"I was going to confess today, but I didn't."
Riku slumped onto the club room sofa.
"Why not?" Yuki asked.
"The success probability seemed too low."
Aoi laughed. "You're judging romance by probability?"
"But isn't maximizing expected value rational?"
"Interesting approach," Aoi opened the notebook. "Let's analyze it with probabilistic thinking."
Yuki showed interest. "How?"
"First, list action choices. Confess or don't confess. Consider results and probabilities for each."
Riku became serious. "If I confess, it's either success or failure. Success probability is... about 20 percent?"
"That's low," Yuki sympathized.
"But," Aoi continued, "what's the utility of success?"
"Utility?"
"Happiness level, satisfaction. Try quantifying it."
Riku thought. "If successful, happiness plus 100. If failed, minus 30. If I don't confess, zero."
Aoi calculated. "Expected value of confessing is 0.2×100 + 0.8×(-30) = 20 - 24 = -4"
"It's negative..." Riku looked dejected.
"So not confessing is more rational?" Yuki asked.
At that moment, Mira quietly spoke. "Time discount missing."
"Time discount?" Aoi understood. "Right, Riku. You should consider future information too."
"Future information?"
"Even if you don't confess now, success probability might increase over time. Conversely, there's a risk someone else might ask first."
Riku held his head. "Too complicated..."
Aoi said gently, "Actually, probabilistic thinking has limits. Not everything can be quantified."
"Then is probabilistic thinking useless?" Yuki asked.
"No, it's useful. But not perfect," Aoi explained. "The value of probabilistic thinking isn't providing answers, but offering a framework for thinking."
Mira wrote in her notebook. "Structure thinking, not replace feeling."
"Exactly. Thinking probabilistically reveals the structure of choices. But final decisions need emotion and intuition too."
Riku stood up. "Then I'll confess after all."
"Even with negative expected value?" Yuki was surprised.
"It's not just about expected value. There's value in not having regrets."
Aoi smiled. "Good judgment. Minimizing regret is also a form of rationality."
"That's probabilistic thinking too?" Riku asked.
"Broadly, yes. There's a strategy called minimax regret - minimizing the worst possible regret."
As Riku was about to leave the club room, Mira handed him a small note.
"Courage = information you can't quantify"
Riku laughed. "Courage is information that can't be quantified, huh."
"Living youth with probabilistic thinking is fine," Yuki said. "But if you calculate everything, it might not feel very youthful."
"Balance is important," Aoi admitted. "Think probabilistically, but sometimes act irrationally."
Riku turned at the door. "Senpai, predict the outcome probabilistically."
"I don't know," Aoi answered honestly. "That's what makes youth interesting."
"Enjoying uncertainty," Yuki murmured.
"Yes. Probabilistic thinking is a tool for accepting uncertainty."
After Riku left, the three looked out the window.
"His confession, what's the success probability?" Yuki asked.
"Just subjective probability," Aoi thought, "but around 30 percent?"
Mira shook her head. "50 percent."
"Mira is optimistic."
"Hope updates prior," Mira smiled slightly.
Yuki laughed. "Hope updates the prior probability. That's probabilistic thinking too."
"Living youth with probabilistic thinking," Aoi summarized. "Calculate while feeling. Use both data and intuition."
"A balanced way of living," Yuki said.
The three quietly watched over their youth, swaying between probability and emotion.