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Yes if you have all of the information. Without the info it is a 50/50 chance. Sorry I didn’t explain that at all well.

Switching will always give you a 50% chance. Not switching gives you a 1 in however boxes were there chance. With the 100 box example. You pick one so have a 1% chance of winning. If 98 incorrect were to be removed leaving either the correct one or another incorrect one (if you have the...

I guess another way of looking at it would be to switch it. So if you were asked to pick a box but then told you could swap it to the other two boxes then would you? Surely the answer is yes, so that is effectively what you are doing when one of the others is removed.

Because when you made your initial choice it was a 33% chance of winning. Given that there is always going to be two wrong answers with the initial choice then one box can always be removed but it can’t be the box you chose. So the chance of it being the box you chose was always going to be...

This is the classic error. The way I explain this to people is to ask whether they would rather take a choice about a one in three chance or a one in two. Obviously people would rather a 50/50 shot but this puzzle is interesting because it kids you into thinking the odds are 50/50 for both...

But when one of the other boxes is removed (which will always be possible no matter which is picked)

This is a great puzzle. I know it but I am a data analyst and used to like a gamble so have a good understanding of odds and implied probability. I will read the comments with interest but not write the answer here.