Akiyama's strategy

With this strategy, Akiyama plans to win the second round of the Tournament.

SPOILER FOR EP3

Round Two: Akiyama's winning strategy

Nao doesn't care about the prize money, she just wants to get out of the game.
Akiyama came up with the idea of creating teams for this purpose.

There is a total of 22 participants. From these, he creates a team (1) of 8 members, including Nao and Akiyama.

When a question is set, each half of the team votes for YES and NO respectively.

Example:


Logically, half of the team is going to proceed to the next round.
At the first question, the closest outcome possible is when the players not in the team split up with 6 votes against 8.
(with 7 against 7 it ends up in a draw)

↓
10 players remain in the game.

At the second question, the team is again divided into half. The closest outcome possible is when the other players split up with 2 votes against 4.
(with 3 against 3 it's a draw again)

4 team members remain in. Once again, they are divided up equally.
This leaves only two possible patterns of answers:

(1)

(2)

If the voting results in the 2nd pattern, it's a draw, so the voting will be repeated until the 1st pattern emerges.
That means, that in the end one of the players is bound to remain.

Now what if there is no close outcome?
Let's assume that after the 1st question we get this:

The following question will lead to:

This decides the game - with only two players remaining, there is no minority vote.



★ Distribution of prize money using this method:

(1) if one player wins:
The winner receives 2100 million yen.
Half of this money goes back to LGT Office for not taking part in the third round.
1050 million yen remain.
The other 7 members need to return 100 million yen each to the Office, for losing the second round.
For this, 700 million yen are needed.
The remaining prize money amounts to 350 million yen.
Divided through 8 members, each person ends up with a share of 4,375,000 yen.
(for the losers the game has already ended, so they don't need to pay half of their prize money to get out)

(2) if two players win:
Each person receives 1000 million yen.
Each of them needs to return half of their prize money to LGT Office for not taking part in the third round.
This leaves each of them with 500 million yen.
The 6 team members who dropped out before are divided in two groups, assigning 3 of them to each of the winners. They need to return their debts of 100 million yen to the Office, so each group ends up with 200 million yen.
Dividing this amount by 4 members per group leaves each person with 50 million yen.

This means that in both scenarios, all team members have a chance to win money.

★ Why have 8 members?
This number allows each member to get the highest amount of money while ensuring certain victory as few members as possible. 9 or 10 members would work as well. But if the number gets any higher, there is only debts to win. And if we have only 7 members...


Closest possible outcome for the first question:

And now, if we assume that the second question ends on the closest possible outcome again:


Now we have one member against three other players. Certain victory has become impossible.
Something like this might happen:

With even less members, say 5 or 6, certain victory is out of reach.

Problems:
○ The team members. The strategy fails if there's a traitor inside. Akiyama had the members sign contracts.

○ The unknown player "X" who stole 100 million yen from Michiko Takada. Because X already has 100 million yen (making it 200 million yen with the money for the second round), X could pay for his debts even after losing in this round.