I take some issue with the idea that we can simply just rely on another equilibrium refinement and say "no big deal".
It seems a bit silly to observe some behavior in a game and say "See that's a Nash Equilibrium, so game theory works", and then to turn around and observe some non-NE behavior and say "well in this game, BNE is clearly the right model, so game theory still works". And then yet again to observe some more behavior that conflicts with the theory (or to get rid of silly equilibrium) and say "ah, now we simply use perfect Bayes" or trembling hand equilibrium, or actually we were totally using correlated equilibrium this whole time.
In any case, it feels weird that a theory should behave like the "No true Scotsman" fallacy. We can always get the equilibrium by simply redefining what we mean by equilibrium.
You could show the same thing by relaxing those assumptions. It would just require a lot more algebra. The key insight is that, holding everything else constant (which is done in the lecture), weakening your accuracy to one side increases the probability you target that side.
I think you need to do the algebra. You can't make a blanket statement like you want to.
You have taken things to an absurd extreme and gotten one result, I can "relax the assumptions" to the opposite extreme and get the opposite result:
Suppose the goalie only blocks 10% of shots when guessing correctly, and the kicker makes 80% to the strong side and 50% to the weak side. In this model it is obviously better to always kick to the strong side.
Game theory doesn't become computationally intensive until you reach mixed strategies, which start about half way through the first chapter. (If this comment is referring to the PDF preview on my website, the PDF only contains the first lesson.)
When I started making the videos back in 2009, my concern was just showing how to solve games. Details were details, especially since your average YouTube viewer does not have much an attention spam that lasts past five minutes.
But you're right, the other things are important. I eventually get to them in some of the later (and longer) videos, I talk about them in the textbook. The first lesson is a free PDF on my academic website wjspaniel.wordpress.com, so you can check it out if you are interested.
