"Senpai, I have a question."
Riku had an unusually serious face.
"What is it?" Aoi asked.
"A friend is trying to confess, but doesn't know how to think about the success rate."
Yuki listened with great interest. "Is that a probability problem?"
"In a sense," Aoi opened the notebook. "We can think of this with random variables."
"Random variables?"
"Variables whose results are determined probabilistically. For example, let X be the confession result. X = 1 if success, X = 0 if failure."
Riku started taking notes. "Then what's the expectation?"
"E[X] = 1×P(success) + 0×P(failure) = P(success). In other words, the success probability itself."
"But if the expectation is 0.7, how should we interpret that?"
Yuki thought. "If you confess 10 times, you succeed 7 times?"
"Good intuition. But if you only confess once, the result is either 1 or 0. Expectation is the long-term average."
Aoi gave another example. "Roll a die. Let X be the number shown. E[X] = 3.5."
"But you can't roll a 3.5," Riku pointed out.
"Right. Expectation isn't necessarily a realizable value. But if you roll many times, the average approaches 3.5."
Yuki suddenly thought of something. "Then to increase the expectation of confession?"
"Increase P(success). Prepare. Know the other person. Choose the right timing."
Riku laughed. "But you can't completely control it, right?"
"That's the nature of random variables. There's uncertainty."
Aoi wrote on the whiteboard.
"Not just expectation. Variance is also important. Var(X) = E[(X - E[X])²]. It represents the spread of results."
"Spread?"
"Even with the same expectation, high variance means high uncertainty. Low variance means stable results."
Yuki calculated. "For confession, since X is 0 or 1, variance is P(success)×P(failure)?"
"Exactly P(success)×(1-P(success)). When success probability is 0.5, variance is maximum."
"Most uncertain?"
"Yes. When it's completely fifty-fifty, prediction is hardest."
Riku asked seriously. "So what should my friend do?"
"Maximize expectation while understanding variance. But..." Aoi chuckled slightly. "You can't fully explain romance with random variables."
"Why not?" Yuki asked.
"Human emotions don't follow simple probability distributions. Context dependency, memory, growth. Everything influences."
Riku looked relieved. "So calculation alone isn't enough."
"But the thinking helps. Accepting uncertainty. Considering not just expectation, but worst and best scenarios too."
Yuki added, "Plus, doesn't the confession itself generate information?"
"Sharp. Confession is an observation act. It partially reveals the hidden variable of the other person's feelings."
"Like quantum mechanics," Riku said.
"Similar. Before observation, it's a superposition state. After observation, it becomes definite."
The three fell silent for a moment.
"In the end, what should I tell my friend?" Riku murmured.
"Trust the expectation. But prepare to accept the result. Variance is part of life."
Yuki smiled. "Because it's a random variable, it's interesting, right?"
"Yes. If we could predict everything perfectly, life would be boring."
Riku stood up. "I'll tell my friend. Your romance is also a random variable."
"Philosophical advice," Aoi laughed.
As Riku left the club room, Yuki said quietly to his back, "Good luck, random variable."
Because it's random, we can have expectations. Perhaps that's the beauty of probability.