"How should we decide life choices?"
Yuki asked with a serious face. At Café Shannon's counter, four people had gathered.
Professor S answered while slowly brewing coffee. "There's no perfect answer. But probability theory gives us clues."
"Probability theory?"
Aoi supplemented. "The concept of expected value. Evaluate each option's result weighted by its probability."
Riku showed interest. "Specifically?"
"For example, suppose Yuki can choose two paths. A gives reward 60 for certain, B gives reward 100 with 50 percent probability, 0 with 50 percent."
"The expected value?" Yuki began calculating.
"A is 60. B is 0.5×100 + 0.5×0, which is 50. So by expected value alone, you should choose A."
"But," Professor S said quietly, "humans don't move by expected value alone."
"What do you mean?"
"There's a concept called risk tolerance. Even with the same expected value, some people prefer risk and others avoid it."
Riku laughed. "I'd probably choose B. I like gambling."
"That's low risk aversion," Aoi explained. "In utility theory, we consider not the amount itself but its value to that person."
Yuki pondered. "So there's no correct answer?"
"It depends on situation and values," Professor S answered. "But choosing with knowledge of probability differs from choosing without."
"With information, we can make better choices."
"Yes. In Bayesian decision theory, we combine prior information with new observations to determine optimal action."
Aoi drew a diagram in the notebook. "There's also a method called decision trees. Represent outcomes branching from each choice in a tree diagram."
"Visualization makes it clearer," Yuki nodded.
Riku listened seriously. "But there are choices where probability isn't known, right?"
"Sharp," Professor S acknowledged. "Decision-making under uncertainty is difficult. When even probability is unknown, how do you choose?"
"Assume the worst case?"
"That's one strategy. Called the maximin principle—choose the option with the best worst-case result."
Aoi supplemented. "Conversely, optimists choose by best results. The maximax principle."
"Which is correct?" Yuki asked.
"Neither is correct," Professor S smiled. "It depends on personality and situation."
Riku pondered. "So what does making probability your ally mean?"
"Understanding probability and combining it with your own values to judge," Aoi answered.
Professor S added. "And having the resolve to accept that choice, whatever the outcome."
"Probability doesn't guarantee results."
"Right. Low-probability events can still occur. So choices come with responsibility."
Yuki took a sip of coffee. "But knowing probability allows better choices than not knowing."
"Exactly. The essence of information theory is quantification of uncertainty," Aoi said.
Riku laughed. "I've lived by intuition till now, but maybe I'll try calculating a bit."
"Intuition isn't bad," Professor S acknowledged. "Intuition cultivated from experience performs implicit probability calculations."
"Unconscious information processing?"
"Yes. But consciously considering probability allows more refined judgment."
Yuki took notes. "Youth theory of making probability your ally—I think I understand."
"Youth is a succession of choices," Aoi said quietly. "Which club to join, who to befriend, what to study."
"All probabilistic choices."
"But if you don't choose, nothing begins," Riku said forcefully.
Professor S nodded. "By taking action, you gain new information. And the next choice becomes better."
"Updating in a Bayesian way," Yuki understood.
"Life is a drama woven from probability and decisions," Professor S concluded.
Outside the window, the sunset was beginning. Countless people continue making choices, calculating their probabilities or following intuition.
"What choice shall we make next?" Riku said brightly.
"After calculating probability," Yuki laughed.
"But decide with the heart in the end," Aoi added.
The three stood up. Youth with probability as an ally continues onward.