Math Story: What Is an Imperfect Information Game

As I wrapped up the discussion of perfect information games, Arin listened attentively.

“Heheh, this is fun!”

“Okay, Arin, do you remember how I divided games into two types earlier?”

“Yep! Perfect information games and… imperfect information games!”

“That’s right. But everything we’ve looked at so far has been a perfect information game. Chess, Go, and the stone-removal game. They’re all games where the opponent’s pieces are all visible.”

“I see.”

“But imperfect information games are completely different from that. It’s hard to explain just with words, so—”

I stood up and took a deck of playing cards out of the drawer.

“Let’s try it directly.”

Shuffle-shuffle-...