“Wouldn’t we need Keiko or someone else to watch?” He immediately asked about the logistics of the game, which was expected since I knew he’d be happy to earn the points.

  “If this were a higher stakes game, then sure. We’d need to agree to the stakes in front of Keiko beforehand.” I paused until Nobu made eye contact and nodded in agreement. “This is different. We can just agree that we’ll exchange any points we win and lose.” He slowly looked away before continuing.

  “I’m not sure if I’m comfortable risking my elimination…”

  I warmly nodded before smiling again.

  I knew he wouldn’t be.

  I’d never expect him to risk that.

  “That’s the perfect part about my game.” He looked up to face me, and I confidently smiled to put him at ease.

  “You have complete control over how many points you lose and gain.” I softly chuckled before continued. “These are the rules, you can always agree or disagree to play once you’ve heard them out.” I grabbed a piece of paper and the pen from his desk, and I immediately started writing down the numbers one, two and three spread out across the page. Below them, I wrote zero, zero and 9500 respectively.

  “What are you writing?” Nobu got off his bed and leaned over my shoulder to have a look at the piece of paper.

  “I’ll explain the rules using this as an example.” I turned my chair to face him and I started explaining.

  “I currently have 9500 points.”

  I had to lie.

  I lied about my points during ‘Democracy’, and 9500 would be the number of points I had if I was telling the truth back then.

  “I’ve split them up into three groups. Groups one, two and three.” I picked the piece of paper up and passed it to him.

  “I see, so you’ve assigned each group zero, zero and 9500 points?” He took the piece of paper and sat back on his bed before continuing. “How does this determine the number of points I get?” He stared at the numbers before looking back at me.

  “On your own piece of paper, you’ll have groups one, two and three as well. You’ll write the number of points you want to take from me from each of those groups.” I started writing an example on another piece of paper. When I was finished, I showed him the three groups with the numbers 1000, 1000 and 3000 beneath them.

  “If your number is higher than my number, you have to give me those points.” I took a brief pause, letting him understand.

  “So I’d have to give you 1000 points for the first two groups?” He carefully switched between looking at me and the two pages.

  “Exactly.” He started nodding again as his understanding of the rules grew.

  “However, if your number is smaller than my number, I’ll have to give you the number of points that you wrote.” I leaned back in my chair as he listened to the final rules.

  “So I’d get 3000 points for the last group? Overall, you’d give me 1000?” He glanced at me, waiting for my confirmation.

  “Exactly. There’s four important rules.” He stared at me intently as I continued.

  “1: My three groups must add up to 9500, or the game is invalidated and we ignore it.” This rule was necessary so I couldn’t cheat by writing all negative numbers and then giving him points for free.

  “2: None of my groups can have more than 4500 points.” He tilted his head for a second, but he held eye contact so I kept going.

  “3: All point exchanges will be considered simultaneously.” He seemed confused, so I quickly elaborated. “If this rule didn’t exist, in the example you’d lose 2000 points before gaining 3000. In other words, you’d be eliminated. This rule gives you more safety and gives you more control over how many points you gain or lose.” I waited until he nodded before continuing.

  “4: You can ask me one yes or no question about each group’s point total. Once you’ve asked all three questions, I can lie about one of them, but I have to tell the truth to at least two of them.”

  “So, should we play?” I softly smiled, writing down how many points I’d like to put in each group.

  “Yeah, let’s do it.” Nobu’s determined look instantly put me at ease. Now that I’d successfully pulled him out of his apathy, I started thinking to myself as he began writing on his piece of paper.

  This game would never be an official game.

  It’s rigged for Nobu.

  Each group can have a maximum of 4500 points. If I tried to put 4500 points into two groups, I’d still have 500 points left over for my third group. That means he could simply take 500 points from all my groups for a total of 1500 points earned.

  Normally, I would never propose a game like this, but this was different.

  If Nobu gets eliminated before his relationships with the others are fixed, then it’s possible that he never lets go of his spite.

  That’s why I had to let him earn some points.

  I just had to make sure I wouldn’t make myself vulnerable by giving him too many.

  I flipped my page over so Nobu couldn’t see it, and I took a look at what he was writing.

  It was a mathematical proof.

  As I expected, Nobu figured out that at least two of my groups had 2500 points. He’d proven it very formally, but it was much simpler than that.

  If I had two groups below 2500 points, their maximum combined total would be 4998. In order for all three of my groups to sum to 9500, my last group would need 4502 points, which violates my second rule.

  This deduction is the key to the entire game.

  There’s no way I can “win” this game against a logical opponent, but that’s exactly why it’s the perfect choice to give to Nobu. I can guarantee that he gets his safety while still feeling like he earned it.

  However, I could make decisions to limit how many points I give him.

  The first step is to figure out what questions Nobu will ask.

  I knew Nobu would figure out the “small group” restrictions. From there, I knew he’d see the two scenarios.

  I could have either one small group, or none.

  He’d use his questions to figure out whether I had one, but that’s not it.

  If I had no small groups, then he’d guess 2500 points for every group and he’d win 7500 points. However, if I had one small group, he’d need to design his questions to figure out which group it was.

  Because he has to ask all three questions before I answer them, he’s forced to be efficient since he has to uncover a small group’s existence while simultaneously pinpointing its location.

  “I’m ready to ask my questions.” He abruptly turned to me as he dropped his pen and waited for my response.

  “All right, what are they?” I warmly smiled as I invited him to continue, and he quickly double checked his calculations before asking the questions.

  “1: Does your first group have 2500 points or more?

  2: Does your second group have 2500 points or more?

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  3: Does your third group have 2500 points or more?”

  He looked back at his working out and confidently nodded as he waited for my answers.

  I’ve always known that behind his innocently friendly persona, Nobu was intelligent.

  It comes across in the way he speaks and manages social dynamics, and even the way he approached this game.

  That’s why I knew he’d find the most methodical approach and ask the same question for all three of my groups. If he’d randomly asked about different numbers for each group, he’d basically just be asking to get lucky.

  More than that, he’d identified that 2500 was a special number in this game.

  He knows that I can only have one group with 2500 points or less. That's why he designed his questions to try and force me into a situation where he could use that information to figure out which of my answers are a lie.

  “The answer to all of your questions is yes.” I smiled at him warmly and noted his surprise as I started wondering what Nobu was thinking right now.

  He’s probably analysing both scenarios one at a time.

  I was either telling the truth, or I was lying about one group.

  If I told the truth and Nobu guessed 2500 points for each group, he’d win 7500 total.

  If he guessed 2500 for all the groups and I lied about one of them, he’d lose 2500 points. He’d then gain 5000 points from the other two groups, for a net gain of 2500.

  Guessing 2500 three times wasn’t his only option though. He could try asking me specific questions and watching my reactions, noting any tells. That’s where the hidden aspect of this game kicks in.

  The psychological side.

  Nobu only has 500 points.

  He’s not actively looking for a jackpot.

  He just wants some safety.

  That’s why he’d be happy settling with three guesses of 2500. He could win 7500 if he gets lucky, but he was also guaranteed 2500 completely risk free, and that would be enough to give him some safety for our next games. He wouldn’t want to risk making any psychological reads on me to try and grab any extra points.

  “Ok. I want to take 2500 points from each of your groups.” His voice was filled with confidence as I flipped over my paper and handed it to him.

  “Damn… you had the perfect scenario…” I innocently looked at him as I tilted my head.

  “Scenario? What do you mean?” I wanted to figure out the extent of Nobu’s logical thinking, so I waited for his explanation. Instead of speaking, he simply slid his paper to me, and I saw that it was split in two. Scenarios A and B on one side, Scenarios C, D and E on the other.

  “I found the maths quite interesting so I played around with it and I discovered that you could only have one group with less than 2500 points.” He smiled and his voice held an enthusiasm I hadn’t heard before.

  “That was the fundamental axiom I based my logic on, and it led me to an important realisation - I realised I needed to explore every option. " He briefly paused before rereading his work.

  "You could have three groups above 2500 points,” he pointed to scenarios A and B. “Or, you could have two groups above 2500 points and one group below 2500 points.” I patiently nodded along and he kept going.

  “I started by exploring the first possibility. What if you had three big groups above 2500 points?”

  He took another pause and pointed at scenario A.

  “This scenario was the most fun. You could lie and say “No, Yes, Yes,” or as I’ve written, N/Y/Y. I started getting stressed, but then I realised the actual order didn’t matter which made things way easier.”

  He took another quick look at me before continuing.

  “But anyways, If you did this, you would’ve walked into a logical inconsistency. I would’ve used that to figure out you were telling the truth when you said Yes.” He quickly pointed at a little diagram he’d drawn.

  “I was surprised to find so many proofs by contradiction in this game.” He let out a chuckle and I smiled along with him. “If I assumed that one of the Y’s was a lie, then by definition, that group would have been below 2500 points.” He then pointed to my fourth rule, which he’d written down.

  “Since you can only lie once, that must mean your N was true, but that’s the contradiction! I already proved you could only have one group below 2500 points, so this is impossible! Therefore, I would know with absolute confidence that both your Y’s were truthful, and I could bid 2500 points for both of them.” I nodded along as he underlined both of the Y’s.

  “But that’s when I realised it wouldn’t be so easy. Annoyingly, I couldn’t use any logic to figure out if your N was a truth or a lie, so I would’ve played it safe and guessed 500 since every group must have at least 500 points.” He circled a number that he’d already underlined several times.

  “So, if we were in Scenario A, you would’ve won 5500 points?” He immediately nodded his head in response. “Yikes. That would’ve been bad for me.” I gently chuckled before he continued explaining.

  “Now, what if you truthfully said yes to all three?” He paused as he looked at Scenario B. “This one was way more simple. I guess it’s a bit silly since it’s a core mechanic of the game, but it didn’t actually matter whether you lied about any of them. I’d guess 2500 points for each group and I'd win 7500 points.”

  “Wouldn’t you be concerned that I was lying about one of the groups? If I did, your bid would be higher than mine, and you’d have to give me 2500 points.”

  “That leads me directly into the other scenarios. What if you had one small group and two large groups?” He paused before rereading his logic. “In Scenario C, I question what would happen if you truthfully said N/Y/Y. Then I realised it’s actually the exact same logic as Scenario A! I’d end up getting 5500 points again.” He pointed back to Scenario A before continuing to the next one.

  “For Scenario D, as you pointed out, you could lie and say Y/Y/Y.” He paused, letting out a dejected sigh. “I realised it’s the exact same logic as B. I’d guess 2500 for each group, deliberately risking getting one of them wrong so that I could guarantee a net gain of 2500.” He took a deep breath in and out as he looked at my piece of paper again.

  This was the best possible scenario for you.” We both looked at my groups, which had been 2000, 3500 and 4000.

  “What’s Scenario E though?” I was genuinely impressed with how thorough his logic was. We've all known one of Nobu’s strong points was maths, but seeing him integrate logic so seamlessly was useful information.

  “This situation was the most boring. Let’s say you lie about one of your big groups, saying N/N/Y.” He quickly pointed to the last unexplained section. “Since I already knew you could only have one group below 2500, one of the N’s had to be a lie, but I wouldn’t know which.” He pointed to his calculations beneath the logic before finishing his comprehensive explaination. “I’d guess 500 for both the N’s, and 2500 for the Y group for a gain of 3500 points.” He slowly made eye contact before continuing.

  “Not only was the logic so simple, but the point reward was nowhere near the better options.” He sounded annoyed even though this situation didn’t come up, and I quickly realised he enjoyed solving the problem more than earning the points. After seeing how broken he looked when I first started talking to him, I felt a lot of relief watching him have fun.

  “I guess I got lucky then…” I tried to be humble, but he immediately called me out.

  “No… you didn’t, Akira.” I looked at him and waited for him to continue.

  “You already knew everything I said, didn’t you?”