OP Kiyone COTE

Vol 3 Chap 3: Marionette

Chiaki scratched her head with the back of the pen with which she was writing.

I took a peek at the paper and saw some potential mappings and threads of outcomes. Truly a dedicated individual.

Well should I point out the error in her half-strategy?

"Chiaki... I understand why turning into traitor works-"

Kei started to speak. Did she find the obvious mistake Chiaki made? That's unexpected. Not that she is an air head like Maya, but I didn't expect her to contribute or participate much in these special exams.

Did something happen? I don't see any discrepancies, but I do feel something.

"Wait Kei, explain why 'Always turning a traitor is a viable strategy'?" I asked her.

I want to know her thought process. Precisely, I want to know if someone or something influenced it as of recently.

"Well... I mean, look at the outcomes, even if they don't turn into traitors, whether they get accused or not, they suffer consequences."

That's true, but her argument is lacking. This is not enough to reach a conclusion.

I locked eyes with Kei, not looking away.

"*Sigh* You want me to continue? Fine... Think like this, if my strategy is to always become a traitor, possible outcomes are 1, 2, 4, 5, 6 and 8. For traitors, the best case is outcome 5, which widens the gap by 120 CP and worst case is outcome 4, where the gap widens by 150CP, not in their favour."

Well, everything so far is easily inferable by average ANHS students. And Chiaki nodded her head along, so no doubt; she didn't miss this sequence of thoughts.

The key is that, if you think everything as a random choice and event, 3 events are in favour of them, 3 are against them (Q, R class).

Even though the worst case scenario outweighs the best case by 30 points, the other two worst cases are actually neutral where everyone loses 50 CP.

So the expected values of class points, should be positive for Q and R class if you consider them becoming traitor and random choices for everything,

This overall gives a pretty good Mathematical reasoning that 'If you get a Q or R class, always become a traitor' is a good strategy.

"Kei, you are only backing up what I am saying, why did you think this partial strategy won't work?" Chiaki asked her.

I can understand Chiaki's point of view. Considering ideal scenario of random choices in a complicated set of rules is a common strategy.

If she is able to come up with a similar strategy for A-class, combine these two and hope that the opponent hasn't figured out.
Then everything boils down to 'luck' or probability, which is fine.

And by the math, she is choosing a positive expected value strategy, hence has a slightly more increase in the chance of winning rather than being 50 50.

With similar reasoning if the opponent is able to see through this, they will opt for a similar strategy, nullifying, making everything truly random.

"Yea, after you showed me the math, it became much more clearer, though I didn't understand this 'Expected value' concept right away, it made sense, but..." Kei fiddled around.

She most likely intuitively understood Chiaki's flawed logic, so I guess she is not able to tell how and why. Expressing your thoughts using words is difficult, most of the time.

"But what?"

"Isn't your strategy and being completely random matches almost? I don't see any big benefits.