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).
Comments
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).