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Comment by strgcmc | Hacker News Reader

A potential poker analogy is probably just getting lost in leveling games.

Level 0: My opponent made a large bet because he has a strong hand. I should fold.

Level 1: My opponent made a large bet because he knows that I will think it looks like he has a strong hand, when in fact he has a weak hand. I should call.

Level 2: My opponent knows that I think his large bets are bluffs, so he is now making a large bet assuming that I will wrongly assume he is bluffing. I should fold.

Level N: (if N is odd, I should call; if N is even, I should fold)

Beginner players will only think at level 0 or 1, but intermediate/advanced players may sometimes end up "leveling" themselves into a bad decision.

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Also called the "Iocaine Powder" strategy in Rock Paper Scissors (RoShamBo) [1]. The question being, how many "levels" of meta is optimal given the opponent(s) involved?

RoShamBo strategies attempt to predict what the opponent will do. Given a successful prediction, it is easy to defeat the opponent (if you know they will play rock, you play paper). However, straightforward prediction will often fail; the opponent may not be vulnerable to prediction, or worse, they might have anticipated your predictive logic and played accordingly. Iocaine Powder's meta-strategy expands any predictive algorithm P into six possible strategies:

P.0: naive application Assume the opponent is vulnerable to prediction by P; predict their next move, and play to beat it. If P predicts your opponent will play rock, play paper to cover rock. This is the obvious application of P.

P.1: defeat second-guessing Assume the opponent thinks you will use P.0. If P predicts rock, P.0 would play paper to cover rock, but the opponent could anticipate this move and play scissors to cut paper. Instead, you play rock to dull scissors.

P.2: defeat triple-guessing Assume the opponent thinks you will use P.1. Your opponent thinks you will play rock to dull the scissors they would have played to cut the paper you would have played to cover the rock P would have predicted, so they will play paper to cover your rock. But you one-up them, playing scissors to cut their paper.

At this point, you should be getting weary of the endless chain. "We could second-guess each other forever," you say. But no; because of the nature of RoShamBo, P.3 recommends you play paper -- just like P.0! So we're only left with these three strategies, each of which will suggest a different alternative. (This may not seem useful to you, but have patience.)

[1] [https://news.ycombinator.com/item?id=20073703]

I was scrolling through and thinking of RPS exactly. Very interesting post.

I once played my younger brother to 50 wins (whoever got there first was the unquestioned champion of RPS). It got very, very meta and there was drama in every round. We would pace around planning the next move and then meet up and shoot. An unexpected outcome after that much planning and pressure created some hilarity.

Long story short, I beat him 50-28, so I do feel I was out leveling/reading him to some degree. Maybe some obvious pattern I picked up on but didn't notice.

Ps, we were both adults. Great game though.

My brother and I would play a variation of rock, paper, scissors, where, prior to making a play, you'd have to tell the other person what you would play though lying was acceptable. We felt like it added a psychological dimension to the game - but I'm not really sure how it affected play. Neither of us could reliably detect when the other was lying.

I feel like this could be the basis of an interesting, what, Comedy Central show maybe? Get two semi-famous people together every week. Have them play RPS to 10 or 20 wins. Just enough to get to the meta mind games and drama but not long enough to drag on.

Maybe design some kind of goofy little arena for them. Let them dress up in costumes. Put some medium stakes charity donation on the line. An announcer and color commentator calling the match.

I wanna see Ken Jennings take on Annie Duke. Dennis Rodman battle Sebastian Bach.

The escape hatch is deciding based on some pseudo-random criteria in your vicinity. This also reminds me of the TNG episode Peak Performance where Data starts going down this meta rabbit hole.

Do you know of a way to generate pseudo random numbers in your head? (Honest question)

Can't remember the source, but using the nasal cycle[1] as a source of randomness has been suggested before. The only drawback is the cycle length is on the order of 30 min to 6h so drawing more then 1bit/day is probably infeasible.

[1] - https://www.rhinologyonline.org/Rhinology_online_issues/2018...

The conventional technique in poker is to glance at the seconds hand on your watch

Oh nice thanks

In fighting game terminology via David Sirlin, this is also called "yomi".

So what’s the good decision?

The best players will avoid trying to make an exploitative decision (e.g. guessing the correct level the opponent is thinking on), and instead make something approaching a game-theoretically optimal one (e.g. a maximally unexploitable strategy).

For example, if you're facing a big bet where you can only beat bluffs (e.g. all missed draws), but lose to any value bets (e.g. sets, straights, flushes), then you'll need to mainly be folding, but to avoid being exploitable you'll also need to call down with some percentage of these mid-strength hands (where the exact number depends on the bet size relative to the pot).

To decide which bluff-catchers you want to call down with, you'll want to pick hands that don't block any of your opponent's bluffs (e.g. you don't want to be holding the Ace of Spades on a flop that had two spades but a third didn't come by the river, since having this card eliminates a number of likely missed flush draws that your opponent might be bluffing with). In addition, you'll also want to pick hands that DO block some of your opponents value bets (e.g. your hand contains one or two cards that block your opponent from having straights, flushes, sets).

Naturally, calling down with the correct ratios is rather hard and only the best players can do so with any consistency, but it does remove the whole levelling guess work and reduces the decision to something you can reason about.

At higher levels, assume they are playing optimally and betting the strength of their hand, with maybe 5-10% bluffs (including some deviation above and below the true strength of their hand) thrown in to gain an edge.

It depends on many factors that can be mainly categorized in personal experience with the player(s), position and range:

Personal experience: Are you playing against a good player? Bad players tend to make very wonky decision, which makes it harder to make good assumptions on what they are playing. In that case, you play by the book on probabilities, because over time you will make more money. There's also "tighter" and "loser" players, who will bet more/less respectively with better or worse hands. Finally you could have a tell or a feel for a player you know for a while.

Position: Betting is highly dependend on the relative position he has at the table. Let's consider two situations, both pre-flop, with five players at the table: First situation, the person after the small blind bets a largre amount. He still has 3 people "behind" him, where he has 0 information on what they are going to do. They could re-raise him, call or fold. He puts himself in a very risky situation by handing over control to the people "that have position" on him.

Second situation, the same player makes a raise as the big blind. In this situation, everyone before him either folded or called, implying they don't have strong hands. He can use this situation to push more people out of the pot, or prepare for a larger bet on the flop. ("Preparing" in the sense that a larger pot makes it more difficult for people to fold to bets. If you have a flush draw and are supposed to pay 20€ to see the next card, the value is very different if it is a 40€ or 200€ pot).

Range: This is the trickiest and coolest part of playing poker. Basically you are trying to find out what cards your opponent holds so you can make a better decision. At the same time, you would like to conceal what cards you hold yourself. Consider the two situations from before: A large bet in second position does imply 1 thing: You probably don't want many players to join for the flop. This in return implies you have something good, that could easily get overturned if someone hits a flop. Small Pairs are very likely. In the second situation, it is much more difficult to limit your range. You are defending the big blind, so you're already invested. You are either raising for value because you have a strong hand (AK, AQ, 89 suited etc.). Or you realized no one raised so you want to "act" as if you have a strong hand, potentially steal the blinds or set yourself up for a later bluff.

Edit: I probably should've just posted Daniel Negreanu's channel, he's a much better player than I am and probably also better at explaining. https://www.youtube.com/playlist?list=PL3N4X2KgtefdYT6dGleeo...

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