Chapter 36 - Katsuragi 1 - To Accept or Decline?

---Notice—

Please read the end notice of this chapter; it will explain the statistics of this game in more depth so that it doesn't confuse you later on anything super complicated or any insane math, I promise.

Anyway, I told you this chapter may take me some time, but here it is enjoy

Have you still not given me your power stone? PoWeRStOnEs are greatly appreciated, and so are reviews. I would really appreciate more reviews.

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"In the end, the game comes down to one thing: man against man. May the best man win." ~Sam Huff

The lounge was filled with excitement. Students were grabbing drinks and snacks, getting ready for the big match.

"It's almost starting, right?" one student asked.

"Yeah, hurry up and get your drinks before it starts," another replied.

"Is Light late?"

"Not yet, but he will be soon."

The lounge was packed with students eager to watch the high-stakes competition. It was the first day of the special exam, and this match had drawn the biggest crowd yet. Nearly 95% of the students were there to watch the game between Katsuragi and Yagami.

"What do you mean? Obviously, Yagami is going to win!" Ishizaki shouted at Totsuka and the other Class A members of the Katsuragi faction.

"Yeah, right. In your dreams. Katsuragi is going to destroy Yagami. Just watch!"

"Why don't you put points on it then, huh?" Ishizaki yelled back.

"That isn't a bad idea," Ryuen said with a smile, holding his sparkling water. His voice, though not loud, commanded attention in the lounge. Quickly, arguments turned into bets, making the place feel like a bar full of adults watching a professional sports game.

"Your Class C must be very confident, Ryuen. It's just like before the last special exam. Not one of your classmates seemed worried," Ichinose said, looking around the lounge and comparing the expressions of Class A students to those of Class C.

"We are the best class in the school, after all. But still, support seems completely split between Yagami and Katsuragi outside of Class C," Ryuen responded.

"True, outside of Class C, expectations are split. But that's why people are gathered here, right? It's supposed to be an intense match between two elites that could go either way," Ichinose replied.

Kanzaki interrupted, "Still, where is Yagami? The rules were explained to all of us watching already, but won't he be disqualified if he's much later?"

Ryuen didn't even entertain the thought as he looked at the screen televising the competitions. On the screen were three individuals: Kohei Katsuragi, the exam administrator, and the random third member announced to partake in the exam today, Rokusuke Koenji.

Unlike the other two, who seemed focused on what was in front of them, Koenji simply stared at himself in a mirror in the room as he brushed his hair.

Ichinose spoke up again, talking to Horikita, who was nearby beside Ayanokoji. "Looks like Yagami really lucked out getting Koenji as a random third-party participant. Koenji really doesn't care about the outcome of this game, so this may be a smooth ride for him."

Horikita nodded but didn't further engage with Ichinose.

"Don't bother with her, Ichinose. She's still upset about how badly she lost to me in our game earlier," Ryuen explained.

And his words were true. Horikita was mad. Once again, it felt like she was being read like a book, but this time by Ryuen and not Yagami. She suspected some sort of foul play that somehow Ryuen cheated, but she had no proof of this.

Horikita cleared her mind as she saw Karuizawa walk past her to the drink area. "Karuizawa, did Yagami tell you anything about his strategy for this game?" Horikita asked before Karuizawa could escape.

"Not really. He implied these games were no big deal like it didn't matter if he had to play at a minute's notice," Karuizawa said nonchalantly before leaving.

"Do you have any idea what he's planning?" Horikita asked Ayanokoji.

He shook his head. "No, I can't say I do. He might be planning to lose this game on purpose, but that's not his style. I don't think he's the type to accept losses."

"Lose on purpose? Why would he do that?" Horikita asked.

"It's simple. It's a trick often used in gambling. It's mostly a psychological tactic to make people second-guess their actions or competency. But again, I doubt that's what he is going for," Ayanokoji explained.

As Ayanokoji finished speaking, the one everyone was waiting for finally walked into the game room to play Katsuragi. Everyone was watching through TV screens, and the moment silenced the room.

"Sorry, I was almost late, but I made it," Yagami said.

"Finally, you're here. Although I was hoping you'd show up late so I could go back to my afternoon plans," Koenji said as Yagami entered.

***Staff Bar***

"Two minutes before the start of the game, he barely made it, Sakagami," Mashima said mockingly.

"But he's there, that's all that matters," Sakagami responded.

"Hihi, drinking with you guys is the best," Hoshinomiya said, wrapping her arms around Chabashira, who pushed her off.

"I think you should lay off the drinks, Hoshinomiya," Mashima said.

"Nooo, the game just started! I need my alcohol to enjoy it to the fullest!"

"For once, I must agree with Hoshinomiya. I'm sure we are about to witness quite the show from Yagami," Sakagami said with a smile.

"Is that so? Are you willing to bet my next round of drinks on that?" Mashima responded.

"It depends. Are you willing to bet mine?" Sakagami snapped back.

"Oooh, I'm in too! Don't leave me out!" Hoshinomiya chimed in.

"Hmm, free alcohol, huh? Sounds like a plan," Chabashira finally spoke. "I must say, I'm more confident in that Katsuragi boy than I am in Yagami. From experience, I think Katsuragi is likely more ruthless in terms of tactics."

"Oooh, really, Sae-chan? I was sure you'd pick Yagami. Honestly, I was split between both, but I don't mind putting my bets on Yagami. He's capable and cute, so that's all that counts," Hoshinomiya said happily.

"Then it's settled," Sakagami said, and Mashima nodded.

"Although I'm curious, Sakagami. You always seemed most confident about Ryuen's future results in your class, but it seems Yagami has gained your confidence, too."

Sakagami thought before responding to Mashima, "That's true, but I guess seeing his confidence and results in the island special exam put him on equal footing with Ryuen for me. Plus, the theme of this test is intellect. Knowing that I'm more than confident he can bring about results now."

***

In a large red room decorated like a royal palace, three individuals sat at a game table. Light Yagami was across from Kohei Katsuragi, while Rokusuke Koenji, still checking himself out in a distant mirror, was to Yagami's right and Katsuragi's left.

The game table was designed to prevent any cheating or peeking, with walls blocking the view of each side. Katsuragi's and Koenji's sides were empty, but Yagami's side had two folded notes and a 1 yen coin, folded to prevent prying eyes. These were his fake lotteries, one of which he might later add to the lottery box.

Overseeing the three was the exam administrator.

"So, can we commence this little game of ours now, Yagami?" Katsuragi asked.

"Of course, we may commence," Yagami replied.

Hearing both Yagami and Katsuragi's words and seeing the clock hit 9 PM, the exam administrator began the special exam.

"I will now commence the drawing, starting with Katsuragi," he said, reaching into a small black box in front of him and taking out a folded note identical to those in front of Yagami.

He opened the note, scanned it, and then handed it to Katsuragi, who quickly opened and closed it before placing it on his desk.

He soon handed a folded note to Yagami, checking it once again. Yagami did the same as Katsuragi but also picked up and checked his fake lotteries to be aware of their position and what they said before placing all 3 of his lotteries folded down on his table.

"So, Katsuragi, how has your day been?" Light asked, collecting himself.

"So that's the way you want to go with this. So be it. My day has been productive, to say the least. I've been looking forward to this game to see what you have in store for me and whether you are a fraud."

"A fraud? Is that what people think of me now?"

"Only a select few, but there are some who believe you're nothing special, simply a dog following Ryuen's orders."

"Oh, those rumors. Well, let people believe what they want. It doesn't affect me. But I am curious, Katsuragi, what's your evaluation of me?"

"I don't think you've done anything truly remarkable, but it's undeniable you've had moments of genius. Even if you were really a dog, it takes a certain level of competency to accomplish a job."

"I see. Well then, Katsuragi, how about we get into this game? Tell me, what does your note from the box say?"

Katsuragi analyzed Yagami before responding. The room was quiet for a few seconds as he decided on his next move.

Katsuragi took the folded note on his table, opened it, and presented it to both Yagami and Koenji.

Both of them glanced at Katsuragi's note, although Koenji did so more casually than Yagami, who seemed slightly surprised by Katsuragi's actions.

Yagami understood that what Katsuragi showed had to be the real deal. It couldn't be a trick. When Mashima listed the items allowed for the test, it was clear that only the clothes on their backs were permitted. The second Yagami entered this room, he was stripped of his possessions by an administrator. This test was broadcast to all students, and allowing phones or other items may shift the focus from intellect, the theme of this exam, to something else, reducing problem-solving ability to a side thought.

"Oh, did you not expect me to actually show my note? Well, I've thought about it. There's not really any risk to me showing you what my note says other than maybe losing some of my edge when it comes to tricking you about my motivations. But still, even at this moment, you don't know what my motivations are, do you, Yagami? You gave me the edge in this game, but put yourself in a hole. Now, all that's left for me to do is bury you. Think of this as my only gift of kindness to you in this game," Katsuragi said, tossing the note over to Yagami's side of the table.

Written on it was, "Win Condition: Katsuragi declines Yagami's one yen coin."

"Yagami, tell the truth. Your win condition is for me to accept your coin, isn't it?"

The room went quiet. Yagami seemed to have no intention of answering Katsuragi's question. He was still processing the situation he had now found himself in. For the first time, it seemed Yagami had been caught off guard by someone outside his class.

"Right, of course, you don't answer because I'm right, aren't I? Your goal is definitely to get me to accept your coin. That's why you were surprised when I showed my note. Not only were you surprised by my actions, but you realized you are at a disadvantage here. The odds didn't work in your favor. Then again, they were never meant to."

Yagami finally responded, "No, you're wrong. You have no clue what my win condition is. You wouldn't guess, based on such basic evidence, for all you know, I'm acting. You have your assumptions but can't be sure enough to act on them."

"You're right. I can't read you perfectly and I can't be certain of what your win condition is. But I can be certain of one thing: you took me for a fool in the creation of this game. You introduced the idea of the fake lotteries because you thought you could play me. Well, Yagami, you've failed. I dare you if your win condition is really for me to decline your coin, then don't put in a fake lottery."

"Why would I do that?" Yagami responded.

"Well, if your win condition is for me to decline your coin and you don't input a fake lottery, I will definitely draw an 'accept coin' paper. Your chances of victory will statistically increase by 16.67% since I wouldn't be able to prove your win condition is to get me to accept the coin. Now, if I pull a 'decline coin,' well, that's game over for you, Yagami. So I dare you, Yagami, prove me wrong, or are you too scared to try?"

"T-that doesn't make sense," Yagami stuttered. "Obviously, in my position, anyone—no, it would only be common sense for me to add a lottery no matter what you say."

"Yes, technically, but you're not accounting for the fact that I know that. Yagami, I know your best moves; therefore, I know your next moves. I've analyzed every possible scenario in this game, and there is not even one where I am ever at a disadvantage."

Katsuragi's words left Yagami in deep contemplation.

"I'll let you and everyone else watching this in on a secret. I've been practicing for this game since you and I agreed on it. I've played everyone in my class, a total of 143 games. Of those games, I've only lost 31. That makes my record 112 out of 143, meaning I achieve victory in over 75% of games. Do you understand now? I told you, Yagami, your grave has been made already. All that's left for me is to bury you."

Everywhere on the cruise ship, this game was being watched intently. There was one thing every spectator of this game could agree on the intensity of the match between Katsuragi and Yagami was unlike any of the games before.

Even more surprising than the intensity of the match was the fact that Yagami seemed to be facing pressure playing against Katsuragi. The question came up: has Yagami met his match? Was the one many saw as a perfect genius finally going to get defeated? And was a new genius on the rise? Was it time for Katsuragi to show everyone what it takes to get into Class A?

Everyone watching the game had one thing in common: they wanted to see how this would end.

Would this game tarnish the perception of Yagami's abilities, or would it elevate them to a whole new level? And what would Katsuragi do next?

IMPORTANT NOTICE KINDA: I RECOMMEND YOU READ BELOW.

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I recommend you guys read my notes below if you have a hard time understanding the game above and want to understand it for the next chapter.

How do you guys like that chapter? Let me know. I appreciate comments, reviews, and powerstones.

What do you think about the competition between Light and Katsuragi? Do you think I've presented it well so far?

I'd love to hear your thoughts on what you believe will happen next; I believe there is enough information to come to some conclusion on what will happen in this game, and I love to hear theories, so go crazy.

EXPLANATION OF LIGHT v KATSURAGI

Let me explain some things because this game may be confusing for some.

Katsuragi initially got a "decline coin" note from the lottery, meaning when Yagami got his note, there was a 66% chance it was an "accept coin" note. There is a 66% chance in the lottery box that there is currently 1 decline and 1 accept note left and a 33% chance there are 2 accept notes left.

By this logic, if Yagami has a decline note, there is always a 100% chance that on the second draw (if Yagami doesn't input a fake), Katsuragi will get an accept note (because there are only 2 of each note). He wouldn't be able to prove that Yagami has an accept note as the location of the final decline note would be unknown, but if Katsuragi pulls a second decline note, then he would be in possession of both declines, meaning he can be 100% certain that Yagami has an accept note. 

Let's assume accept notes are + notes and decline notes are - notes.

Knowing this, if Yagami adds a note, the only possible combinations of notes in the box are +++, +-+, and -+- before Katsuragi makes his second draw. If you do the math, Katsuragi basically has a 66% chance of drawing a plus. However, he also knows that Yagami initially had a 66% chance of drawing a plus himself.

What Katsuragi is saying is that no matter which note he pulls out, if Yagami puts a note back in, it could be either a plus or a minus with equal chances. This means, from Katsuragi's perspective, there's a 50% chance Yagami puts a fake accept in and a 50% chance Yagami puts a fake decline in. Therefore, it's just as advantageous to not put any note at all because the odds of the gamble won't change. Essentially, Katsuragi is saying the 66% chances even out to 50-50 when considering all this.

So from if Yagami really has a decline coin note hes theres not a real disadvantage to not putting in a note or faking that he is taking a risk to trick katsuragi.

Now that you understand the game, you can understand that Katsuragi has every advantage in this game, and I'm not pulling any BS, so I'd love to hear how you think this will all end do you think lights win condition is to get Katsuragi to accept the coin or to decline it and what would you do now in either light or katsuragi's position.