Let's leave Monty Hall on the sideline for at least a while, since it has the capacity to sidetrack us into dozens of pages of discussion! Suffice it to say that far more eminent statsiticians than either of us have, over the years, found it anything but 'simple'!When you look back at the monty hall it is very simple. Your first guess gives you a 1 in 3 chance of winning therefore a 2 in 3 chance of losing. Changing you mind after seeing the goat then gives the opposite of this therefore 2 in 3 chances of winning and 1 in 3 chances of losing. 1 in 3 becomes 2 in 3 and 2 in 3 becomes 1 in 3. (Just hope your first guess is wrong then change your mind) It is so simple when you kick yourself.
As I said, you can have as many piles as you like, with as many coins in each pile as you want, provided only that there are at least as many coins in each pile as there are numbers of piles. You can weigh as few or as many coins as you want in the 'one weighing', and you don't have to keep them in their 'piles' for the weighing (i.e. if there are 10 in a pile, anything from zero to all 10 of them may be included in your one weighing).I thought the piles (here wrongly assuming again I am) had to stay in tens although it may be permitted to weigh more than one at any time ie 10,20,30, 40 or 50.
Hmm need a rethink now
Kind Regards, John.