I think the 100 box explanation misses a subtlety in the problem. Conditional on those 98 boxes being empty, box 17 and box 68 are equally likely to have the pr

I think the 100 box explanation misses a subtlety in the problem. Conditional on those 98 boxes being empty, box 17 and box 68 are equally likely to have the prize. The key is that you have a large probability of backing the host into a corner as it were: forcing him to choose 98 of 98 openable boxes vs 98 of 99. This is where your large probably of winning comes from, but it's no clearer in the large (100-box) example than the small. Therefore I posit that the large example exploits a misunderstanding about the solution rather than elucidating it.