Gambit said the only equilibrium was mixed, with 1/5 each of (blue sword, blue armor), (blue sword, green armor), (yellow sword, yellow armor), (green sword, yellow armor), and (green sword, green armor).
With a stylin' bonus of ε points per duel (if a win is 1 point and a loss is −1 points), Gambit says for ε≤1/4 the equilibrium is:
(blue sword, blue armor): 1/5−(4/5)ε
(blue sword, green armor): 1/5−(3/5)ε
(yellow sword, yellow armor): 1/5+(4/5)ε
(green sword, yellow armor): 1/5+(3/5)ε
(green sword, green armor): 1/5
I do not see the logic behind this. Why would you ever choose to wear blue armor? No matter what weapon the opponent has, the best armor is either green or yellow. The blue weapon is only optimal against blue armor, but nobody should be wearing blue armor.
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?