Is not as large as you might think...

In order to win it, you must first of all select it - that's a 1 in 22 chance.

Having selected it, you must then be selected - that's a further 1 in 22 chance.

That means a 1 in 484 chance on any given show that you'll be sat at the table with the quarter million in your box.

Assuming you play to the end, you must stick with the box, and not take any swap.

HOWEVER...

the probability that the quarter mill will hit the table is 1 in 22.
That means that, even at the end pair, with the QM still in play, you've still only got a 1 in 22 chance of having the QM in your box.

The obvious thing to do, then, is to take the swap if it's offered (as Nev would have done today) - since there's a 21 in 22 chance that the box you don't have will be the winner.

You're quite right about the chances not being as large as you, or Noel, may think.

It really irritates me when he goes on about how "statistically it should've been won by now" - what statistics is he basing that on, then? LOL

Like you said, not only wouldit need to be on the table, it would also need a gambler to go right to the end and not swap it!

Sorry, but this is rubbish...



Not really - the players aren't selected totally at random. It's decided in advance who's going to play, and those who have been there longer are much more likely to be picked.



Nope. At the start of the show, there's a 1 in 22 chance of your box having the £250k, yes. But every time you open another box, you get new information, and the odds therefore change. If you keep the £250k all the way to the final two, then there's a 50% chance of it being in your box.



Well, going by your logic, as there was a 1 in 22 chance of the other box having £250k at the start of the show, there must still be a 1 in 22 chance of it being there at the end. Which leaves a 20 in 22 chance of it being in neither of the boxes that are left.

There's no real advantage to swapping, assuming it's not ALL A BIG FIX. But there's no disadvantage, either, except for the fact you'd feel like a bit of a nob if you swapped away a big amount for something rubbish...

I don't see why the odds of being selected are involved.

And if Im reading your post right, your probabilities are waaaaaaaaaaaayyyyyyyyyyyyyyyyyy off. At the Deal of 2 (2 boxes remainig) the chances of either value being in your box are 50% or 1 in 2. Fact.

EDIT: Beaten by some quick replies. . .

Yes, sorry, but I also agree that the probabilities aren't quite right.

But like I said, I agree that there is more to it than what many people, apparently including Noel, might think:

Noel goes on about how "statistically it should've been won by now" - how can he say that when it depends on so many factors? - such as, the £250k being on the table in the first place, and then having a true gambler playing who would not swap it, assuming the swap is offered.

As ever, folks who don't understand probability wade in.

Let's get this straight. When you pick your box, you have a one in 22 chance of picking the winner. The further information you get does not change the probability that you've picked the QM.

Since you don't pick again, it doesn't matter how many other boxes get opened, the probability that you have picked out the £250,000 remains the same - you still have a 1 in 22 chance of having picked the winner. If Noel was to open your box first, what would the probability be that you've picked the QM?

22/1 is the answer

However, if you are offered the swap at the last pair and the 250k is still in play, you should take it - this is a variation on the Monty Hall problem (have a look at http://www.amstat.org/publications/jse/v13n2/carlton.html (you need to scroll down a bit to get to it).

I know it seems counter-intuitive, but the maths is correct.



The information you get does not change the probability that you picked the box containing the QM. That was set when you picked the box.

And that seemingly large 484/1 odds that you, as a player, will get to the table with £250k in your box is also correct. The pick is supposed to be random - although it does, I grant you, seem weighted to players with 16 or more games under their belts.

However, I suspect that the argument will rage for a while.
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Yep, indeed, I was reading about that a while back, actually it was a few months ago, doesn't time fly, eh?! Anyway, I'm not sure about all the probability stuff. I think bits of what you are saying is correct, and bits of what Dan is saying is correct...I think.



Actually, to be fair, they do pick the player in advance - and even Noel knows at the beginning of the show who is going to be playing. It was once said by Channel 4 that the player was picked at random, however I believe that someone, possibly Channel 4 themselves, have since said it was the press office that released that statement, not Endemol, and in fact the players are not chosen at random, the flashing names at the beginning of the show are just there for effect.

Think about it - if the players were chosen at random, you could in theory get players who are there for a huge number of shows, and some who are there for only a few. And take Lucy, who played on her 50th show, which was obviously pre-planned, as she had a box with 50 on given to her by the Banker, and she lived in Bristol, meaning she was able to be on DOND for such a long time, as it's filmed in Bristol.

Afraid not



No, afraid not.

There are two "pools" of boxes. Yours and the 21 others. At the time you sit at the table, there's a 22/1 chance you've got the £250k and a 22/21 chance it's in the 21 box pool.

If you open all the boxes in the 21 box pool, one at a time, and get to the 21st box without showing the £250k, there's still that 22/21 chance the £250k is in the 21 box pool. So you should swap.


Now, if Fred Bloggs wanders in, and is offered a chance to pick one of the two boxes, he has got a 2/1 chance of picking the £250k

You've picked one from 22 - he's picking 1 from 2

Let's try it a different way.

You pick a box. It's got a 1 in 22 chance of being £250k. If you're offered the chance to either open it, or you can swap it for all the other boxes, and win the highest amount in them, which would you choose?

In this second series the banker has been on the waky baccy with his offers, so the player is more likely to deal.
There won't be a 250K winner for a while, and if there is i'll do a bork and consume a hat.

My maths is correct - assuming that everything is completely random.



I'm not quite so certain. Unless, of course, the players don't know, and only the production team does. I've got a feeling that it's a random pick from a list that's weighted by appearances - something along the lines of each time you appear they add your name to the list - so on your first game you're not on the list, but by your 22nd your name appears on it 21 times - that kind of thing.

However, from what I've seen and heard and read, the box pick is totally random.

The idea that your odds are reduced for winning the QM at the end if you take the swap is ludicrous. By any reckoning, they are 50/50 at the two box stage if it is still in play, unless people put some kind of spiritual significance on the numbers of the boxes for them, such as leaving their "lucky box" until the end! The reality is that the odds of winning the £250,000 is realistically greater than 1 in 22 because how many people have risked going all the way to the end when it is still in play? Fewer than most. Generally, people need to leave more high red numbers in play as well as the QM to go to the very end such as Morris and Kirsty with £75,000 and £20,000 as insurance. Jennifer, who dealt at £120,000 did not have that fall back so didn't go to the very end.The odds of seeing the last two boxes the £250,000 and anything between £50,000 and £100,000 are 1 in 77 for example. Based upon research on the odds, gameplay, and tactics employed during an analysis of every show since last October, it is likely that statistically, you would expect to see one jackpot winner annually, a similar equation to Who wants to be a millionaire. So on that basis, we are overdue a jackpot winner on Deal Or No Deal. Let's hope that's soon, and to the right person!!

At every box selection, there's a greater probability that the £250k will be opened on one of the wings - but the actual odds of having the £250k in your box never changes. What does change is the Banker's strategy - and he's calculating odds.

Up until today, which was weird, I've been able to predict his offers to within 5% (when he hasn't been taking the mickey) and they're all calculated to maximise his chance of teasing a no-dealer into betting his offer against the top three boxes. It's very clever - he always gives longer odds than the probabilites would suggest, but, the closer to the end of the game, with two large numbers up there, he'll almost always make offers that are more advantageous than the 22/1 against the highest box.

Where possible, he'll pitch his offers between the three highest and the next lowest - and where I say "he", I mean him and his team.

Unfortunately, you're mistaken, as any PhD in Maths would tell you. Indeed, as any bookie would tell you.

Go and read up on the Monty Hall problem, and you'll see.

http://en.wikipedia.org/wiki/Monty_Hall_problem may help.

It is] counter intuitive, but my maths is correct.

Oh, the irony! I think Wakey has a new friend!

Just to be clear about these probabilities, and information.

Here's what you know about your box - and it doesn't change. It's got a 22/1 chance of having the QM in it.

Here's what you know about all of the other boxes as a group - they have a 22/21 probability of having the £250k in the group. And that doesn't change, since your box can't be opened to prove otherwise.

Since we're only interested in the £250k, the fact that 20 boxes in the 21 group are opened and shown not have it in it changes nothing. The probability that the £250k is in that group does not change.


Note that all of this is conditional on getting to the last two boxes with the £250k still in play. In that situation, you should swap.

Here's how to prove it:

It takes two people.

Select 21 black cards from a deck, and add the Ace of Hearts.

Shuffle them well, and then you (the player) slect one, at random, face down. Don't look at it.

Now get your partner to collect all the others up, and look at them. If the partner holds the Ace of hearts, he must place it face down in front of him. If not, then any other card must be placed there. This simulates the last pair of boxes with the 250k in play.

Turn them over. If you have the Ace of Hearts, you win the 250k

DO this 44 times and record the results.

How many times did you have the Ace of Hearts? How many times would you have won had you swapped?

Try it - in 44 goes, you'll win two or three times if you don't swap, and 41 or more if you do.

Do it as many multiples of 22 as you like - the more the merrier. Post the results up here, and we'll tally them up.

You seem to know quite a bit about probability Davedorn but, with respect, I don't think you are quite applying it correctly to the DOND scenario.

The Monty Hall problem is as set out below. Read the highlighted bit to see why your principle doesn't quite apply in the DOND situation.

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"Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the other doors, opens another door, say No. 3, which has a goat. He then says to you, 'Do you want to pick door No. 2?' Is it to your advantage to take the switch?"

This problem was given the name The Monty Hall Paradox in honor of the long time host of the television game show "Let's Make a Deal." Articles about the controversy appeared in the New York Times and other papers around the country. Marilyn's answer was that the contestant should switch doors and she received nearly 10,000 responses from readers, most of them disagreeing with her. Several were from mathematicians and scientists whose responses ranged from hostility to disappointment at the nation's lack of mathematical skills.

This question seems to have a non-intuitive answer. Why were so many convinced that Marilyn Vos Savant was wrong? They had all decided that it did not matter if the contestant switched or did not switch. There may be a reason so many disagreed with her. Omitting one phrase in the statement of this problem changes the answer completely and this might explain why many people have the wrong intuition about the solution. If the host (Monty Hall) does not know where the car is behind the other two doors, then the answer to the question is "IT DOESN'T MATTER IF THE CONTESTANT SWITCHES." The change in the statement of the problem is so slight that this might be the reason this problem is such a "paradox."

Yes it does! Imagine that you reveal the £250k in the first box opened - is it still a 1 in 22 chance that it's in your box? No, of course not...the chance is now 0, as we know it's not in there.

At the start of the game, there's a 1 in 22 chance of Box 1 having the £250k, and a 1 in 22 chance of Box 2 having it. If I have Box 1, keep Box 2 to the end and keep the £250k in play, then there's a 50% chance of it being in 1 and a 50% chance of it being in 2. According to you, there's a 1 in 22 chance of it being in each one, which leaves a 20 in 22 chance of it being in none of the boxes! How many times have you seen that happen?? (Granted, there was the "valueless box" at the end of Chris's game... )

I hate that Monty Hall problem, but I think Duffer's got it right - the difference is that there, the host knows what's behind each door. He's not going to open the door with the car because that would ruin the game. In DOND, however, nobody knows. The only way your theory would work would be if Noel knew the contents of all the boxes, and began the show by opening twenty that didn't have the £250k. (Which would make for a bit of a rubbish show...)

If that was true of the £250,000, it would also be true of ANY OTHER amount. There's nothing special about that amount, apart from it being the biggest one.

If the theory was true, you could equally argue that if the 1p is in the final two, there's a 21/22 chance it's in the "other" box left on the wings, so therefore you should not swap, so what do you do with your 1p/£250k final two? The same applies to any two final amounts, and that's where the theory falls down.

With all due respect, we're talking about a specific scenario here - the scenario where the £250k is still in play at the final pair. [b]At that point[/i] and only at that point, Monty Hall applies - try the deck of cards test for yourself, and you'll see.