At last! After this enormously long and arduous, and indeed Homeric thread I think I have arrived at the answer I was looking for, or at least an answer that I can grasp in my mind.
DonD. The chances of the £250k being in the contestant's box at the start are 19/1 (or whatever the number of boxes are). Of course these odds apply to any of the values, including £1. When the game reaches just two boxes then whether you consider that the odds are still at 19/1 for holding the £250k, or 2/1, the same odds apply to the £1. So there is no advantage in swapping.
To emphasise this, if there were an advantage in swapping we would have to come to the conclusion that for any two values the higher would be on the counter side 19 times out of 20, and that would be silly.
Monty Hall is far more devious and deceptive. It deceived me for a long time. The crux, and the deception, is that Monty is not simply offering a swap between one box and another. If he were, then there would be no advantage in swapping. Monty is actually offering a swap between the contestant's box and both of his boxes, one of which he has already shown to be empty. So the contestant who swaps effectively gets to look in both of Monty's boxes, and takes the higher value. The odds for swapping are 2/3.
Many MH websites are misleading in that they state that it is MH knowing what's in the boxes that makes the difference. It isn't, by definition the swap isn't offered unless an empty box has been opened: how it is opened, by chance, goat or otherwise, is irrelevant. The difference is that the swapper sees inside two boxes.
If DonD came down to three boxes, and Noel offered a swap with the box on the counter that contained the higher value, the contestant should swap. That would be classic Monty Hall.
Thanks to everyone who has posted to this thread. I haven't understood all the posts, but no matter. I think that all that is left now is for us to tend our goats. Rgds.
