The advantage

"The advantage of a random gun is that it should have a roughly equal hit rate on any type of movement."

This isn't technically true. It only holds true if the given targeting covers the same range of locations that the movement does. If the movement covers less area, then the targeting will be less effective.

For example if you have your average random gun, that fires randomly at GF -1 to GF 1. That seems like a pretty good random gun. But it will not hit all movements at about the same hit rate. While it is possible it could have the same hit rate, in practice the hit rate will be much lower against certain movements.

For example, if an enemy robot always stays at GF 0.8. Well then most of the time your random gun will not be firing at 0.8, and so will likely miss fairly often. The same could be said for a robot that uses stop and go movement and only covers GF -0.2 to GF 0.2. Your hit rate will suffer.

Surfers have this down to a T. If your gun fires at a certain location, the way the surfer responds is to avoid moving towards that location under those circumstances. Meaning every hit a random targeted makes on a surfer further restricts the GFs the surfer will visit, thus lowering the hit rate against your -1 to 1 random gun.

But feel free to tell me if you think I am completely wrong on this.

With all due respect, I think you are completely wrong.

If a gun picks a GF between 1 and -1, then it is covering all possible future locations of the enemy that the wave would be able to reach. And, by definition, a random gun should have an equal probability of picking each GF. So, there is the same chance that the gun will aim at 0.2 as it will -0.2, and the same for 0.8 and -0.8. The cool thing about random guns is that they cannot be dodged (assuming the random generator is truly random, but for practical purposes, Math.random() works fine), anywhere the opponent might go has exactly the same chance of being hit as any other potential location.

I think you're being thrown off by the difference between equal and better. A true random gun will always have an equal chance of hitting the enemy wherever they go. For example, if the enemy was sitting at GF 0, a HOT gun would have a 100% hit rate, while the hit rate of a random gun would be something like 5% (depending on distance). If the enemy always moved in straight lines (Who cares about walls?), an LT gun would hit 100% of the time, while the random gun would still hit something like 5% of the time (depending on distance). If the enemy was Nene, an unsegmented GF gun would have a hit rate of about 0.0%, whereas the random GF gun would still have an equal chance of hitting no matter what the enemy does.

I agree with Sheldor. It's like saying you have a better chance to hit the lottery if you play the same number each time, or if you don't play the same number each time. It doesn't actually impact your success rate because the lottery is like Random Targeting. (But something about our intuition has trouble with that.)

For each shot, Random Targeting picks a GF. What GF you went to in the past is not relevant - any GF you pick right now has an equal chance of getting hit.