"The game of rock-paper-scissors exhibits collective cyclic motions which cannot be understood by the Nash equilibrium concept."
This is complete bullshit. It is well understood that if your opponent is not playing an optimum strategy, you can gain an advantage by shifting away from the Nash equillibrium yourself.
Example: Image a player that always picks "Paper". By shifting away from a random choice (Nash optimum) to just always selecting "Scissors" will net you a 100% win rate.
This is a common trick utilized in poker, where good players will apply a certain playing style, while placing smaller bets, let their opponent adjust to your style and then suddenly change to a more aggressive style. You can take advantage of the fact that your opponent is trying to capitalize on your previous strategy. He has now introduced a sub-optimal element into his game, which you in turn can capitalize on.
As in the previous example, imagine we wager $1 on rock paper scissors. I pick paper for the first 100 rounds, you always pick scissors and you always win. Now we suddenly change the bet to one million dollars a hand. I change my selection to "Rock", while you play scissors, as that has given you a perfect win rate so far, and I win the money.
You're right that they're incorrect to say RPS can't be understood in terms of the Nash Equilibration concept. Possibly they mistook RPS's lack of a Pure Equilibrium to mean NE is inapplicable. Instead, it has a Mixed Nash Equilibrium.
The advice in the article - bias towards previous opponent win is just an under-specification of how to play a no regret strategy (alter your distribution to match opponent play, which is more or less what your example describes). If you've already installed a random number generator in your brain then playing optimally (in the sense that it will exploit weakness and shift to random as necessary) can be very easily done via a no-regret algorithm such as randomized weighted majority.
This class of algorithm is proven to converge on the NE for zero-sum games while being much quicker than linear programming (this actually has practical consequences for poker bots - see counterfactual regret).
The only reason that sharks can pretend to be fish is that there is real fish out there, that make it an expected win to deviate from nash equilibrium. The fish are not a property of the game, but rather a property of the playerbase.
You can still use game theory to analyze the game though, if you "include" the player model into the game model.
"Rock-paper-fool goes like this. First a coin if flipped without you seeing If tails, you face a fool npc, who will play according to..., if head, you face a (homo economicus) player"
You could then try to analyze the equilibria of this game.
>This is a common trick utilized in poker, where good players will apply a certain playing style, while placing smaller bets, let their opponent adjust to your style and then suddenly change to a more aggressive style.
Pardon my ignorance of poker, but won't the opponent notice that you have suddenly raised the stake and that something could be afoot?
Playing aggressively in poker usually means betting more than your hand would otherwise dictate - but your opponent doesn't know what your hand is.
So - you play for 4-5 hours, folding on weak hands, and always raising on strong hands, and then, once people think you are a grinder, you start betting on weak hands; other players fold because they were used to you betting high stakes only on strong hands, you take their money.
To clarify for the poster who asked you the question, playing aggressively might mean better more than your hand otherwise dictates, but it might also mean betting more often even if you don't change your bet size.
For example, you might always fold low pairs 22-66 initially (and perhaps conspicuously reveal that you folded them) but then start raising with them later. If your opponents were paying attention, then (a) they will think you have a good hand, and may be scared into folding right now, but (b) even if they don't, they won't suspect you of having a low pair, so that if e.g. a 2-6 comes up on the board and gives you three of a kind, you have an advantage because your opponents won't consider that you have this hand.
In my opinion, the parent example was rather oversimplified. If a player started playing more aggressively, that would be an obvious 'tell'. Most opponents would recognise that they should play more conservatively until they figure out what's going on.
However, this strategy really just needs one sucker: if it works, it works.
This is complete bullshit. It is well understood that if your opponent is not playing an optimum strategy, you can gain an advantage by shifting away from the Nash equillibrium yourself.
Example: Image a player that always picks "Paper". By shifting away from a random choice (Nash optimum) to just always selecting "Scissors" will net you a 100% win rate.
This is a common trick utilized in poker, where good players will apply a certain playing style, while placing smaller bets, let their opponent adjust to your style and then suddenly change to a more aggressive style. You can take advantage of the fact that your opponent is trying to capitalize on your previous strategy. He has now introduced a sub-optimal element into his game, which you in turn can capitalize on.
As in the previous example, imagine we wager $1 on rock paper scissors. I pick paper for the first 100 rounds, you always pick scissors and you always win. Now we suddenly change the bet to one million dollars a hand. I change my selection to "Rock", while you play scissors, as that has given you a perfect win rate so far, and I win the money.