Thread:Talk:Phantom/Randomized surfing/reply (13)

If you make a specialist anti-surfer gun, you could PIT many ticks ahead and still hit with near 100% accuracy.

My theory about why random movements performs poorer than deterministic movements is because no one in the rumble is attempting to exploit the determinism.

Game theory model (already posted somewhere in the wiki):

Suppose there were only 3 GFs to shoot at, forward, center and backward. Suppose there were only 3 GFs to dodge to, forward, center and backward.

If both shooter and dodger choose the same GF, it is a hit and the shooter wins, otherwise it is a miss and the dodger wins. If you shoot at the GF with highest occurrences, which is what all statistical guns do, then the best response for the dodger is to move where there are the least occurrences, which is what all active flatteners do.

Suppose the flattener moves in a pattern like this: forward, backward, center, forward, backward, center... GF guns with data decay will shoot anywhere the 1st time, then forward the 2nd time, backward, center, forward, backward, center, and always miss.

If the flatteners instead used a random strategy and moved forward, backward and center each with 1/3 probability, then the shooter would have 33% hit rate, which is higher than always missing against deterministic movements. In this scenario random movement looks weaker than deterministic movement.

But, if, instead of using past data, the shooter hard-coded the pattern and shoot forward the 1st time, then backward the 2nd time, center, forward... it would always hit. Deterministic movements would give 100% hit rate while random movements would give 33% hit rate. In this more evolved scenario, random movement is stronger than deterministic movement.

The hard-coding counter strategy can also the used by the dodger, which hard-codes the shooter pattern and instead move backward 1st time, forward 2nd time, center 3rd time... and the hard-coded shooter will always miss, again.

This hard-coding of opponents patterns creates a cycle which is only broken if both shooter and dodger instead opt for random strategies. Random movement and random targeting. In this simple game it is 1/3 chance for shooting at each GF and 1/3 chance of dodging at each GF. This way, even if you reverse engineer the opponent, there is no room for improvement.

Rocobode is more complex than the 3 GFs shooter/dodger game, and I guess the most conservative (counter-proof) strategy would be a weighted random movement and weighted random targeting, which takes in account multiple waves and walls.

It is also interesting to note that if you shoot with 1/3 chance at each GF in the simple game, you would achieve only 33% hit rate against SittingDuck. Counter-proof strategies don't exploit opponents weaknesses. And strategies which exploit weaknesses also make themselves vulnerable to exploits.