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Yeah, I was thinking that the incomplete information aspect has a lot to do with the depth of Robocode as well, but it's certainly also true that the rumble has a lot to do with it's longevity, allowing it to survive quieter periods when some authors are inactive.
The comparison to other NP-complate games like chess, as well as the incomplete information aspect being brought up makes me wonder how chess strategies would differ if the game rules were modified for incomplete information (i.e. you can only see spaces that your pieces either occupy, can move to, or can attack)
Doing a quick search... seems such chess variations do exist: wikipedia:Dark chess and wikipedia:Kriegspiel (chess).
Oops, NP-complete means the perfect move can´t be easily calculated. NP stands for Non-Polynomial runtime complexity.
But yes, imperfect information is a key feature in Robocode.
Perfect information and imperfect information usually leads to 2 completely different paths. The first leading to backward induction style analysis and the second leading to forward induction.