Literally my ninth approach to writing a response.
You were originally listing explanations for how someone could think they had a really bad, unlikely outcome.
I was picking apart what I considered the inappropriate word choices you used to describe qualitatively describe one of those explanations, namely "Either your unlucky and those recipes appear at moments you are not online.". I was not addressing how to compute or judge a long term observation. I was confining myself what I thought was a nuanced imperfection in the description of the benefit in possible unseen rotations.
Your reply refocused back on assessing long term observations. Your reply ends up working at cross-purposes with what I was saying.
The portion of your post that I charitably think most dovetails with my point is, if I have correctly interpreted your intent, more directly worrisome than the phrasing I started with. But, if on the other hand, you were not trying to address the point I was making, and instead were always focused on your point, well than it's a complete non-sequitor.
"But because you missed 8 rotations the chance to be unlucky has been massively increased."
I read that as "But because you missed 8 rotations the probability to get an unlikely bad outcome from those 8 missed rotations has massively increased." Because my post was all about computing and describing the benefits you could have received if you had picked up those missed rotations. And that interpretation is exactly the mathematical nonsense that I was addressing. The 8 missed rotations are an independent event, unrelated to the 20 observed rotations. It doesn't matter if you saw 2, or 7 (or 0 or 20) Pet Foods in the 20 you observed, you will always expect that you were most likely to have seen 2 more if you had observed the other 8. (It doesn't matter if you looked had looked at the other 8 and had seen 0, or 1, or 8, you still would have expected that 2 was the most likely). Odds don't mature.
But, given your conclusion was about compounding effects, snowballing into 3 week and 7 week outcomes, maybe what you wrote was meant as "But because you missed and keep missing 8 rotations a week you are more likely to have a worse outcome over 3, or 7 weeks, has increased compared to if you had seen all the rotations each of those weeks.." Which, well, is obvious.
Outside of that, I have issues with your math, both in the computations you compute, and the comparisons that you make. First, let's start with questionable computations.
Direct errors (I think)
The chance to get no Pet Food in a single event is 75%. The Chance to get no Pet Food in 28 is (75%)^28, which is 0.032%, or 1 in about 3150, nowhere near the 1 in 523.828.085.474.749 value you give. I don't know where you got that value. The really unlikely event, the odds of getting 28 Pet Food in 28 is (25%)^28, and is about 1 in 7.206*10^16, or almost 14 times lower than the number you gave.
The chance to get 7 Pet Food in 8 is (25%)^7 * (75%)^1 * Combin(8,7), or about 0.037% or 1 in 2730, not 1 in 4096. Among other possibilities, 1 in 4096 is the odds of getting 0 Pet Food in 6 rotations.
A poor choice of equivalence
Then, there's the matter of your opening discussion of 2.3% The 2.3% outcome, that you equate to 1 out of 44 people, was the percent of people who, having already gotten 2 Pet Food out of the 20 observed rotations, would have been expected to get the 5 out of the 8 missed rotations such that they would have had an overall average outcome. That's 2.3% out of an original 6.7%, or about 0.15%. about 1 in 649 people.
Comparisons
What's the point of these computations? Big number, small number, okay, but why? what do they mean. I get the feeling that at this point because I think you are mixing and matching conditional probabilities, you are comparing, not so much apples to oranges, as the tip of an apple slice to a portion of an orange section and then comparing them both to a drop of jelly made from three and a half grapes. It would is useful to compare the odds of 2 vs 5 out of 8 missed rotations. It would be useful to compare the odds of 2 vs 7 out of 28 total rotations. Whether using your comically dissimilar (and wrong) 1 in 523.828.085.474.749 compared to 1 in 4096 , or what I believe are my correct (and way closer to each other) values of 1:3150 compared to 1:2730, I don't see any meaning in comparing the odds of 0 in 28 total rotations with those of 7 in 8 missed rotations.
*Whew* That took me a bit, but I think I actually covered my problems with that post, in a way that I think people will have a chance of correctly inferring what I've tried to imply.