But green sword/blue armor loses to something else. Dominance reasoning isn't supposed to guarantee that your strategy beats everyone.
Oh! I thought you were using the game-theoretic definition of "dominance", where one strategy always beats (or always beats or matches) another strategy. For example, in this game, any red-sword strategy is dominated by the corresponding blue-sword strategy.
Well I was, but I didn't mean to say that blue/green dominates everything else (imprecise language on my part). If you iteratively remove dominated strategies on both sizes you're left with blue/green - which is thus a Nash Equilibrium. At least on my table, but I don't trust my numbers anymore.
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?