. 1 to no. 8: one black left from each version, the reds know there are two mafia. The suspicious: no. 1, no. 7, no. 4, no. 3. Red no. 2 loudly announces the rule and shows it on his fingers: "No. 1 is nominated first, no. 1 and no. 7 vote. No. 7 second, no. 4 and no. 3 vote. No. 4 third, no. 2 and no. 5 vote. No. 3 fourth, no. 6 and no. 8 vote." The mafia in no. 5 does not put a hand: everyone finishes off no. 5, and the mafia is found. Then the town chooses the other colours by the usual rules.

Self-check questions

Why at eight must one black have left on each of the two versions?
Why does each candidate have exactly two hands?
What happens to a player who did not add a hand?
How to explain the scheme to the table so that it is not sabotaged?

Practice

Solve the eight workshop tasks. Then take a game recording and find the round at eight: check how many candidates were nominated and how the hands were distributed.

Typical mistakes

Applying without the condition (when a black trio is possible).
Changing the scheme by mood.
Not explaining to the table and not showing on the fingers.
Not finishing off the one who broke.
Removing the sheriff or the false sheriff before the critical round.

Source of the idea. The chapters "Mathematical victory" (introduction to the section "Moves") and "Lifting four at eight players. A pair of blacks in the game" from Dmitry Novik's book "50 Shades of Red" (2021). The risk calculation, the example and the explanations were compiled for the Academy; the workshop task conditions belong to the author.