This is super tangential, but I think you’re making a technical error here. It’s true that poker is imperfect information and it’s true that this makes it require more computational resources, which matches the main text, but not this comment. But does imperfect information suggest mixed strategies? Does optimal play in poker require mixed strategies? I see this slogan repeated a lot and I’m curious where you learned it. Was it in a technical context? Did you encounter technical justification for it?
Games where players move simultaneously, like rock-paper-scissors require mixed strategies, and that applies to SC. But I’m not sure that requires extra computational resources. Whether they count as “imperfect information” is subject of conflicting conventions. Whereas play alternates in poker. I suspect that this meme propagates because of a specific error. Imperfect information demands bluffing and people widely believe that bluffing is a mixed strategy. But it isn’t. The simplest version of poker to induce bluffing is von Neumann poker, which has a unique (pure) Nash equilibrium in which one bets on a good hand or a bad hand and checks on a medium hand. I suspect that for poker based on a discrete deck that the optimal strategy is mixed, but close to being deterministic and mixed only because of discretization error.
That makes sense. Perhaps the opposite is true—that if all Nash equilibrium strategies are mixed, the game must have been imperfect information? In any simultaneous game the opponent’s strategy would be the hidden information.
This is super tangential, but I think you’re making a technical error here. It’s true that poker is imperfect information and it’s true that this makes it require more computational resources, which matches the main text, but not this comment. But does imperfect information suggest mixed strategies? Does optimal play in poker require mixed strategies? I see this slogan repeated a lot and I’m curious where you learned it. Was it in a technical context? Did you encounter technical justification for it?
Games where players move simultaneously, like rock-paper-scissors require mixed strategies, and that applies to SC. But I’m not sure that requires extra computational resources. Whether they count as “imperfect information” is subject of conflicting conventions. Whereas play alternates in poker. I suspect that this meme propagates because of a specific error. Imperfect information demands bluffing and people widely believe that bluffing is a mixed strategy. But it isn’t. The simplest version of poker to induce bluffing is von Neumann poker, which has a unique (pure) Nash equilibrium in which one bets on a good hand or a bad hand and checks on a medium hand. I suspect that for poker based on a discrete deck that the optimal strategy is mixed, but close to being deterministic and mixed only because of discretization error.
That makes sense. Perhaps the opposite is true—that if all Nash equilibrium strategies are mixed, the game must have been imperfect information? In any simultaneous game the opponent’s strategy would be the hidden information.