This post is incorrect. You do need to consider the individual matchups, not the average damage taken and given. My suggestion loses 2-3.
I understand the same-color bonus, but it seems to break the results when you set the stylin bonus to 0. For each (blue, yellow, green) sword, I get the damage against (blue,red,yellow,green) armor to be:
Blue Sword: (6240, 6160, 6400, 6080)
Yellow Sword: (6150, 5975, 6500, 5700)
Green Sword: (5940, 6210, 5400, 6840)
For a sword distribution of (.4,.2,.4) and an armor distribution of (.4, 0, .4, .2) , I get expected values for swords of (6272, 6200, 5904) and for armors of (6102,6143,6020,6308).
That’s not an equilibrium, is it? Against that population, why would I not pick the Blue Sword with the Yellow Armor, for an expected payoff of (6272,6020)?
This post is incorrect. You do need to consider the individual matchups, not the average damage taken and given. My suggestion loses 2-3.
I understand the same-color bonus, but it seems to break the results when you set the stylin bonus to 0. For each (blue, yellow, green) sword, I get the damage against (blue,red,yellow,green) armor to be:
Blue Sword: (6240, 6160, 6400, 6080)
Yellow Sword: (6150, 5975, 6500, 5700)
Green Sword: (5940, 6210, 5400, 6840)
For a sword distribution of (.4,.2,.4) and an armor distribution of (.4, 0, .4, .2) , I get expected values for swords of (6272, 6200, 5904) and for armors of (6102,6143,6020,6308).
That’s not an equilibrium, is it? Against that population, why would I not pick the Blue Sword with the Yellow Armor, for an expected payoff of (6272,6020)?