Take it from someone who plays pool for money, if random chance noticably influenced my results and I could not anticipate future probable outcomes based on past performance I'd be living in a cardboard box under a highway overpass.
That's a nice appeal to authority.

On the flip side, I used to gamble to supplement my income, and I promise you that random chance does not mean probable future outcomes cannot be anticipated.

You're logic is based upon the assumption of random chance and the supposition that over time there will be a wide fluctuation of results eventually leading to a random distribution of all possible outcomes. AH is not a game of chance like drawing cards from a deck, it is a game of skill for the most part. When getting airborne again for the 1,000Th time it is actually very likely they will repeat past performance as chance has very little to do with it. It would be illogical to assume that a person could suddenly deviate wildly from their proven poor skill level based performance to the point it would be to their benefit statistically to rearm.
Yes, it is very likely they will repeat their past performance. But if we are assuming a probabilistic approach in our decision over whether or not to rearm, then
we don't change k/d probabilities simply because we landed one kill; we are not talking about large deviations. Moreover, we both know that games of skill are not immune to probabilistic analysis, e.g. Baseball, so I don't quite understand the relevance of AH being a game of skill. I'm not saying that whether or not a pilot lands a kill or dies is a matter of random chance. I'm saying that just because you landed a kill and you average 1:1 K/D, that doesn't mean you're worse than 50/50 to kill or die when you take off. Small deviations in performance happen all of the time in this game, and sometimes in ways that are totally out of our control (like the tail-less Niki that fell into my windscreen last night

).
It is only if landing one and only one kill takes priority over K/S that there is no benefit to rearming when your aircraft is undamaged and you landed a kill.