please empty your brain below

*impressed that dg has clearly spent so much time researching this*

Ta for pointing out those odds dg, I was one of that early 7\\% *cough*

I think the only way we'll get to see a £250,000 winner is if all the low boxes are opened early, and that £100,000 and £250,000 are left. I mean, if there was a gamble between those two values, people are more likely to do that than a gamble between £1 and £150,001.

*less impressed that dg has clearly spent way too much time thinking about this*

Of course you also have to factor in the fact that most people's thinking is that whatever amount of money they walk away with is still more than the amount they walked in with.

I'll bet he worked it out on the tube on his way to work (or even on the shortish walk to the tube station)

Hmmm.... interesting. But not in the way you seem to think it is.

Statistics don't mean a whole lot in a game that, as you point out, you only get to play ONCE. I read through the statistical analysis in that PDF (although it's more about risk aversion than winning prizes) and the standard deviation on prize winnings versus the contents of the box is *HUGE*. Huge enough to make the results effectively meaningless.

With only eight boxes in your example, you'd have to be able to play the game dozens of times for the averages to have any meaning whatsoever. Effectively, there is no wrong choice when you only play once. It's all about how much money you're willing to "lose". (though it wasn't yours in the first place)

One other thing in your example (only eight boxes, one try) is that the median will end up being more relevant than the mean. If you take that as your starting point, then the first offer is a good bet.

To be fair I don't think the poll was worded that well. I ony answered question numer 4 and left 1,2 and 3 blank so you don't know whether I would have dealt or not at the lower amounts.

If other people did as I did, then I'm afraid your survey results are wrong and therefore your analysis is pointless.

dg writes: No survey is perfect when carried out by people who don't read the instructions. I had hoped that "What would you do in each case? (please give four answers)" was clear enough.

Only caught a brief bit of one of these shows, but the was no fascination in greed being fanned (if that's the right expression), or in the attempts by the host to wind up the tension - which seemed to be absent anyway.
But then I don't find Big Brother of the slightest interest either.
I do, however, like diamond geezer's blog (smarm, smarm).

Ohh I see that's an excellent poi.... Zzzzzzzzzzzzz

Sorry.. where was I? Ohh yes, statistics... fascinating. Takes all the fun out of things mind you

This sounds like both the glory and the problem of this game. It's not random chance, it is a game of complicated probabilities. But the people with the computational power in their heads are all playing professional poker.

This sounds like the sort of experiment economists do all the time (with slightly smaller amounts) to model risk aversion. Perhaps Deal Or No Deal is just a front for some huge economics experiment - that's right, you've all been glued to the telly watching economics live in action. More interesting than it sounds, isn't it?

Er....I'll name that tune in three?

Yesterday I thought I understood the rules.

This morning I became confused but thought I did again at the end.

Reading through your interpretation of our responses again I'm no longer sure.

You're determined to make me watch Noel Edmunds aren't you?

Agree with Chz. I also started by calculating the average expected winnings of $39,000 and then quickly threw that number out as meaningless in a population of 1. Also agree that the median of $2,875 is more relevant to the decision given the sample size.

Not having seen the program, I missed the point that if you choose 'no deal' you get to try again after 3 more boxes are gone. That makes DG's argument that you have a 2/3 chance of getting another shot at the $250,000 persuasive.

I had a quick look at a few minutes of this prog as I got home early but found it terminally boring and so slow - it's years and years since I've had the misforture to see Edmonds on TV and he is an irritating idiot.

But... as you point out yourself, this game isn't about simple arithmetic probabilities.

Imagine a more extreme version of the same game: I give you two options. Option A - I give you a billion pounds, no catch. Option B - we toss a fair coin; if you get it right I give you THREE billion - get it wrong, I give you nothing. Just about everyone would choose A, because the billion quid would make such a difference to their lives that the chance of an extra two billion isn't worth it versus the chance you might come away with nothing. Even though, strictly speaking, your EXPECTED winnings were higher with option B.

Noel's game is the essentially the same, but with a series of evolving Option A vs Option B choices. Your analysis that the 250K stays 64\\% of the time is correct, but about as much use to the player as knowing that in my game the chance of guessing the coin is 50\\%.

The best strategy is to have an idea of how much you'd like to win, and then bail out when the banker offers you something close.

This amount will be different for everyone that plays. And it's precisely BECAUSE, not in spite of, this human angle that the programme is so popular.

Quite agree.
We must do maths on here more often

Anybody else seeing great big blue font all the way down to the end of the March 22nd entry? And all the amounts in this one as "?00" or similar?

Okay, it appears you want the ISO-8859-1 character set switched on. But from here it still looks like the "close font" tags for the £5 and £50 boxes in the second line are lacking the initial "<". Strange.

I've checked the code,
and both of those >s are there, honest.

I enjoyed the statistics, I'm writing a blog about the same. The game is crazy the way people are acting and are affeted by the game.

Firefox must be seeing "£" followed by a number and a "<" as some kind of control code. I made a bug report to Mozilla.

Cheers OG - although I can't see the same bug in my version of Firefox.

Thinking some more, perhaps the best strategy is to pretend to be fairly well-off, not really interested in any of the prizes except the 250K.

If you can bluff that, perhaps the banker can be fooled into going higher.

Ahem. Enough.

I watched this for the first time a few days ago, and at first I did think that an expectation-based strategy would be best. I quickly changed my mind, though, when I realised that by the end of the game the distribution of the possible winning amounts is extremely discontinuous. I came up with the same strategy given in the "half-arsed maths" link - definitely wait until the offer you're given is more than than current "middle" position on the board.

I had a go on the US one and won a million dollars! (Mind you, I would probably have dealt sooner).

On reflection,I got that wrong. I "no dealed" when the choice was between $75,000 and $1M and ended up with the former. I think.

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