Since we’re halving at each step and the 568ml pint is only 20% bigger than the 473ml pint, that difference won’t buy us even a single additional subdivision.
It might be the case that the inferior US pint could get us to e.g. not quite 26 mathematicians, so we settle for 25, while the superior British pint gets just over the hump to 26 mathematicians. But that’s the maximum improvement: 1 extra mathematician.
Far more likely is that both the US & British pints get us to e.g. 25, but not to 26. So no extra mathematician at all.
I’m not really a big Guinness fan, but I don’t really get the hate. It’s not all that thick or bitter - it’s far less bitter than a good IPA, and it has fewer carbs and calories than a Budweiser.
But are the mathemeaticians really going to get out a molecular analyzer and separate the beer into its individual components, to reconstitute them at the end? Probably not their mathematicians not chemists. They are just going to pour them into smaller and smaller cups and hope for the best.
The problem of course is that if one of the later mathematicians is actually slumming statistician he may complain that his may not have contained any actual molecules of beerium. So the question becomes how many molecules of beer can the smallest drink have to make sure that every glass has at least one beerium molecule.
Well if we use the simplified model that each molecule in the beer has p probability of being beerium, and that p is much smaller than 1, then the probability that a glass containing N molecules will have no beerium is approximately exp(-N*p). If I want to make 95% sure that my final glass has at least on beerium I want
N>log(0.05)/p or in other words about 3/p. If the last glass has a probability greater than 95% than the other glass will have a near certainty of containing beerium.
If you just leave it to chance with N=1/p then a quick calculation shows that eveyglass will have beerium only about 53% of the time. If you bump it up to 4/p you get a 98% chance of everyone getting beerium.
TLDR: You may want to cut your mathematician count by a couple just to be 98% sure that everyone gets a molecule.
In the US, it is “beerium”, but in the UK, it is “beerinium”. The beerium you find in the US has a “flavor” that is best obscured by serving it cold, whereas beerinium is more commonly served at room temperature because the UKians are masochists.
Naturally NIH has weighed in on what beerium / beerinium really is:
This learned fellow tells us there are a couple thousand distinct molecular species in beer:
Analyzing any of this is beyond my nodding acquaintance with chemistry.
But ISTM that some of these minor constituents have real high molecular weights, at least compared to simple stuff like water and ethanol. The result of which is that we won’t have to do too many subdivisions before we get the first sample lacking one of the rare and heavy molecules. Our OP’s infinite horde of mathematicians may be culled to a (collossal WAG) mere 10 or so; the rest being disappointed at being left outside the exclusive velvet rope.
Taking @Buck_Godot’s statistical argument at face value, it seems we can’t even count on a single ordinary sized serving of beer containing all the requisite chemistry. So the only way to improve the statistical odds of really having complete beer in your beer is to … have more than one beer.
If we can posit an infinite number of mathematicians, then we can also posit the ideal beer, infinitely divisible, composed of ideal beer particles beerons, which are infinitely small. Hence a half pint of ideal beer will have only half, but equally infinite, the number of beerons as a full pint of ideal beer.
