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At sufficiently close range, perfect dodging and perfect shielding would not be possible. While strategies besides rambots might be viable, they would need to be close range strategies.

As an aside, robocode with tick-bullets (even with invisible bullets) could be interesting. With the currently usual bullet power values, I'd suspect that would make it possible though, for bots to make wide enough bullet interesection "shadows" in waves to always stay 100% safe. With smaller faster ones that might not be such a stalemate though.

The sadist in me says apply Heisenberg uncertainty to the visible bullets. You can know their position, or their momentum vector, but not both at once. ;)