rosyatrandom comments on Swords and Armor: A Game Theory Thought Experiment - Less Wrong

14 Post author: nick012000 12 October 2010 08:51AM

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Comment author: rosyatrandom 12 October 2010 09:58:42AM *  3 points [-]
 D S D*S a1 a2 a3 a4 s1 100 80 8000 6336 6256 6400 6080 6268
s2 80 100 8000 6120 6120 6000 6080 6080
s3 150 50 7500 6210 6035 6500 5700 6111.25
s4 50 180 9000 6156 6426 5400 6840 6205.5
6205.5 6209.25 6075 6175 Da -12 -8 -20 0 Do 0.1 0.15 0 0.24

My first instinct was to make the table above, which may or may not be readable here (EDIT: mostly readable, some tab glitches). I first calculated each sword's damage per minute (obviously, in general you want the highest value here), and then worked it out as applied to each armour type.

Here's where it gets... tricky, as you want the sword that maximises damage to all armour types, and the armour that minimises damage from all sword types. Do we look at average values? That could leave you open to being gamed by someone whose choices are poor except against your specific choices.

The best average choice here, by the way, is clearly Sword 1 (Blue) and Armour 3 (Yellow). But Sword 1 is not the best choice against Armours 2 and 4, and Armour 3 is not the best choice against Swords 1 and 3.

Nevertheless, the difference is small enough that I would still go with them; in the end, I think, being optimal like that is still the best strategy, as players with worse choices will be outcompeted. I am niggled by the thought that the optimal armour is not actually optimal against the optimal sword, but I don't think you can really do anything about that