How Nature Preorders Random mathematical Outcomes
The jar is basically a random sample of of the vat.
So what Ergo is suggesting is that the proportion in the jar will be always be even.
In statistic we would never make an absolute claim like that, because statistic is the science of uncertainty, but we would create a null hypothesis:
Versus an alternative hypothesis
Pa: At least one of the proportions is different.
We would then have to take a jar and measure the results against a null distribution to figure out the probability of the observed results given the null distribution is true. We would then use this p-value or test statistic, to make a conclusion about the hypothesis.
And this is where Ergo's mistake is: He is assuming that given the null is true we will always get an even distribution, because in a fair test after all the math is done we will fail to reject the null; either 90, 95, or 99.95 (typical standards) percent of the time, but there is no always. Yes, we can use the math to approximate a normal distribution but it is called "normal" for a reason.
Here is a simple rundown of the Empirical Rule: http://www.statisticshowto.com/empirical-rule-2/
The process includes an element of uncertainty, and in statistics the conclusion will never be the null is true, it will always be there is strong/weak evidence for (or against) the null (or the alternative which ever may be). And we would make that conclusion based on the probability of the observed results given the null is true.
Statistics does not measure certainty, it measure uncertainty.