4 ms·

This is untrue. Nash equillibriums in general, and especially in poker, can be exploited in situations where one player is playing a negative EV strategy which

by Kranar 3y ago

This is untrue. Nash equillibriums in general, and especially in poker, can be exploited in situations where one player is playing a negative EV strategy which happens at loose games. Morton's theorem can be used to derive examples where a player playing optimally under the assumption that all players are acting independently loses out to another player playing suboptimally under that same assumption due to the presense of yet a third player playing a negative EV strategy. These kinds of scenarios are known as implicit collusion, basically the two players who are implicitly colluding together have an advantage over the single player who is making optimal decisions. Ignoring the fact that there is no known GTO solution for more than 2 players, GTO only applies under the assumption that everyone is acting independently for some fairly formal and strict notion of independence. This requirement is broken in many real world games with more than 2 players potentially playing loose and wild, where they may not actually be colluding or coordinating with one another, but they behave as if they were.

petesergeant 3y ago
If one player can exploit the situation with a unilateral strategy, wouldn’t that mean it’s not a Nash equilibrium?
- Kranar 3y ago
  Depends what you mean by unilateral. You can have a Nash equilibrium and also implicit collusion, for example if one player is playing GTO, that is they are playing optimally under the assumption that all other players are acting independently, and two other players are implicitly colluding with one another, you can still have a Nash equilibrium so that none of the players stand to gain anything by changing their strategy, and also the player playing GTO will have a negative expected value. Imagine a situation where the collusion was explicit, you are playing GTO against two opponents who are colluding with one another. A Nash equilibrium will still exist in that situation but your EV will be negative. Now explicit collusion is considered cheating but you can imagine a scenario where two players play in such a way that even though they are not explicitly colluding with one another, they behave the exact same way as if they were. This happens among a group of loose players where their actions as a group rewards the group as a whole against players who are acting independently. In other words, just because a strategy is optimal does not mean that it results in a positive expectation. You might be in a situation where playing perfectly just minimizes your losses, but you will still lose anyways.
ilc 3y ago
When I was playing I called this the "School of Fish" phenomenon. If there are weak players they can effectively end up colluding against a stronger player who is playing "More Optimally". Understanding the table, is a key skill. There's still a human element in the ring game.
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highfrequency 3y ago
In heads up no-rake NLHE where GTO exists: do you agree that anyone playing GTO has nonnegative EV against any player regardless of their strategy? I agree with you that you can probably construct some pathological multiplayer situations where collusion forces negative EV on a "GTO" player - assuming GTO exists in this setting. Going back to the original parent comment: > If you have a table full of clowns who are playing a range of strategies (ranging from being spiteful to just all-ining every hand, to barely knowing how to play poker), you will very quickly go broke with GTO, because you didn't adjust. I feel pretty strongly that this is not representative of practical reality. I don't believe that caveats about implicit collusion against a GTO player should prevent one from calling out a harmful belief that is also provably wrong in the heads up setting (the setting where GTO is actually known to exist). In practice, I have never seen anyone who played remotely close to Nash have negative EV against very bad players. On the other hand, I have heard a hundred times someone complain that they are losing money because their opponents are "too bad" (for their presumably excellent strategy to work as planned). This is close to ridiculous in most practical settings and also quite self-limiting.
- Kranar 3y ago
  >In heads up no-rake NLHE where GTO exists: do you agree that anyone playing GTO has nonnegative EV against any player regardless of their strategy? In heads-up, no-rake, NLHE implicit collusion is not possible, so yes playing GTO has a non-negative EV. >I agree with you that you can probably construct some pathological multiplayer situations where collusion forces negative EV on a "GTO" player - assuming GTO exists in this setting. GTO always exists, but in the presence of implicit collusion it may result in a negative EV. > feel pretty strongly that this is not representative of practical reality. GTO is not representative of practical reality. Very very few people, if anyone, really plays GTO poker consistently. It's an excellent theoretical result, and using GTO solvers and simulators can build up good intuition, but the idea that there are these poker savants playing GTO poker in 6+ handed games is mostly a myth. Also your claim that you have never seen anyone play against poor players have a negative EV kind of gives away that you are likely overconfident and possibly naive about your position. I highly doubt you have been in a position to calculate someone's EV while playing poker, or assess whether someone is playing GTO poker against multiple opponents who are bad. And assuming you did possess this amazing power, GTO poker does not guarantee against losses against bad players over any particular night or week of poker. So if you've never observed that then you are likely biased in your observation. You forgot/underweighted the scenarios where someone playing really well lost money to bad players and overweighed the scenarios where someone playing well made money against bad players. My experience is that talk about GTO poker is mostly used by people to add a more sophisticated and technical dimension to poker, people like to say that a poker play was GTO because it makes it sound authoritative and you can geek out over it, so to speak. People do the same thing across many hobbies including sports. In reality the best advice for playing poker if you want to be profitable is to find fish and play against them. The sad truth is that there's no shortage of gambling addicts to take advantage of, or people who overestimate their abilities but lack discipline, or heck are simply rich and play poker socially and have no problem losing money and have fun doing so. That's far more likely to yield profitable results than pretending that you can play an incredibly volatile and dynamic game like poker with anything remotely resembling game theory optimal.

by Kranar 3y ago

petesergeant 3y ago

If one player can exploit the situation with a unilateral strategy, wouldn’t that mean it’s not a Nash equilibrium?

Kranar 3y ago
Depends what you mean by unilateral. You can have a Nash equilibrium and also implicit collusion, for example if one player is playing GTO, that is they are playing optimally under the assumption that all other players are acting independently, and two other players are implicitly colluding with one another, you can still have a Nash equilibrium so that none of the players stand to gain anything by changing their strategy, and also the player playing GTO will have a negative expected value. Imagine a situation where the collusion was explicit, you are playing GTO against two opponents who are colluding with one another. A Nash equilibrium will still exist in that situation but your EV will be negative. Now explicit collusion is considered cheating but you can imagine a scenario where two players play in such a way that even though they are not explicitly colluding with one another, they behave the exact same way as if they were. This happens among a group of loose players where their actions as a group rewards the group as a whole against players who are acting independently. In other words, just because a strategy is optimal does not mean that it results in a positive expectation. You might be in a situation where playing perfectly just minimizes your losses, but you will still lose anyways.

ilc 3y ago

When I was playing I called this the "School of Fish" phenomenon. If there are weak players they can effectively end up colluding against a stronger player who is playing "More Optimally". Understanding the table, is a key skill. There's still a human element in the ring game.

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highfrequency 3y ago

In heads up no-rake NLHE where GTO exists: do you agree that anyone playing GTO has nonnegative EV against any player regardless of their strategy? I agree with you that you can probably construct some pathological multiplayer situations where collusion forces negative EV on a "GTO" player - assuming GTO exists in this setting. Going back to the original parent comment: > If you have a table full of clowns who are playing a range of strategies (ranging from being spiteful to just all-ining every hand, to barely knowing how to play poker), you will very quickly go broke with GTO, because you didn't adjust. I feel pretty strongly that this is not representative of practical reality. I don't believe that caveats about implicit collusion against a GTO player should prevent one from calling out a harmful belief that is also provably wrong in the heads up setting (the setting where GTO is actually known to exist). In practice, I have never seen anyone who played remotely close to Nash have negative EV against very bad players. On the other hand, I have heard a hundred times someone complain that they are losing money because their opponents are "too bad" (for their presumably excellent strategy to work as planned). This is close to ridiculous in most practical settings and also quite self-limiting.

Kranar 3y ago
>In heads up no-rake NLHE where GTO exists: do you agree that anyone playing GTO has nonnegative EV against any player regardless of their strategy? In heads-up, no-rake, NLHE implicit collusion is not possible, so yes playing GTO has a non-negative EV. >I agree with you that you can probably construct some pathological multiplayer situations where collusion forces negative EV on a "GTO" player - assuming GTO exists in this setting. GTO always exists, but in the presence of implicit collusion it may result in a negative EV. > feel pretty strongly that this is not representative of practical reality. GTO is not representative of practical reality. Very very few people, if anyone, really plays GTO poker consistently. It's an excellent theoretical result, and using GTO solvers and simulators can build up good intuition, but the idea that there are these poker savants playing GTO poker in 6+ handed games is mostly a myth. Also your claim that you have never seen anyone play against poor players have a negative EV kind of gives away that you are likely overconfident and possibly naive about your position. I highly doubt you have been in a position to calculate someone's EV while playing poker, or assess whether someone is playing GTO poker against multiple opponents who are bad. And assuming you did possess this amazing power, GTO poker does not guarantee against losses against bad players over any particular night or week of poker. So if you've never observed that then you are likely biased in your observation. You forgot/underweighted the scenarios where someone playing really well lost money to bad players and overweighed the scenarios where someone playing well made money against bad players. My experience is that talk about GTO poker is mostly used by people to add a more sophisticated and technical dimension to poker, people like to say that a poker play was GTO because it makes it sound authoritative and you can geek out over it, so to speak. People do the same thing across many hobbies including sports. In reality the best advice for playing poker if you want to be profitable is to find fish and play against them. The sad truth is that there's no shortage of gambling addicts to take advantage of, or people who overestimate their abilities but lack discipline, or heck are simply rich and play poker socially and have no problem losing money and have fun doing so. That's far more likely to yield profitable results than pretending that you can play an incredibly volatile and dynamic game like poker with anything remotely resembling game theory optimal.