12A猫で学んだこと-Memoir-

...What are you learning now?

るる鯖さん....ありがとうございました！ 4Aで学んだこと-Memoir-....

るる鯖さん閉鎖されるのですね....長い間ありがとうございました！
オンライン人狼「るる鯖」が5月に閉鎖へ
るる鯖さんがなければ、自分の人生でブログも人狼もやることはなかったですね。

せっかくなので、昔取った杵柄、純粋なパズルとしての勝率解析をやってみますか。
ruru-jinro.net
案山子として参加させていただいた4A村。

4Aは、2日目朝の地点で、狼1村人1占い1か、狼1村人2の配役になるゲームです。
このエントリでは、このゲームについての村勝率を(均衡解の意味で)求めます。
「同じ条件ならすべてのPLは等しい確率で吊られる」というシンプルな仮定を置くと、
このゲームの村陣営の勝率は以下のパラメータで与えられます

  • 2日目朝の地点で、配役が狼1村人1占い1となる確率 $P$ (既知の公開情報とする)
  • 村陣営が、1COの占いCO者を吊る確率 $X$
  • 狼が占いを騙る確率$Y$

ルールとして、以下の条件をつけます。 * 占い師は必ずCOし、視点の狼を確定させる * 村騙りはなし

2日目朝の状況について下記のいずれかが発生する確率が$(P, Y)$ 組み合わせで決まります。

  • w.p $ P \times Y $: 占い生存、狼が占いを騙る場合
    • 村勝率: $\frac{1}{2}$ (狼の騙り失敗) + $\frac{1}{2} \times \frac{1}{2}$ (狼騙り成功) = 3 / 4
  • w.p $P \times (1-Y)$: 占い生存、狼は占いを騙らない場合
    • 村勝率: $(1 - X)$
  • w.p $(1 - P) Y$: 占い非生存、狼は占いを騙る場合
    • 村勝率: $X$
  • w.p $(1 - P) (1- Y)$: 占い非生存、狼は占いを騙らない場合
    • 村勝率 $\frac{1}{3}$

そのため、村人の勝率を$V$と置くと
$$ V(X, Y) = \frac{3}{4}PY + P (1 - Y) (1 - X) + (1 - P) Y X + \frac{1}{3}(1 - P) (1 - Y) $$ となります。

この式をまとめると下記となります。

$$ V = \frac{1+2P}{3} - PX + XY - \frac{1}{4}PY - \frac{1-P}{3}Y $$

X, Yでそれぞれ偏微分をすると.... $$ \frac{\partial V}{\partial X} = -P + Y $$

$$ \frac{\partial V}{\partial Y} = X - \frac{1}{4}P - \frac{1-P}{3} $$

なので、

  • 狼視点が均衡解の戦略をとる場合、確率$P$で占いCOをする　　
  • 村視点が均衡解の戦略をとる場合、確率 $\frac{1}{3} - \frac{1}{12}P$ で占いCO者を吊る

となります。この時の村陣営の勝率は$\frac{1}{12} ((P+2)^{2})$です。

自明な場合である $P=0$, $P=1$ の結果と照らし合わせて、計算間違いはなさそうです。 これが、4Aの場合、理性的なPL達が永久にゲームを積み重ねていったら、上記の村勝率に収束していくことが予想されます。

補足

狼側の戦略決定は「占いの生存確率」と同じ確率で"騙れ" となります。
その時に村側の戦略によらず、勝率一定値になるのは、直観的に分かりやすいです。

一方、村側の戦略決定を感覚的に納得がすることが難しいです。 直観的には$P=0$ (真占い非生存)であれば、常に$X=1$ がよさそうな気がします。
そのため、 自分で納得するための思考過程を書いてみました。

  1. 村側陣営が$X$の値を決めてから
  2. 狼側陣営が$Y$の値を決める

とします

すると、$X \neq \frac{1}{3} - \frac{1}{12}P$ の場合、$\frac{\partial V}{\partial Y}$ の正負によって、 狼側は村人勝率を最小化するため、$Y=0$か$Y=1$を選択してきます。 それは $\frac{ (2+ P)^{2} }{12}$ と同じか小さくなってしまいます。

$P=0$の場合を考えます。 $P=0$ の時は下記が村勝率となります。

$$ YX + \frac{1}{3}(1 - Y) $$

$X=1$にすると、狼視点は$Y=0$を選び、村勝率は$\frac{1}{3}$. $X=\frac{1}{3}$ とすると、狼視点は $Y$の値にかかわらず、村勝率 $\frac{1}{3}$.

...このようになり、どちらの場合でも、村勝率は合致します...相手が後から戦略を選べる場合は、 "正しい" 推測をしないことが安定的な戦略になるのが、やっぱり気持ち悪いですね... (簡単のために$P=0$で上のことを調べてみたけれど、$P$が微小の正の数でも、 $X$は1に近くならないのが、安定戦略となることを意味しているから...)

補足2

  • 「占い師がCOしなくても構わない」
  • 「村人陣営の村騙りを許容する」

などの要素を入れると、また違った観点がたくさんでてきます。 特に、$P$が小さい時に「占い師がCOしない選択もできる」 などとすると、勝率は変わりますね。
....難しい。　

実際の村との関係

上記で4Aの解析の話は終わりです。 ブログにて、戦略の解析を行う中で、実際の村に活用できる知見として

  • 一方の陣営の戦略が均衡解からずれている時、対抗陣営の最適解は純粋戦略である

ことが多い、というものがありました。

戦略を確率で決める前提で、 勝率が戦略に対して線形性をもっているとき、偏微分の値は定数になります。 そのため、最適戦略は確率0か1になります。

上の要素に関連していると推測しているのですが、 (状況が確定している時のセオリーとして、) 陣営視点 "正しい"戦略がある / "間違っている"戦略があるという認識がされがちです。

しかし、それは対抗陣営の戦略が均衡解になっていないことが原因です。 対抗陣営の戦略が均衡解となれば、どんな戦略をとっても有利不利は変わりませんし、 逆に対抗陣営の戦略が均衡解から、反対方向にずれれば今まで最適戦略だったものは、 最悪の戦略に変わることも多いです。

実際の村は複雑すぎて、自分には解析ができないですが、この定性的な性質は間違っていないと確信しています。 (実際の村で勝率を高める目的には役に立たない性質の理解ですけどね！)

上の知見に基づいて、るる鯖で遊ばせていただく時、 「戦略が前提としている仮定は何だろう？」 ということを考えさせていただいた気がします。

「自分と相手の前提は違う」というのがコミュニケーションを難しいものにして、 時にイライラして、時に自分の枠の超えたものを学び、時に生きることをすごく面白くしてくれるのかもしれません...
願わくば、微笑みを浮かべながら、前提の違いを楽しめる時間が長いことを。

来週が素敵な7日になりますように！

Review of Spy School Goes to North.

Note that this submission includes a spoiler about Spy School series up to Spy School Goes To North.

I think Spy School is one of great novels.
English is not my mother language, but I can recommend this series to many people with confidence.

This month, the latest book of the series Spy School Goes To North was published. Is this a good book? "Not bad, but not great." is my comment just after I've finished reading it.
I feel both of excitements and disappointments in this story.
The idea comes to me that it would be beneficial to sort out my ideas why I could not enjoy Spy School Goes To North thoroughly.

In my reviews, I would like to focus on 2 perspectives, contrasting the contents of the latest volume Spy School Goes To North against the previous books.

The abrupt development of relationship between Zoe and Svetlana and rebellion of Svetlana

I am sure that the author succeeded to describe a large part of relationship between agent-in-trainings unless they are related to Zoe up to Spy School Goes to North.

I immersed myself in development of relationship between Ben and Erica. At the first part of Spy School, it was one directional admire from Ben to Erica, although Erica found Ben's remarkable personalities in the latter part of this book.
After the first book, their multiple missions continued. They nurtured their trust while they dealt with the various problems and they confronted the difference of their vision of lives in the middle of these processes.
For example,
"Cooperation with other people is required or not?"
"Friends are weakness or assets in espionage?"
Their ideas conflicted while they succeed to solve missions.
Via their interactions, their mind changed a little by little. Especially, Erica's interpersonal policy had changed clearly. It is clear that mutual trust was very firmly established in Spy School Revolution, in which Ben believed her innocence no matter what happened and Erica determined to regard this trust as a romantic love in Spy School at Sea, where she kissed Ben at the last scene. I enjoyed these evolutions of relationship very much.

In contrast, description of some relationship of Zoe was not good.

In Spy School at Sea, it was revealed that Murray had unrequited love toward Zoe.
I assumed there was no foreshadowing about this fact. This plot was not necessary for remembering the password for stopping the detonator.
Though, this point is not closely related to the pivot of the story, so it is not so critical. It may be useful to support the situation where Zoe felt disappointment in romantic relationship between boys and girls, though.

In Spy School Goes to North, both of Svetlana and Zoe fell for each other at first encounter. I do not deny the romantic relationship between girls, rather than that, I have a good impression for introducing romance between girls after Zoe was upset about bitter relationship with boys. I also do not criticize the relationship which starts from crushes of first sight, though there was some opportunism that both of Zoe and Svetlana fell for each other without their interaction.

What I could not understand is that Svetlana betrayed her grandfather, colleagues, and country because of only the crushes toward Zoe, which is not typically sufficient motivation. Other factors or interactions with Zoe are required to justify this development. For example, I would have understood her action if she had embraced very deep negative emotions toward their family and country in prior to betrayal. Or, I would be intrigued by the plot if the mutual trust had been established between Svetlana and Zoe and it had surpassed Svetlana's loyalty to her family and country at the moment when Svetlana had to decide her side.
However, these processes were not described. This made the character of Svetlana very flippant and I felt she was just a machine to proceed the story, not a human or a respectable character.

If Svetlana disposes her family and country only for emotional desire toward one person, she needs the extraordinary profound feeling similar to the one between Ben and Erica, which was nurtured with 10 volumes of series. I would be very glad if the author used at least a part of one book to establish the mutual trust between Svetlana and Zoe.
Or, though it is sub-optimal, the author could provide the reason of mutual feelings and trust between Svetlana and Zoe by introducing the past events prior to the story as the author did for chivalry and trust between Mike and Ben. (For example, Zoe and Svetlana were childhood friends when they were little. ) I could not understand motivation of Svetlana at all since there was not this kind of contrivances.

Unsophisticated correspondence of Ivan and submarine crew and break of the structure of concise binary opposition

Typically, the plot of Spy School is splendid, however, the plot of Spy School Goes to North was somewhat sloppy for the events related to Ivan, the grandfather of Svetlana.

There is lack of reasons and motivations that Ivan betrayed Russia and his crew submarine crew members. Saving Svetlana was not sufficient motivation for Ivan to stop destroying Alaska since it seemed not difficult for achieving both objectives of rescuing Svetlana and destroying Alaska. He could pretend to accept the offer by Erica. Then, he could order the captain of the ship to detonate the oil reserve after securing the safety of Svetlana.
Ivan was a patriotic and competent spy of Russian and had obsessed grudge against United States. It required very strong reason for him to betray his country.

In this series, the author utilizes the relation of the simplified binary opposition of good versus bad very effectively such as "CIA versus Spyder". The criminals or villains were completely bad. Their motivation for crimes are typically self-centered and very egoistic, which are straight-forward but persuasive so that readers can logically understand the actions of criminals. At the finale of the book, the good people such as Ben or Erica thwarted evil plans and the readers became satisfied that the evil perished and the good thrives. Readers could close the book very satisfactorily. This is the basic formula of the plot of Spy School. It is simple and effective. In Spy School Goes to North, the author destroyed this structure by betrayal of Ivan.

Demolition of structure itself is not bad, however, the development is too abrupt and unreasonable. If the author wants to destroy the fundamental structure of the story, sufficient preparations are required.
Ivan was depicted as the evil (for United States) till the last part of the book, which is similar to other villains of the series.
There was no reason for Ivan to convert from the villain for the United States. The author assumed that the family love was sufficient for Ivan's behavior, which was brought from Alexander's inspiring persuasion. The family love was used previously as one of factors to affect the villain's action. In Spy Ski School, Leo Shang could not escape from CIA because he could not take the plane alone, discarding his daughter Jessica Shang. However, Ivan was in the different situation from Leo Shang' case. He could solve independently the problems of his love to his daughter and his country. I felt the author failed to provide satisfying evidence to justify destroying the structure of the good and the evil. It was very sad that concise and beautiful structure is sullied at the finale of the story, abruptly and unreasonably.

Conclusion

I feel the author considers various ideas to introduce stimulating plots while he has to differentiate them from the previous ones in this very long series. The author succeeded in this point at Spy School Project X. The existence of internet conspiracy theorists made the structure of the plot more intriguing.
At Spy School Project X, the new element of the plot is attachment or addition to the existing binary opposition of the good versus the evil (CIA V.S. Murray), so enormous description or preparation in the story may not be necessary.

On the other hand, the author tried to change or destroy the existing binary opposition at Spy School Goes to North, which should require sufficient work to convince the readers about the justification of the change of plot.
I felt author's work was insufficient.

Spy School series is a very interesting story. I am sure that I will definitely buy the next book. The author has very high level of skills for describing the scenes and humors. I could not count how many times I laughed while reading this book. The development of relationships, especially the one between Ben and Erica are very splendid.

I think the author can create however complex story when he put the same enthusiasm into the steady processes of plots and change of emotions as he did as in depiction of Ben and Erica.

I am looking forward to reading the next book of Spy School. I wonder what kind of surprise or twists the author skillfully will prepare!

April 2023

自分が初めて12A猫に参加させていただいてから、大体9年ですか... 9年！ 自分が小学校１年生の時に参加したとしたら、もう中学校を卒業ですね。

最初の3年間ぐらいと、その後で自分のプレイスタイルは結構変わった気がします。 参加し始めたころは皆様についていき、ゲームの勝利を目指して動くことに精一杯だったけれど、 慣れてきてからは、どのようにゲームを味わうかということに考え方がシフトしていったかな？

自分には人狼の強さとかはよくわからないけれど、 後からログをみたときに、「いいゲームだったな」と思える時間をたくさん作れたら、 それがきっと、"人狼ゲーム"の勝利なのだろうなーと思います。

人狼でも現実でも、 うまくいかないときもあるけれど、 明日も頑張っていきましょうー！

March 2023, ... prior to 3 days.

こんばんは、 StudentSです。
PCのファイルを整理していたら、
人狼の特殊村用と思われるメモがありました。

12月24日深夜。雪が綺麗に舞う中、ようやくバイト先から解放される。  
駅前はお祭り騒ぎの余韻が残り、カップルたちのイチャイチャが聞こえてくる。   
  
耳をふさいで帰路につく。  
誰もいない玄関のドアを開けて、自分に向けて「今日もお疲れ様。」と声を出す。  
  
...それは、こんな人でも、楽しめるものですか？  
ほええええ！  
それはクロウカードですか？  
雪兎さんへの気持ちはYESだったのかな

(注: おそらくCNが"桜")

恋の残り香はまるで雪の結晶のように。  
雪華図説ですか？  
松阪牛じゃない。  
「高い食材」より、相手のことをちゃんと考えて料理をする、  
そんな気持ちが大事だと痛感できる料理ですか？  
それは、お姉ちゃんの元カレが高校の担任の先生になるのと同じぐらい気まずいことですか？

どんな気分で上の文章書いていたんだろうなー

さてさて、まだ寒いですが気をつけていきましょうー
来月がいい1か月になりますようにー！

2023, Feb.

村に参加させていただきました。 下記の村は反省でですね・・・

No.504067「騙りに優しい12A猫」村

  • (強反省点)Nulさんから指摘されましたが、初日の狂人さんの投票要素には気がついておきたかった。
  • (検討点)初日のギドラCOは一考したけれど、狩人CO者狼を強めに見てしまいましたね...

情報整理の勘が鈍くなっていることは間違いないなー
次に本格的にやらせていただくときには観戦と村を数村させていただいてから・・・だな・・・