This example is a very good illustration of how I too understand the difference. In my language (which I've used in NAL123's threads about this before), saying that 'anyone could win' is a way to express a theoretical possibility, whereas saying that 'you might win' is a way of expressing a real possibility.
NAL123 has to try to understand these two very different kinds of possibility.
1) Your child might do better with a different teacher.
2) He is the type of person who might appear in a fashion magazine.
3) The experience was, you might say, a glimpse into the future.
4) You might think he would try to run away, but this is Hollywood and he comes up with a different plan.
1) No, this is clearly intended to be real. The interpretation is that someone is talking about a real possibility for the child.
2) I think this could be both but it's most likely that the speaker is thinking hypothetically. That is, he's not really ever going to appear in a fashion magazine, but given his good looks, it's at least imaginable.
3) Forget about this example. It is not meant to express a real possibility, no, but it's best treated as a fixed expression (you might say), with a specific use.
4) Again, I'd advise you to ignore this example. You should treat this as part of the idiomatic expression You might think. It's not particularly helpful to analyse the parts of fixed expressions.
Is "I might think" a fixed expression too?
The episode also seemed to exemplify a sense that female anger no longer had the place in the mainstream that it had during the 1990s, when Clarkson was growing up listening to Alanis Morissette; she feels this is changing, raving about both Adele and country singer-songwriter Miranda Lambert's latest Pistol Annies project. "I looooove Pistol Annies!" she gushes. "Anything to do with harmonies, I love, and how bare is that production? Miranda is one of my favourites. Have I thought about collaborating with her? Uhhh – I might think about it every day! I run into her all the time and I swear to God she thinks I'm stalking her and she hates me.
Here are other examples of it: https://ludwig.guru/s/I+might+think