But green sword/blue armor loses to something else. Dominance reasoning isn't supposed to guarantee that your strategy beats everyone.
OTOH, my 4x4 table doesn't look like the one rosyatrandom linked to, so I may have made a computational error.
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.
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?