Practically speaking, it's impossible to roll 6 one hundred times in a row on fair dice. Not technically impossible, but we each get to calibrate our skepticism based on how far out the probabilities are.

In this case we can be sure the dice aren't fair because there's significant motivation for them not to be, or at least it's easy to imagine a manufacturing defect in the dice.

This is a 1 in 50 chance we are dismissing as practically impossible though.

It's absolutely possible, but it means that you need a lot of good evidence for a 210 IQ to outweigh the odds that the score is a mistake or a lie.

Even if we could positively confirm that the person is smarter than literally every human who has ever lived... that would be about IQ 200, still far from IQ 210. (The required number of humans grows exponentially.)

The tallest man in history was 8'11".

If a 14' man shows up, an absurd outlier even among outliers, is all we're able to conclusively say that he is taller than 8'11"?

Yeah, this is a mistake everyone makes, and it is difficult to explain to people who didn't study statistics.

The short version is that intelligence is an ordinal value, not a cardinal value. You can say that person A is more intelligent than person B, but not that person A is exactly 3.14515x more intelligent than person B.

Intelligence is simply measured in percentiles, that's all. You can't be more intelligent than 100% of the population. The 100% of the population is the population of Earth. You cannot get a higher IQ score than that.

That's right. If the event has a 1 in 390B chance, and there are 8B tries, you would expect to observe the event 2% of the time you conduct the 8B tries. So if you did 8B tries 50 times you would expect it to happen once. And its something higher than 8B - current population isn't the correct sample size.

There's a lot of things that are theoretically possible, but to realistically consider them based on the known likelihood is something I'm not entertaining here.

That's assuming that the distribution is purely gaussian and nothing weird happens at the tails.

I agree 276 is unlikely (and how would you even test/norm such a thing?)

IQ isn't some intrinsic property that we can measure that has a probability distribution. It's something we construct to have a specific probability distribution. Essentially, you have >145 IQ not because 0.1% people happen to have that high of an IQ but because we define 145 IQ to be the cutoff between the smartest 0.1% of the population and the dumbest 99.9%.

As a consequence, an IQ above ~3 standard deviations is basically unmeasurable with more tests, and by 6 standard deviations I'm not sure is even possible to theoretically construct since I don't think what it's trying to measure can be meaningfully defined to discriminate the order of just 8 people on the entire planet.

It's not impossible, but improbable.