Our hero Westley, in the guise of the Dread Pirate Roberts, confronts his foe-for-the-moment, the Sicilian, Vizzini. Westley challenges him to a Battle of Wits. Two glasses are placed on the table, each containing wine and one purportedly containing poison. The challenge, simply, is to select the glass that does not lead to immediate death.

Roberts: All right: where is the poison? The battle of wits has begun. It ends when you decide and we both drink, and find out who is right and who is dead.
Vizzini: But it's so simple. All I have to do is divine from what I know of you. Are you the sort of man who would put the poison into his own goblet, or his enemy's? Now, a clever man would put the poison into his own goblet, because he would know that only a great fool would reach for what he was given. I'm not a great fool, so I can clearly not choose the wine in front of you. But you must have known I was not a great fool; you would have counted on it, so I can clearly not choose the wine in front of me.
Roberts: You've made your decision then7
Vizzini: Not remotely. Because iocane comes from Australia, as everyone knows. And Australia is entirely peopled with criminals. And criminals are used to having people not trust them, as you are not trusted by me. So I can clearly not choose the wine in front of you.
Roberts: Truly, you have a dizzying intellect.

The scene, beyond providing some comic relief on the theme of common knowledge, also has an important lesson on strategic moves; if the rules of the game may be changed, then the game can be rigged to one player's advantage:

Vizzini: let's drink -- me from my glass, and you from yours.
[allowing Roberts to drink first, he swallows his wine]
Roberts: You guessed wrong.
Vizzini (roaring with laughter): You only think I guessed wrong -- that's what's so funny! I switched glasses when your back was turned. You fool. You fell victim to one of the classic blunders. The most famous is "Never get involved in a land war in Asia." But only slightly less well known is this: "Never go in against a Sicilian when death is on the line."
[He laughs and roars and cackles and whoops until he falls over dead.]
[Roberts begins to rescue Buttercup, the girl over whom this battle was staged in the firstplace]
...
Buttercup: To think -- all that time it was your cup that was poisoned.
Roberts: They were both poisoned. I spent the last few years building up an immunity to iocane powder.

The movie contains several other scenes with game-theoretic themes, including many on bluffing.