Somewhat surprisingly, I don't see a question about this.
There is a team-building (or just fun mathematical) game where a group of people hold hands with each other, usually trying not to hold hands with someone right next to you. The goal is then to "untangle the human knot" thus formed.
Folk wisdom says this can always be "solved", in the sense of twisting and moving to demonstrate the knot formed is just one unknot, but this isn't so, since you can form all sorts of knots. Probably forming a simple non-trivial link of circles would be easiest to demonstrate this.
But I am intrigued by a lack of easy-to-find references on the probability of such a configuration being the unknot. There is this MathOverflow question, which however has devolved into whether any link can be formed, which is NOT what I am asking. See also this Reddit thread and this Quora thread.
In any event, not only do I feel like probably there is a known answer, it is also not possible to search on this site for questions on MO, so hopefully it is appropriate to ask on MSE this question:
Given any reasonable set of definitions of this game and reasonable probability distribution given your definitions, what is the probability that such a link is the unknot, as a function of $n$ players?
Presumably this will vary by some assumptions on arm length or the exact rules (can you grasp your neighbor's hand, how are people arranged), so there could be multiple answers. I suppose it's likely the parity of $n$ will be involved as well.
As a hint, there is a comment to the MO question suggesting some possible references in somewhat difficult-to-access resources - but I don't care about references per se, I would like answers that are publicly available on a user-friendly and well-indexed site ... such as this one!