the 250k has made it to the table 8 times in 294 programmes, (that's 1 in 36.75, you'd expect 1 in 22 - nearly 14 visits) while the 10p has made it 16 times and even the 50p (yet to be won!) has made it 14 times (bang on target).

The 100k has 12 appearances, the 75k 14, the 50k 12 and 35k 9 times.

The Rock, though, has 19 appearances, with 10k on 16.

155 games have featured a blue box on the table, and only 55 have had a Power 5 box at the table. (you'd expect closer to 66)

Anybody else think that the box selection may not be all that random?

I swear the 100k has done 13 appearences... Being an avid £100k fan, I should know them all...

1. Sara
2. Jo
3. Elaine H.
4. Charles
5. Patrick
6. Gentleman James
7. Johnnie
8. Sandra
9. Gaz
10. Lance
11. Barbara
12. Jeff
13. Kelly

Yep. I knew it.

Well, a random process isn't always going to give you exactly the 'expected' number of appearances. If it were that predictable, it wouldn't be random!

Because I know you like the maths, Dave, here's some probability distributions for you, given a fair game.

NUMBER OF APPEARANCES OF THE £250k ON THE TABLE IN 300 GAMES
5 or fewer appearances: 0.6% chance
6 or fewer appearances: 1.6% chance
7 or fewer appearances: 3.5% chance
8 or fewer appearances: 6.9% chance
9 or fewer appearances: 12.2% chance
10 or fewer appearances: 19.5% chance
11 or fewer appearances: 28.6% chance
12 or fewer appearances: 39.1% chance
13 or fewer appearances: 50.2% chance
14 or fewer appearances: 61.0% chance
15 or fewer appearances: 70.8% chance
16 or fewer appearances: 79.1% chance
17 or fewer appearances: 85.7% chance
18 or fewer appearances: 90.7% chance
19 or fewer appearances: 94.2% chance
20 or fewer appearances: 96.5% chance
21 or fewer appearances: 98.0% chance
22 or fewer appearances: 98.9% chance
23 or fewer appearances: 99.4% chance

So the quarter-million being on the table only 8 times in 300 games is a 6.9% shot. Small, yes, but nowhere near small enough to doubt the fairness of the game.

Argh!! I'm a fractions man (way too old for all this furrin percentages nonsense!)



But it's less than a 6.9% chance for exactly eight in 300, isn't it? ANd yes, I would much prefer to consider the empirical data over a much larger sample - say 3000 games or so. By then the distribution ought to be much more even than it currently is - all appearances should tend towards their once in 22 games expectation.

However, I'm beginning to think that the player choice (as opposed to the box pick) does have some bearing on the frequencies of appearance. The following text is me thinking out loud, not necessarily positing a theorem.

For instance, we now know that a certain number of people each day will not be picked to go to the table. That's 19 of them, Bringing it down to a single game, surely the player must be allowed first pick - otherwise what's the chance of them picking the 250k ball out of the bag - is it that it must be diminished by the very fact that any one of the players before them could have picked it? It's beginning to look that way! (and yes, I know, the maths says different!)

Next, we're told (although it hasn't been confirmed, I don't think) that the pick of boxes is done via ping-pong balls and a bag. Does each player pick, or does a crew member? If the latter, how random is his picking style? Are all the balls completely identical in every way (aside from the numbers on 'em,)? Could there be a bias towards the 250k being heavier or lighter (old bingo machines could be "fixed" with a small weight in certain balls) It's not for nothing that the Lotto balls are very, very heavily scrutinised and weighed to the nanogram.

How do contestants (if it is they) pick? My own method, when it's been required, is to shuffle the balls (or paper billets) around, and pick from the bottom. If the 250k ball is lighter, my chances of picking it are reduced - it'll tend towards the top of the bag.

Next, in 300 games I think it entirely reasonable to suggest that we should really have seen a 250k winner, if not four or five - there have been enough people who were hell bent on going to the bitter end and not swapping (and I still say that it's 3/2 in favour of swapping if the 250k is in play) - and yet not one.

Something's adrift in all of this. While the probabilities and the maths says it's within the bounds, it simply doesn't feel right - the margins are too great for what many would call coincidence. I feel certain that Endemol is aware that a 250k winner would peak the figures for a few weeks, and that they'd drop off rapidly thereafter if 250k winners popped up every 22 games or so. Or that folks would simply hop elsewhere, having seen the top prize go - the one thing that brings many back.

Yes, but seeing as though your argument is based on the idea that 8 times seems too few for a fair game, that implies that fewer than 8 would also be too few. So the relevant probability is for 8 or fewer appearances, which is 6.9%


Indeed, although there'll still be variation from the 'expected' amount no matter how many games you look at. Calculating the probabilities, as I did above, tells us how unusual the variation is. I'd say that the probability of the observed events occurring by chance has to get down below 1% to raise any serious doubts. But still remember that amazing coincidences can and do happen. Just ask Brenda.

As for the rest of what you wrote; if the cold, hard mathematical facts don't convince you that there's no real evidence to suspect foul play, then I'm not sure that anything will. I know you're aware that mathematics can explain counterintuitive phenomena (e.g. Monty Hall). So why don't you trust the maths when it goes against your intuition this time?

It's not the maths I don't trust.

Maybe it's my journalist background, but there's a feeling in my bones that there's a story brewing at DOND towers. Intrinsicaly, I'm cynical about all things televisual - where ratings and advertising income are considerations (and the two are very, very closely allied) there are huge monetary stakes involved.

Programme makers inevitably formulate an "ideal" direction for any show, and will often grasp whatever opportunities they can get to manipulate or massage things to fit that ideal.

The prolonged absence of the 250k from the table, while not statistically significant, is valuable for the show. Very valuable, I'd say. There is an aura about it that, when it does appear on the table, it will be won - that's certainly being fuelled by Endemol by way of Noel.

See, I've never got that impression. My feeling is that Noel is saying (incorrect) things like "the quarter-million hasn't been here for ages so it HAS to appear soon" in an attempt to stop people turning off in the belief that the big prize will never be won because it's never there to be won. If the producers did want to engineer things, they'd put it on the table more often. That way, Noel wouldn't have to resort to these inaccurate claims that the big win must be just around the corner. The audience would know that it could be won soon because they'll have seen that it really could be in front of the player.

I have no doubt that the producers do want to manipulate the game to try and make the show be whatever they want it to be at that time. For example, they can influence the direction of any particular game quite a lot, just by the way they set the Banker offers. If they want a feel-good show, they'll offer high to ensure the player gets some good money. If they want edge-of-the-seat excitement, they'll offer low to persuade the player to take the gamble. They can do all of that without forcing any particular value into the player's box.

Ah, but here you endow the viewing public with rather more intelligence and facility with probability than they in fact have. The way things are, we've seen precious few games where the 250k has stayed until the 5 box stage - indeed, in goldfish memory time, it's been knocked out quite early in the game. If it gets to 5 box with the 250k intact, there's an expectation that it's on the table at the moment - purely because it hasn't been for so long. That makes for compelling telly.



And they do - but I'm still exceedingly curious to know the methodologies they employ to select the box values. We know the excel sheet failed due to seeding errors - or should we say that they stopped using the excel sheet because the seed errors were noticed - but do we know exactly how boxes are filled, what level of confidence is there that it's as random as it could be, when linked with player selection?

For instance, when are the boxes seeded? Is each set seeded just before the show it's going to be used in, or are three sets seeded for each day (with a fourth in reserve) and then drawn for each show in a random way?

We've gathered that contestant draws happen just before each show - but we also know that the contestant for each show is known in advance - so in what order do they draw? If the seeding of the boxes is random, is there any need for contestants to draw again - why aren't the boxes simply placed in number order on the wings?

If the contestant is the last to draw his box, how does that influence things? In effect he didn't pick it at random - it was forced on him. The only way he can have picked at random is if he has first pick - otherwise his choice is limited by his place in the queue.

If he's 15th in line, what are the chances that the 250k has already been picked by those prior to him in the queue? Surely there's a 14/22 chance that he cannot pick the "winning" box, because it's already gone.

For each player's game to feature exactly the same chance of winning, they must pick first, surely, so that there's no chance that the 250k (or the 1p) is not available to them.

And yet they show surprise when they are chosen to play, so one might reasonably assume that either they don't pick as I've suggested, or they're too thick to spot the pattern! (and I can't believe that).

That, therefore, suggests that it's not an even playing field. If that game's contestant does not pick first, then all box values are not available to him, which is inherently unfair.

This is fascinating, but I really don't know who to listen to as it all contradics each other

Actually, I was doing just the opposite! Whereas you're assuming the public will all go along with the flawed 'Mally's Law' way of thinking (if the big money has been away for ages, it must get to the table soon), I was suggesting that they might instead believe the equally flawed 'black widow' school of thought. That is, that the big money will be attracted to the same place each time; that place obviously not being the playing contestant.

A belief that the big money could be won is the thing that Noel is trying to push, so he hypes up the 'Mally's Law' thinking. But he wouldn't have to if the £250k made it to the table more often.



If the producers were in the business of choosing the amount in the player's box, I still say they'd put the £250k there more often. Either the player will win the jackpot, or we'll have the drama of seeing that they could have won the jackpot. Either way will definitely provide compelling telly.



I seem to recall Geordie saying that he picked from left to right because that's the order which the ping-pong balls were chosen out of the bag. Hopefully he's reading this and can confirm or deny this.


Do you mind a bit more maths here? I hope not.

Say the player is indeed 15th in line. Then, as you rightly point out, there is a 14/22 chance that they cannot pick the £250k. However, there is a 8/22 chance that the £250k is still available, and seeing as though there are only 8 picks left they'll have a 1/8 chance of choosing it. So we have the following...

OVERALL CHANCE THAT 15TH PLAYER WILL END UP WITH THE £250K
(14/22 x 0) + (8/22 x 1/8) = 0 + 1/22 = 1/22

In fact, no matter what the position, the overall probability will always end up being 1/22. So it really doesn't matter what order the boxes are chosen. Every player has an equal (1/22) chance of getting the quarter-million whether they pick first, last, or somewhere in between.

Not really. What everyone is saying is that you'd expect the £250,000 to come the table once every 22 shows but in reality this will never happen, due to the random selection process.

Think of rolling a dice 60 times, you'd expect to roll a '1', '2', '3', '4', '5' and '6' 10 times each but this would very rarely happen.

And just because a '6' hasn't appeared in the last 20 rolls doesn't make it any more or less certain to happen on the next roll. It's Noel's job to get people watching so he'll tell everyone a '6' is due soon to get people watching, even though it's just as likely to appear from one roll to the next.

Hope I've not dumbed down the maths too much!

You'd think so, wouldn't you?

But here's the thing. Let's change things round a little. You have 22 boxes, 21 of which contain nothjing, and one which contains a rubber duck. There is no way to tell them apart.

Player one is offered the chance to pick a box - any box. The chance of him picking the box with the duck in is 1/22.

The box he picked is noted and it's marked in a way that no-one can tell, other than an x-ray machine, what was in the box. It is returned to the pile of boxes. Player 2 then picks. He, too, has a 1/22 chance of picking the box with the duck in. His box is marked the same as player one's.

Fifteen boxes are then removed at random. Player three is then asked to pick a box. He cries foul - fifteen boxes have been denied him - he cannot guarantee that the rubber duck box can be picked from them, he has only seven to pick from, and while players 1 and 2 knew that the rubber duck was in the pile somehwere, player 3 cannot know that - because there's a better than 50/50 chance it's already been removed.

In other words, if the process of picking the player was random, then, yes, the order of picking the box would not matter one iota - it's a random pick from a random distribution of boxes.

BUT, because the day's player is already known, he MUST be allowed to pick first, so that every value is available to him - that way, everybody gets exactly the same bite at the cherry.

As I say, if he was last in line, he has no choice - he gets what he's given, and all the values are not available to him, bar the one that's left.

If I was the producer, I'd be cutting Noel's spiel short, anouncing the day's player, having him pick a random ping-pong ball (borrowing the Lottery machines to do it, maybe!) and then just chuck the other boxes out in numerical order along the wings, them having been in plain sight from the opening of the show.

That way, there's absolutely no doubt about it - every player picks his box in exactly the same way, it's seen, and there can be no accusations or consipracy theories.

The player can then either go by numbers or by people, choose to shuffle the boxes or not, whatever - but the main thing is, everybody will do it exactly the same way.

I would think so, yes. In fact, I do think so.


This, of course, is describing a different situation than we've been discussing above. This cannot apply to Deal or No Deal because we cannot have two players with the same box in Noel's game. Because of that, it's largely irrelevant.


But Players 1 and 2 could turn round and cry foul since they had 22 boxes to choose from whereas Player 3 only has 7 boxes. If the duck is still there, Player 3 has a much better chance of finding it than they did.

Of course, their argument would be just as flawed as your argument. The fact that the big prize could have already been taken is exactly balanced out by the fact that if it hasn't yet been taken, less boxes to choose from means you've got a better chance of getting the top amount.


And that final box has a 1/22 chance of containing the big prize. Whether a player gets to choose their box first or last, they'll still have a 1/22 chance of getting the jackpot box. All 22 boxes are randomly allocated to the 22 players. Every player has exactly the same chance of ending up with the £250k as they do the 1p. The order that the balls are drawn does not affect that fact one jot.

I would think so, yes. In fact, I do think so.


And that final box has a 1/22 chance of containing the big prize. Whether a player gets to choose their box first or last, they'll still have a 1/22 chance of getting the jackpot box. All 22 boxes are randomly allocated to the 22 players. Every player has exactly the same chance of ending up with the £250k as they do the 1p. The order that the balls are drawn does not affect that fact one jot.[/quote]

Surely that only applies where the player is randomly picked from all players. In that situation, we're picking a box at random, from, if you like, a shuffled deck.

But we are, in effect, not talking about a random pick. We're actually talking about combinations and permutations.

In order for whoever picks at, say, tenth in line to have the 250k available to him, the preceeding nine picks must not be the 250k.

The probability of that happening is 59.09%. However, if you're picker number 15, the probability of all the preceeding picks not being the 250k reduces to 31.81%

If you're picker number 5, the probability of the previous four picks not being the 250k is 77%.

In the DOND scenario, the "picker" is known before the pick - his position in the pick order is also known, it would seem. It just seems that, in order to maintain a level playing field, with no chance of any conspiracy theories, the methodology I outlined above would be much better.

It answers all the possible points that might be raised.

1: The maths shows that it doesn't matter when you pick, you still have a 1/22 chance of picking the 250k. OK - so let the player pick from all 22 boxes. That way every player has the 250k available to him - guaranteed.

2: It actually doesn't matter what boxes the other players have, or the order in which they pick once the player has picked. OK - so let the player choose between shuffled wings or numerical order wings.

3: The audience is now the independent adjudicator as well, insofar that they have the boxes in plain sight all the time before the player has picked his - and after. There's no chance of jiggery - or pokery.

In other words, it's seen as being fair - in that every player does it exactly the same way, on camera, and with a live audience.

Let's just put it a slightly different way. If you had to pick an ace from a deck of cards in order to save your life, would you rather pick from a full deck, or from a deck from which 26 cards had been removed?

No, we're really not. Combinations and permutations are not what you're describing at all.


Yes, but what you're consistently not taking into account is the fact that if those previous picks are not the £250k, then because there are fewer boxes remaining at that stage, the chance that player 10 will pick the box containing the jackpot will be higher than the chance that the earlier choosers had. So it all balances out.


Depends whether I knew how many aces had been removed within those 26. If only one ace, or even no aces had gone, then I'd much rather pick from the reduced deck, thank you very much.

If nobody knew how many aces had been taken already within the 26 removed cards, then I really have no preference for the full deck or the half deck. I'll get one card randomly, and 51 random cards go elsewhere whatever. I'll have a 4/52 chance of getting an ace no matter what the process used to allocate the card to me.

I'm really not sure whether you're disputing the maths that says that the position doesn't affect the 1/22 chance (because it really doesn't affect it at all), or whether you're accepting that but arguing that psychologically it 'feels' better to have the hotseat player picking first. Personally, I think that Noel's 'housekeeping' questions can be irritating, but that'd be nothing to having to actually watch the player choose their box, then having to watch the other boxes being given to the people on the wings (or even just cutting to after that happens). That doesn't strike me as being good from a TV point of view. It slows things up when we'd much rather be learning about the player, or even just getting on with the game itself.

I'm not disputing the maths - already said that. It's the psychological side, and the possibility of conspiracy theories. As I've said, I think there's a story in DOND towers - I just don't yet have all the info I need to put my finger on it.




It'd take less time than the (to me) irritating "this is how Paul threw his life away on the whim of a former goalkeeper from the outer hebrides and went away with just 7p, but that 250k hasn't been at the table now for 7,349,216 games so it just has to happen today".

Start the show with "It's Bartholemew's game today - Bart - pick your box!" He does, roll the credits, and Robert's your father's brother. Sorted.

I'm sorry but that is some of the most spurious logic i've ever seen. I can't believe MisterAl has explained to you numerous times how the probability of picking boxes works and you still don't understand it.

If i was a player, i'd be happy for every other player to pick their box and i'd have what was left. I'd have a 1 in 22 chance of getting the 250k, just as if i picked first.

And as MisterAl says if i knew nothing about whether any aces had been removed or not i'd happily pick from either the full deck or the reduced deck - this kind of ridiculous spurious logic should not be allowed to spread, as it can be exploited for profit, as can Mally's Law (in all those books sold about the lottery where you keep track of numbers to discover what will come up next!). So reread MisterAl's posts a bit more carefully and avoid using such logic or suggesting pandering to it for psychological reasons - the world would be a much better place without it.

BZZZZTTTT! Wrong! I know exactly how the maths works. Trust me on that one. And I also know about tests for randomness. Re-read what I wrote. I know that no matter when you pick, if it's truly random, then you have an equally likely chance of picking the 250k as the 1p.

I also know, now, that players pick in their order on the wings. That's cool, too. However, we do not know how the box values are selected. How long is it since box 22 had the 250k?

I'll ignore the rest of your thinly disguised attack - but will suggest that, if you read what I've written without busting a blood vessel at what you think I mean, you'll see that what I'm advocating is a completely transparent method of picking what box gets to the pound table.

Yes ok, i accept you know how the maths works for the random selection - but i think in the way you have phrased and emphasised your argument you don't make that particularly clear.

I also think that how the boxes are allocated their values is probably a very minor thing - obviously if we could spot a specific pattern (low numbers always end up in high boxes, 50k is always in box 10 etc) then it would be worth debating, but we can't. There's nothing to suggest it isn't random - as far as i'm aware - and until that evidence comes to light it seems careless to popularise theories based on spurious logic as a supposed solution to a supposed problem that may well not even exist.

If the box values aren't allocated at random, surely a simpler solution than the convoluted one you suggest (which in turn panders to people's belief in a harmful and non-existent system of maths logic), is simply to alter that so that the box values ARE allocated at random.

Values allocated at random, boxes selected at random. Everyone has an equal chance of getting any value. problem solved..?

I have made clear what I want to make clear - does that statement have any resonance for you?



Which is where we differ. For there to be an equal chance for every player to arrive at the table with the highest value box, the allocation of numbers to boxes, and their eventual allocation to players must be perfectly random. Pseudo-random is not good enough (as we saw with the Excel fiasco), "almost" random is not good enough.

Not only that, but the processes must be transparent and checked for bias. Now, there are two happenstances that, taken individually, count for little more than nothing - that is the lack of the 250k at the table for, what is it - 107 shows? and also that the 250k has not been in box 22 for nearly as many shows.

These are exactly the kind of thing, taken together, that would prompt an enquiring journalist to dig deeper. Yes, even taken together there's little mathematical evidence to suggest non-random picking. The maths says "no - it's OK, it's fine. Looks random to me - let it get to 400 each and we might have a case".

The journalist says "hang on a mo. That looks a tad weird. There might be something in this. I'll have a hunt about and see whether there's anything I can turn up while I keep an eye on things". And then he (or she!) sets about trying to find out just exactly how things are done, being a little cynical about fairness in TV game shows.



Oops - got ahead of meself there...



Yes, it would be. But how do we know? They thought boxes were being allocated values at random with the Excel spreadsheet. They obviously think that it's random at the moment. But, in this thread, I have suggested ways in which bias might creep in - and picking ping pong balls out of a bag is one way - if not, that's exactly what they'd use for the National Lottery.

Instead, they spend loadsa money on very carefully calibrated balls in carefully checked machines that have been soak tested, cross-referenced, minutely examined and specifically formulated to remove all possible variables to the fullest extent that current engineering will allow. And the public gets to see them working.

We, as DOND viewers, get to see nothing of that sort. We know that players are not picked at random - so it's not a double-shuffle pick of the box - and we never get to see the box allocation to the player, nor do we know how that box is allocated its value.