So, uh, after this post, knowing that some people are going to see the mixed strategy equilibrium, some are going to calculate the best combo given all combos are represented equally, some are going to pick based on style, etc etc... the best strategy would then be assign a prior probability to the chances of each analysis being made by your opponent, weight each analysis's "best picks" according to the prior, and build a representation of the field you are likely to face - then pick the best combo against that specific field?
If that's correct then the critical question is how accurate your priors are. So my answer looks something like "Pick the member of the equilibrium that performs best against other members that might be chosen for other reasons, cause they will be over-represented compared to other equilibrium members." That looks like Rayhawk's ε points for style calculation in gambit, except you consider ε to be a constant for "irrationally disposed towards x".
Of course, over time you'd gather statistical data and you could use it to refine your priors on analysis/irrational dispositions, but with that data you don't need any of this, you can just do simple statistics.
Note: this image does not belong to me; I found it on 4chan. It presents an interesting exercise, though, so I'm posting it here for the enjoyment of the Less Wrong community.
For the sake of this thought experiment, assume that all characters have the same amount of HP, which is sufficiently large that random effects can be treated as being equal to their expected values. There are no NPC monsters, critical hits, or other mechanics; gameplay consists of two PCs getting into a duel, and fighting until one or the other loses. The winner is fully healed afterwards.
Which sword and armor combination do you choose, and why?