The featured quote above is mine, and here is the full text would show I was (and still am) asking for a concrete example of a mere stats/dice question.
You ask me to accept as an axiom that mere stats/dice questions are off topic, but what is an example of that? To me, those last three Q's are mere stats/dice questions. You looked at them and you have a different perspective. So clearly, your "mere dice/stats Q's" is different from my "mere dice/stats Q's."
If I accepted or rejected that axiom, it would mean nothing, since we don't seem to agree on what to agree on. I asked you to evaluate those last three Q's, but your reluctance to evaluate them leaves me unable to establish a baseline for what is a "mere stats/dice question" in this discussion. In the absence of that baseline, my acceptance/rejection of the axiom is not meaningful at this moment.
The best I can provide you is, I believe those last three Q's are on topic, and I believe they are mere stats/dice Q's. But it seems that what a mere stats/dice Q is, is unclear and ill-defined, leaving me unable to accept that all mere stats/dice Q's are off topic. What is a mere stats/dice Q to me is evidently not, to you, and by extension, possibly to other users of the site.
Concrete examples from myself
I am interested in seeing a conclusion to this myself, and so I offer up my personal categorization of a few recently asked stats and dice questions. We shall hopefully see in the comments if the Stack agrees with my classification, and whether these are on topic or not.
Method of Classification
I will be adopting the following criteria, as put forth in WrongOnTheInternet's answer and doppelgreener's comment, to classify questions as on or off topic.
Would an RPG expert give me a better/different/more specific answer to this question than a Statistician/Mathematician?
It is presumed that, as this criteria has been established a long time ago and proposed by a diamond moderator, it should fit with the querent's criteria (another diamond moderator). That is to say I am expecting a level of equivalence between two senior members of the site. So a question that does not have answers draw upon RPG experience is a mere stats/dice question; whereas one that does, is not.
My personal illustration of this criteria runs like the following:
Suppose Bob has no experience with RPGs (but he is capable of researching it if needed, probably via Google), and he encounters a question, Q. He provides for it an answer, A1.
Suppose, in an alternate but nearly-identical reality, Bob has plenty of experience with RPGs, and he encounters the question Q. He provides for it an answer, A2.
Q can be said to draw from RPG experience (or would draw better answers from an RPG expert over a mathematician) if A2 would be meaningfully different from A1.
Results of Classification: On Topic
Advantage on damage rolls - is it still balanced? Probability is an aspect of this question, but ultimately they want to consider a mechanical balance in a specific RPG system, and the accepted answer mentions alternative strategies rooted in the game mechanics.
Does Sacred Flame or Firebolt do more damage on average to a Shadow over an arbitrary but finite number of rounds?. This question can ultimately be formulated in a way a mathematician can answer with no RPG knowledge, but the accepted answer shows information about various related game effects that take familiarity with the system to have suggested in the first place.
What is the average benefit of this particular stats rolling scheme? You can calculate the answer of this using pure probability. However, the accepted answer doesn't stop at presenting the results of his calculation, but also offers ramifications of the answer from an RPG perspective, so it has benefited from RPG experience.
How can I compare the damage gain between Bless and Faerie Fire? This question received many answers which consider situations that arise at the table, on top of pure number-crunching.
How long can creatures with no swim speed travel in deep water before they die? The answers take into account game-related settings, on top of the actual number-based question.
Results: Off Topic
How can I calculate the probability of being able to purchase a card in my custom die system? This question is related to RPG game design as explained by the querent here, but it is not something that you have to draw from RPG experience on to answer. A mathematician could crank out a set of formulas the way they developed pot odds for poker.
How does Halfling Luck affect the probability of surviving my death saves? If a mathematician researched what halfling luck and death saving throws are (it's not that hard), they can provide the same answer the accepted answer here has given.
How does Halfling Luck (re-rolling my Nat 1's) affect my dice outcome? For the same reasons as (2), it is off-topic. Notice also that all the answers it drew involved no RPG-related content. It is pure stats/math/programming skills (it even drew an answer from someone who has never played D&D before).
Is this the right formula for the total permutations of a set of dice? This question asks about d2's and d3's (you won't find those at your typical gaming table). The answers draw from no RPG experience at all.
Modelling rolling for stats in Anydice This question is related to RPGs, but someone who has never played an RPG but has used Anydice before will be able to provide the same answer that has been accepted here.
From my application of the critera to the top 10 most recent, un-closed stats questions, it seems half are off topic. The ones that are off topic under this criteria are all those questions a mathematician could answer if they took the time to research some of the game terms. The list includes some Q's that have received a considerable number of upvotes.
The ones that are on topic, according to this criteria, seem to be those that ask about specific game effects or game mechanics that happen to involve random chance. But the Q's do not seem to be about the stats in its essence (and the answers it drew picked up on that), but about the impact of those stats on gameplay.
I would love to list more questions. There's a lot of highly upvoted Q's that, in my opinion, fail the given criteria. However, I think these can serve as a starting point for now.
Which of these questions have I incorrectly classified, and why? Hopefully, with a concrete starting point, we can begin to understand what is a mere stats/dice question.
Ramifications, and an anecdote
One of the first answers I gave on this site is one about stats, about the net effect of GWM and SS on average damage. The top two answers for this particular Q draw on no RPG experience at all, and are just statistical calculations. They are also the two A's that fully address the Q. It was followed by four answers that no longer address the Q, but draw upon RPG experience on how to apply the information in the top 2 answers. These four answers have received low upvotes despite drawing upon experience (one even has a negative score), and I believe it's because they did not actually answer the Q.
I believe this Q fails the given criteria. You can plainly see that the two A's that address the Q do not need RPG experience. Those that did draw upon experience did not manage to answer the Q. It fails all around. And yet it was also the first Q I came across that made me think: I'd like to see more of these, because they're fun to answer. It was my first accepted answer of the three answer's I'd given at the time, and it made a positive impact on me, thinking, perhaps naively, there is a fun place on the internet that can combine RPGs and math.
In terms of the tag usage, I seem to have reached second highest top user next to nitsua for answer score, and sixth highest for question score. In other words, it seems to be one of the tags which I am, through some metric, most expert at, relative to all the other tags I seek out.
Moving these mere stats/dice questions to become off topic (a concrete action to close; not a hypothetical "if they are... then they are...") will decrease my personal satisfaction with RPG.SE. I am not aware of any others who draw fun from RPG.SE in a similar way I do, but I do know there are some users who haunt the stats questions as well, which I have noticed personally by perusing many of the stats Q's myself.
I admit that I have been, over time, finding RPG.SE less fun to haunt. Something about the rigid nature of the Stack (that everybody agrees we can do nothing about) and the massive backlash since I gave this appropriately stats-based answer on fairness of a swingy saving throw mechanic. I am constantly re-evaluating if RPG.SE is still fun for me, and so far, of course, I find that it is. For now, the tags I look out for are statistics and gm-techniques (other than the 5e system tag, it goes without saying). It seems to me that a lot of the existing stats questions on RPG.SE are mere stats/dice questions -- specifically, the fun ones for me -- and of course, good gm-techniques questions are much rarer.
The reason I am asking for examples of what a mere stats/dice question is, is because I want to know if all these questions I see as mere stats/dice questions are aligned with what they should be aligned with.
Are those five Q's I listed as off topic mere stats/dice Q's? Yes, I think so. Do I think they're off topic? No, I don't think so. Will I vote to close them anyway? Sure, I'll go with the flow. But give me a baseline of what is a mere stats/dice Q so that I do not inadvertently VTC what seems to be half of the open statistics questions here.