[BB] “Like in chess, better poker players generally think deeper than weaker players”, Benny the Book compared. “It’s not a clean correlation because it doesn’t help to think incredibly deeply about the wrong things. Chess computers could think many more plies than humans for decades before they could beat the strongest grandmasters.”
[BB] “Poker is a funny game in this respect. You want to think deeper than your opponent, but don’t want to think too much deeper than your opponent. A seasoned pro and a complete neophyte might make the same exact bet for completely different reasons, so you need to determine how deeply your opponent thinks to know how to play against them. You want to be thinking exactly one level deeper than your opponent.”
[BB] “Beginners think at the first level: what cards do I have and how good is my hand? Some beginners are able to adjust for the texture of the board, but most won’t think to devalue their nut flush if the board is paired.”
[BB] “Intermediate players think at the second level: what does my opponent seem to have? But they only have a vague notion of your hand strength: strong, fair, or weak. Sometimes intermediate players prematurely and inaccurately try to place you a specific hand, but that usually doesn’t work out well for them.”
[BB] “Advanced players also think at the second level, but they start you on a fairly wide hand range and try to narrow it as the hand progresses. When they’ve deduced correctly, they can cause you major problems.”
[BB] “Expert players think at the third level: what does my opponent think I have? That’s as far as anyone goes in the games we’re playing in. Which means that if you can go to the fourth level (what does my opponent think that I think they have), you’ll dominate here.”
[BB] “Do you remember the battle of wits scene in The Princess Bride?”1
[JJ] “Of course!” Joey the Juvenile confirmed.
[BB] “Westley, then referred to anonymously as the man in black, shows Vizzini some poisonous iocane powder, turns his back for a moment, then says, ‘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.’”
[BB] “Vizzini tries to deduce which glass to pick, reasoning, ‘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.’”
[BB] “Vizzini is thinking at level three, considering what his opponent, the man in black would think he thinks.”
[BB] “Vizzini apparently solves the dilemma by switching the glasses while his enemy isn’t looking. The man in black doesn’t hesitate to drink from his own goblet, so it must have originally been the safe one. Because of the swap, Vizzini therefore has the drink that’s safe to imbibe, which he does.”
[JJ] “But Westley was thinking at level four!”
[BB] “Right. Although Vizzini did momentarily come close to the right answer, he spent most of his time considering the wrong data. Of course, a wise man wouldn’t ever consider drinking from a glass if there were a 50% chance that it would be fatal, not unlike a coin flip for your tournament life.”
[BB] “Wallace Shawn’s villain character flopped the nut flush draw and concluded that his Ace was good anyway. But he really had no outs as his opponent already had a full house. Both glasses were poisoned, and Cary Elwes’s hero character had spent years building up his immunity to iocane.”
[BB] “So make sure you use the appropriate level of thinking for your opponent. Against Figaro the Fish, there’s no need to go beyond level two. If you explain his actions with any deeper logic, you’ll end up making the wrong move. Against Vince the Veteran, level three is good. He’ll try to put you on a hand, so a little deception will go a long way. And against Deb the Duchess, level four would be right, although I still aspire to that.”
Footnotes:
- If you prefer, here is the transcript of the battle of wits.