I think there is some philosophical elements that invalidate this , or rather constrain the conclusions to an idealized mathematical irrelevance to the real world due to all the other uncertainties involved in the entropy of the universe all the way down.

One might argue that the statistics hold true with a large enough sample size. But what is the noise floor of such a sample size. When all the other real world uncertainties are accounted for, I believe these would accrue far greater than such a noise floor.

Nothing about the situation or mechanism in question is a known or consistent factor in this equation. The orientation, mechanical properties, internal friction, and force applied, should have a significant effect on the outcome of each spin. The distribution of bullets alone is a major factor and not specified. For instance, in the case of 4/6, one must assume the bullets include 2 sequential empty chambers, so how does the imbalance alter the probability. It is likely to have more of a tendency for those bullets to end in a gravitational low point, and therefore a statistically more likely chance for an empty chamber on top in the firing position.

The noise floor of all additional factors being larger than the statistical difference, IMO, means there is not relevance to the statistics outside of academia or situations where many millions of people are subjected to this method and the inputs are normalized with better constrained input factors. The actual sample size may need to be much larger. I’m just picking a big number from my little brain.

If the noise of all the unconstrained inputs is larger than the statistical difference, then the statistics don’t matter at this scale for the individual.

In my experience, mechanical imbalances are an inherent feature of goods produced under capitalism. I likely have a higher probability that the mechanism will have a bad spot where the rotation tends to stop. With a lighter revolving load of a single bullet, this bad spot and behavior should be more prevalent. In all likelihood the single bullet will wind up within 1 chamber of the same point in each spin. The person loading the firearm likely knows this and may invalidate all statistics by simply choosing where to load the chamber. For instance perhaps I am the executioner and am telling you how I load the chamber depending on the size of your nose or how much I like you.

Ignoring loading bias, if the mechanism is indeed imbalanced, as it likely is, I have a much better probability of an empty chamber in a 1 of 6 scenario and a much higher probability of a similar result with a variance of ±1. So I can largely invalidate the statistics of repetition and conclude that, if I survive the first turn, I am much more likely to survive subsequent turns. The result is that, within the real world factors, I have a much higher probability of survival… IMO.