So on that show that used to be on tv "deal or no deal" if someone got down to the last case + their case (26 initial cases), with 200k and 1m left, when asked to swap would this be a stronger strategy to do so? Could someone write the formula for this?

thought about this more and given cases are removed at random here my conclusion is that ya it doesnt apply here and makes no difference if you switch

I think it doesn't. prize is placed in one box and you get to randomly eliminate boxes or switch them. there's no additional info added. let's say there are 100 people and 1 wins something, all have a chance of 1/100. now if it gets down to you and someone else, what would you say your chances are now? 1/2. it's like if you have 10 coinflips and all are heads, what's the chance for 11th to be heads? the chance isn't any bigger just because you were lucky to get 10 heads before.

As you might imagine, there have been several threads in the Probability Forum over the years discussing this very subject.

I encourage anyone interested to search for those threads. I don't know if it matters, but "Monty Hall" is sometimes spelled "Monte Hall" or even "Montee Hall" which might influence how you do your search.

I am going to close this thread, not because I think it is a bad topic, but because we have discussed this at great length in the past. If anyone wants to resurrect those discussions and has something new to add, feel free to post in one of the older threads.

Thanks much.