Alright, let's do some psyker math.
The Imperium rules over "a million worlds", and psykers are about 1 in a million. I'll take that to mean the range beginning at Eta // Theta // Iota up to Alpha Plus. 1d4chan doesn't cite their source but gives Gamma // Delta psykers a rate of 1 in a billion. This is important to give us some sense of how the rarity of psyker grades proceeds.
Now, the population of the Imperium: I'm going to assume the million worlds statistic refers purely to human inhabited planets, not also dead worlds in Imperial territory. This is sort of an issue due to the way the Imperial population is distributed. Agri Worlds in the millions, Hive Worlds up to 500,000,000, at least one Pleasure World over a billion, Civilized Worlds, Death Worlds, Cardinal Worlds?! How in Throne's name to measure that? Well, Lexicarnium puts the number of Hive Worlds in the Imperium at 32,380. Earth would probably be classified as a Agri/Pleasure World at 7 billion, while Holy Terra is said to have "billions". I think it's fair to assume Holy Terra is the most populated world in all the Imperium, and thus would be greater than the runner up of Ichar IV at 500 billion but less than 1 trillion.
Now, Earth is probably among the most suitable worlds for humans possible, but if we take a figure near its population as about an average baseline for the Imperium we get 5 billion times 1 million, which gives the Imperium a population of 5 quadrillion. God damn. I don't think that's fully unreasonable, but let's do some checking. The lowest recorded Hive World is Landunder at just under 1 billion (pathetic), while the highest exempting Terra is again Ichar IV at 500 billion. I went through all the listed populations of Hive Worlds on Lexicarnium and found their mean to be 58.2 billion (set of 18). 58.2 billion*32,380= 1.8 quadrillion.
Well hot damn, 5 quadrillion looks like it's actually reasonable. Granted, no other worlds are going to have that kind of concentration, but if a mere 32 thousand of a million holds nearly 2/5ths of the Imperial population the other 968,000 making up 3 quadrillion isn't unreasonable.
Alright, finally on to psykers. 5 quadrillion/1 million = 500 billion Imperial psykers from Eta to Alpha Plus at any given time. Incidentally, this means that Cheesecake's need for 3.65 billion psykers over 10,000 years is not only possible, the Imperium could feed the Emperor for another 10,000 years and then some with just their current psykers if they could keep them alive. Our psyker baseline begins with the difference between Iota to Alpha Plus and Delta to Alpha Plus, that being 5 million and thus lending us to 4.9 billion Iota-Eta psykers and setting the rarity progression.
The main population of the Imperium goes from Sigma to Kappa, and they're almost 4,999,500,000,000,000 of the population. This is where things get very hard to quantify. Omicron through Kappa are "lucky people" who can subtly warp reality, while Sigma through Tau people are "mundanes", not warp-negative enough to spread a hate plague and shrug off daemons, but warp-negative enough that the psyfire might leave a second-degree burn instead of a third-degree one, or who might not see warp ghosts in the local haunt while everyone can. Everyone has definitely met people who are lucky or kind of dense seeming, so I think it's fair to say that the distribution isn't that skewed towards Rho/Pi. The other thing is that it seems like the distribution should be heaver on psi-positive instead of psi-negative, both because blanks are generally described as more exotically rare and because humanity has been increasing in psychicness, not decreasing.
I looked, and sadly, there's no studies showing what percentage of people are lucky. Alas, I'll just have to do some guess work. Most people aren't lucky, but even fewer should be dense. So... 20% lucky, 5% mundane, and 75% baseline.
Unfortunately, I don't have any way to really measure the true blanks past Sigma, so that's pure estimation based on other numbers.
Nevertheless, this means that the total population of the Imperium, divided by psychic assignment, is:
Omega-Minus: ~Ten Thousands
Omega:~ Millions
Upsilon // Phi // Chi // Psi: ~ Billions
Sigma // Tau: 249,975,000,000,000
Rho // Pi: 3,749,625,000,000,000
Omicron // Xi // Nu // Mu // Lambda // Kappa: 999,900,000,000,000
Iota // Theta // Eta: 4,995,000,000
Zeta // Epsilon: 4,500,000
Delta // Gamma: 450,000
Beta // Alpha: 45,000
Alpha-Plus: ~5,000
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