Tim Worstall

Deal or No Deal?

So Sam Leith tells us about Noel Edmonds new gameshow. He also says this:

This is all, of course, what scientists would describe
in the technical jargon as "cobblers". Deal or No Deal? is a simple
numbers game: skill is entirely irrelevant, and psychology should be.
You could get the whole process out of the way in less than a minute,
if you had a mathematician as a contestant.

If
the Banker is a real person, he is – if the producers have any sense –
sitting in front of a computer running a simple algorithm.

I’ve shown that I don’t really understand statistics (which is of course, an extension of probabilities) and my failing memory doesn’t get me much past the Fibonacci Series and 3! and the like.

So could anyone explain how simple this game really is?

Or would it be too embarrassing to admit to having seen a Noel Edmonds show?

In

11 responses

  1. Colin Avatar
    Colin

    I watch it regularly.
    There are 22 boxes, each containing (not literally) a different sum of money, from 1p to £250000. The contestant has a box, and he progressively chooses the others (who each get a chance to play at a future date) to open their boxes, narrowing the possibility of which amount is contained in his one. After intervals of 5,3,3,3,3 and 3 boxes, a phone rings and the banker calls to offer an amount for the contestant’s box. He has a computer algorithm but also a fair bit of leeway so he can factor individual pyschology into it. The offers usually increase until we get to the last three rounds, where they can catastrophically fall after a single box with a large amount in it, which was distorting the price, is ruled out.
    The excitement comes from watching people gambling large sums of money. The choice is to collect or continue gambling at pretty good odds. Most people bottle out after it gets to about 10000 quid.
    As an example, last night there was a £5 and £100000 box left, and the banker offered £35000. Very few people will actually gamble the 35K on the flip of a coin for 100K.
    Most people go away with 10-20K.
    Actually, I like Noel. I liked him in Swap-Shop, I liked his Saturday evening show, and he’s pretty good at this too. Of course, he’s also a great businessman.
    Tim adds: OK, so it’s playingoff the ownership bias (is that what it’s called? What I have is more valuableto me than what I might get?) As Sam Leith says, humans tend not to actually act as probablities would expect?
    In your example above the expected return was 50,002.50 so selling that for 35,000 isn’t sensible. But then if people actually do act that way then it is, it’s just we’re not calculating what is “sensible” in the correct manner.
    Hhhhm. Big implications for a lot of economics in that.

    Reply
  2. Matthew Avatar
    Matthew

    You just can’t say it ‘isn’t sensible’, as the expected return is not an actual return. Also we don’t know how much money is important to people.
    On the same line, but more interesting given the magnitudes was the paper referred to in last week’s NYT, which found that:
    80 percent of high-scoring [on a kind of IQ test] [student] men would pick a 15 percent chance of $1 million over a sure $500, compared with only 38 percent of high-scoring women, 40 percent of low-scoring men and 25 percent of low-scoring women.

    Reply
  3. auntymarianne Avatar
    auntymarianne

    GW would be interested in this. Noel Edmonds once threw up on him in his helicopter. Presumably in a “Multicoloured fashion”.
    I don’t know how much there would have to be in the box before I could put up with that.

    Reply
  4. Scott Campbell at Blithering Bunny Avatar
    Scott Campbell at Blithering Bunny

    I saw it once. Agree that it could be done in a minute. What was horribly fascinating, though, was that the chavs on the show kept talking about “How the banker doesn’t respect me” — this despite the fact that showed themselves to worthy of no respect at all as probability estimators. Their continual complaint that they weren’t being respected seemed to be entirely a matter of their own sense of self-worth.

    Reply
  5. John Thacker Avatar
    John Thacker

    People maximize expected utility, not expected value, and most people seem to be risk averse.
    Sure, if you knew that you could play this particular fair game an unlimited number of times it would make sense to make judgments based on expected value. However, most people aren’t going to get to play the exact same game again.
    The economist/actor (and son of economist Herb Stein) Ben Stein had a game show, Win Ben Stein’s Money. In it, he competed against contestants in the final two rounds of three. Being an economist, he arranged the game so that the winnings of the contestants were taken from his salary for the show, in order to properly incentivize himself.

    Reply
  6. The Remittance Man Avatar
    The Remittance Man

    But the whole hing isn’t really about the money. It’s about giving some of the brain dead masses a glittering dream and their chance for 15 minutes of fame.
    It’s nothingmore than bread and circuses to distract the terminally stupid from the God awful mess the politicians and their cronies are making of the country.
    Sod it! I’m off to watch some rugby.
    RM

    Reply
  7. Bertie Avatar
    Bertie

    Doesn’t include the Monty Hall dilemma presumably

    Reply
  8. dsquared Avatar
    dsquared

    the contestants are actually a lot closer to vN/M maximisers than I would have thought; they seem to me to be about as risk averse as they would be if they were gambling with their own money, which goes against the well-known Allais experimental results.
    I don’t think it’s at all unreasonable to value a sure £35k more than a 50/50 bet between £5 and £100k. Entirely in the normal range of risk aversion.

    Reply
  9. David Gillies Avatar
    David Gillies

    Even if one puts aside risk aversion, one-shot deals play hob with expectation values. Here’s an example: you buy a raffle ticket with the number 10,000 on it. What’s your probability of winning? You have no idea how many tickets have are available. What’s your probability of winning?
    Allowed repeated tries, in most cases people converge onto what classical game theory would say their expectation value would be. On the flip-side, that’s how you make money running a casino.

    Reply
  10. David Gillies Avatar
    David Gillies

    Delete ‘have’

    Reply
  11. Blulu Avatar
    Blulu

    What interests me in debates about good vs crap tv is how often people jump on the bandwagon to sneer at a genre or personality.
    Those who like Deal, Noel Edmunds, soaps, football and so on, are deemed to be sheep like and brainless. Those who like documentaries, drama, less popular sports (rugby, cricket e.g.) and so on are deemed to be somehow intellectually superior.
    But (IMHO) this argument breaks down in two ways. Firstly because many (me, for example) enjoy a mix of TV from both categories. So am I brain dead because I like Deal, or intellectually superior because I enjoy documentaries and dramas? (I admit that I don’t watch rugby very often – but that’s more to do with time than interest. I am a football addict and enjoy most sports when I get the time to watch).
    My second point about why I think the superior/inferior argument breaks down is about which ‘group’ are being sheep like. Are those who watch Deal, soaps and so on being sheep like for watching mass appeal ‘easy to watch’ tv? Or is it the sneerers who are being sheep like, jumping on the bandwagon to enjoy feeling superior? Especially as they often do so without giving whatever is being sneered at a genuine chance before writing it off as rubbish? If you decide something is going to be rubbish before you start watching it, you are bound to ‘prove’ your opinion to be correct.

    Reply

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