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The weakness with deterministic movements is your opponent can reverse engineer it, then create a specialist gun which would use your own deterministic movement to predict with near 100% accuracy where to shoot.

Random movement is a more conservative strategy which still perform okayish even if someone tries to use a specialist gun against it.

But since no one is trying to create specialist anti-surfer guns in the rumble right now, deterministic movements tend to outperform random movements overall.

Specialized guns can be complex and costly (in terms of development and testing). But it's true that if you had a copy of the enemy robot's movement code and added all its data up exactly the same way it does (during battle) that you would perfectly be able to predict its movement if it doesn't use any kind of random mechanism.

But with even a slight error, the difference will grow exponentially, since essentially robocode robots are very complex systems to which the theories of chaos theory definitely apply.

I, at least, try to minimize the effects of noise, specially when dealing with floating point precision arithmetic. So, chaos theory doesn't apply to my bots. I guess most bots follow the same path.

And, unless someone is trying to flatten virtual waves, it is possible to have perfect information about most deterministic movement systems. Probably all surfers and all active flatteners.

It would be interesting if someone tries to create some kind of "BigBlackBook" bot.

[EDIT: Actually, chaos theory do apply, but additional information gathered in scans done along the battle can compensate for it and still make specialist guns possible.]

Actually, you can't perfectly predict enemy movement even if you have their exact stats and prediction setup because you see their movements a tick later than them. It is probably enough to thrash them pretty thoroughly, but it won't be perfect.

My take on why random surfing hasn't worked out well is because of the same reasons that make a classic Raiko-style random movement not work out as well as surfing: where you currently are affects which locations are reachable. Flattening takes this into account, particularly with 2-wave surfing where you can plan to get to those far-out GFs. Using purely random GF selection will mostly result in GFs you can't reach, or if you try to scale it to where you can reach it will end up being susceptible to statistical analysis from overlaying lots of movements in a classic anti-random-movement style.

My addendum on why random surfing usually hasn't worked out so well also has the following point: In the cases where you scale your random range to where you can reach, there's an additional problem, which is that to my knowledge almost all attempts at such have used a simple goto method or orbit to get to the next GF that was selected, which potentially gives away information about where they were trying to get for that wave earlier than it strictly had to. I suspect that if one adds some smart randomization the timing/velocity/heading during the path used to get to the chosen GF, the result will be blurred as far as the usual statistical analysis is concerned.

Edit for more specific example: If one is using a traditional "orbit until selected GF" method for instance, as soon as you're stopped or begin to decelerate, you've given away exactly where you intend to be for that wave. How early the signal is given away varies depending on how far that GF is from where you ended up on the prior wave, but either way it adds clarity to statistics of where you'll be on future waves. The idea is to add uncertainty to that signal, instead of giving them absolute certainty about where you'll be in a few ticks.

Edit: Sorry, you didn't mean "traditional" surfing, you meant "traditional go-to random GF". :-) But anyway, my latest attempt at random surfing actually randomized the stats that my normal surfing algorithm works from, so it shouldn't have been subject to any tells re: what path I take to get to the "target/random GF".

Why would being one tick late stop you from perfectly predicting their movement?

Skipping a turn or being a tick late may make a difference, since an enemy can move up to 8 pixels in that missed tick. Now I'm not so sure of this, but missing that tick could make your bot's recorded(saved) stats off of the actual ones. But again, it's only 8 pixels so it won't be off that much. The stats would be near-perfect, but not absolutely. Again, I'm pretty new to robocode so I'm not so sure.

Also, I may never release Phantom. The movement sounds a lot more complex than I thought. I'm no expert at robocode(meaning I don't have bots like DrussGT, Diamond, Combat, Nene, RougeDC, etc.).