I don't know if this site is a suitable place to look for examples, but I have a lot of ideas that I would like to find a good example of, and I try to organize these things in a later book. I hope I get to a place where I can discuss my thoughts so that I find people taking these questions seriously, and I think they are thoughts of many people.
I am searching for an interesting example/example of a theorem, issue or case in mathematics, in which there is a specific variable that affects the result, while the intuition tells that the result is independent of this variable.
In other words, I would like a case where intuition fails to estimate the effect of a factor on a particular problem and one thinks it is ineffective, while reality is otherwise.
Are you welcome to find examples of searching for examples on this site?