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.
MisterAl wrote:
James1978 wrote:
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.
FAQ
Posted: Wed Nov 29, 2006 12:37 am Author: davedorn Post subject: 250k in the last two
