how many times, now, has the 250k been in the last two? And how many times has it made it to the table?

swap or no swap....

If you include the proveout stage, 24 times, 8 of which were games with 250K coming to the table.

Let's list them all:

£250k at table:

Natalie
Mally
Daz
Anna
Germaine
Bob
Patricia
Debbie (1)

£250k in last pair but not at table (including proveout):

Maurice
Jennifer
Sara
Lee (1)
Nancy
Kirsty
Gary (2)
Morris
Tom
Drew
Paul (4)
Nev
David W
David J
Tony
Lucy

I make that 16 - it's been in the last pair but not the table twice as much as it's been at the table. Is that statistically significant?

Nope.

Using the hypothesis that it's a 50/50 chance that the £250k is in the player's box, given that it's still in play at the two-box showdown, we get the following probability...

CHANCE OF THE £250k BEING IN THE PLAYER'S BOX 8 TIMES (OR FEWER) OUT OF 24 = 0.07579

That's a chance of around 7.6%, which is quite small, but nowhere near small enough to doubt the validity of the "50/50" hypothesis.

Interesting, cheers MisterAl!

Hmmm... I said a while back that I thought it was 2:1 in favour of swapping. And while the theory night not back that up, the actuality certainly does.

Although, when you're at last three, there's a two-thirds chance that the 250k isn't in your box - and while I know it'll be shouted down, the actual real-life results don't half bear Monty Hall out.

And here's why - In Monty Hall, we know that Monty is always going to reveal a losing box. In DOND, we don't actually have a "last three" stage as such - and to get to last 2 with the 250k in play, you must have emulated Monty and chucked a "loser" out at the "choose from three boxes" stage.

How you got there doesn't matter - it's a given. That you've got the 250k still in play is also a given and that you've chucked out the losing box is a given.

In other words, arriving at that stage carries the same probability that Monty chucks a losing box out - it's 1 - cos you've done it.

At that point, it doesn't matter how you got there - you can ignore the 19 boxes previously discarded, because you've done the deed - remember we're only looking at the situation where the 250k is in the last two - and it so closely mirrors Monty Hall, that it's no surprise that the 2:1 odds in favour of swapping have thus far been borne out.