# Why Deal or No Deal makes no sense

The premise of Deal Or No Deal is that no-one – not even the imaginary Banker, i.e. the programme’s producers – knows the contents of the boxes. This makes the game a very simple game of chance, picking random boxes and making statistical decisions between offered deals and remaining probabilities.

This, at least, should be the mathematical premise of the show. The entertainment premise is the exact opposite – that the game is in some way tactically interesting. It is not. But every effort is made to persuade the audience that an intense battle of wits is being fought between the player, the Banker, Edmonds and even the non-playing contestants standing behind their boxes.

Note, for example, how Edmonds continually quizzes the player about his “tactic” for the game. And the way players respond in a way which implies that they do indeed have a tactic. What tactic is that, exactly? Pick boxes. In some order. It doesn’t matter what order. They’re filled randomly. And no-one knows how.

Edmonds asks the player, “Are you going to change your tactics now?”, or “Are you still following the same tactic you started with?” Players respond with nonsensical answers like, “It’s not going well, I should have stuck to my original plan,” or, “No, I’m going to keep playing the same way.” You mean, you’re going to continue choosing random boxes? Clever play, Kasparov. I thought you might try jumping out of the chair and ramming one up Noel Edmonds’ arse.

Let me emphasise this. It does not matter what order you pick them in. The idea that a particular order you’ve worked out will give you an advantage is the same fallacy that the particular numbers you pick for the Lottery alter your chances in a random draw. Except that, with the Lottery, there are real considerations to be made concerning the likely numbers other people will pick, and hence the number of people you’d have to share a jackpot with if you did win.

But those don’t apply to Deal Or No Deal. You might as well pick boxes in numerical order, or from left to right. You will still almost certainly end up with a similar outcome several boxes into the game: a roughly equal distribution of high and low amounts in the remaining boxes. A rough balance between high and low will probably continue into the “end game”, leading many players to play down to their own box – making the order they chose in totally irrelevant.

Is there any possibility for tactics at all? Well, there is a simple tactic which should be followed by the player when considering a deal. Compare the offer to the average contents of the remaining boxes. Choose the higher figure.

In fact, that’s not quite accurate. The mean average, as any statistician will tell you, can be misleading, since it is skewed by extreme data. Consider the situation where the four remaining boxes contain 1p, 10p, 50p and £250,000. The average of the four is £62,500. The Banker offers £50,000.

OK, so the Banker’s offer is less than the average remaining, and so worth less than the gamble, in strict probability terms. However, since three out of the four boxes contain less than £50,000, the most likely result (a 75% chance) of gambling is to end up with significantly less than the offer. So take the offer.

The rule of thumb should be to take the offer if it is higher than more than half of the remaining boxes. This is easier to work out too, since calculating the average requires pretty good mental arithmetic.

Since this is the player’s best tactic, the Banker’s best tactic is also very simple. If he actually wants the player to accept an offer, he should make the lowest offer that the player would accept, according to the player’s tactic. If he doesn’t (in the example above, he may want the player to play on, expecting him to win less than a pound), he should make an offer which is obviously unacceptable.

If that’s all there is to it, what on Earth does everyone think they’re on about when they start talking about “bluffing”, and other tactical terms suited to games like poker? Bluffing is pretending to have something you don’t, or don’t have something you do. You can’t possibly bluff in a game where you don’t know what you have, where no-one knows what anyone has.

There is, actually, a psychological factor which does have an effect, which we haven’t considered yet. This is risk aversion. Consider the situation above. If the offer of £50,000 were presented to a multi-billionaire, he probably wouldn’t take it. Losing the theoretical £50,000 isn’t a big issue for someone who already has so much money – he might as well take the gamble and try and get the £250,000.

Someone with no money at all would be much more likely to make a deal, since he really needs £50,000 a lot; a small chance at £250,000 is less useful.

Note that this isn’t a tactic as such for the player, it’s just a fact about him. The Banker, though, should take an assessment of the player’s risk aversion into consideration when making his offers: they should be higher for a player with high risk aversion, lower for someone with less.

But this clearly isn’t what the people on Deal Or No Deal are talking about.

Firstly, you can’t bluff risk aversion. It’s simply a property of your financial circumstances and your personality. You can’t pretend to be more risk averse than you are, in order to get the Banker to offer higher figures. To have the guts/stupidity to start rejecting high offers that you really can’t afford to reject, would require that you actually are that risk averse.

Secondly, listen to what people are saying. There’s no indication whatsoever that they’re talking about risk aversion. The conversation isn’t that sophisticated. The player says, “I’ve got a feeling about this [his own] box.” Edmonds, on the phone, says, “The Banker thinks you’re bluffing.” Bluffing about what? Having telepathic powers?

Once you’ve accepted that there is really nothing to this game, 90% of what happens on screen becomes meaningless, redundant and extremely irritating.

The way the audience cheers for the player when he eliminates one of the small amounts – as if it’s an achievement reached through some kind of game-playing skill.

The banter between the player and the other contestants, with them saying things like, “I’m going to try to help you here,” as they open a box, and the player acting either grateful or betrayed when the box is opened.

What exactly are the players there for anyway? They’re not doing anything more than the other players on Who Wants To Be A Millionaire?, sitting around the periphery waiting for their turn. Though they do provide the essential function of opening the boxes.

Talking of which, why the hell are they boxes? They don’t actually contain the money. They just have a number printed on the inside of the lid. Why not have envelopes, or flip-up cards? Or eliminate the other contestants, boxes and studio entirely and just have 21 computer screens? Everything else is superfluous anyway.

Of course, they’re there to add an element of human interaction and drama to an otherwise incredibly tedious exercise in statistics. Which was my point to begin with – the entertainment premise of the show is to pretend that there’s more to what’s going on than pure statistics. There isn’t.

More drama still is provided by Edmonds and his communication via the fetishised big red phone to “the Banker”, who is of course simply the programme’s producers sitting upstairs clicking away on the Windows Calculator. Did I say “drama”? I meant “horrendous ham acting where psychological tension is confused with overwrought, excessively long pauses”. I hope everyone realises that the phone isn’t even plugged in? Edmonds is wearing an ear-piece.

Finally, could there be anything more nonsensical than what happens after the player has made a deal? The game is played on to the end, to “see what would have happened”.

If this were simply opening the remaining boxes to see what they contained, fair enough. But they are opened one by one, under direction of the player, to see how his tactic would have worked out. And at the same intervals, the Banker makes hypothetical offers.

Need it be said that this procedure reveals precisely nothing? The assumption is that this is the order in which the player would have continued to open boxes, and these are the offers the Banker would have made. However, the order in which the player opens boxes during the exercise after having made a deal, is fundamentally unidentifiable with the order in which he would have opened them if he had not made the deal. His mental state is affected by the decision he has made; the circumstances within which he acts have changed.

Exactly the same goes for the Banker – if not more so. How can he make realistic offers which he “would have made”, when there is no question of the player actually accepting them?

All we learn from this exercise is that the programme must fill a set duration of time, and at whatever point the player deals, it must continue for the length of time it takes to open every box and for Edmonds to draw out his dramatic pauses until we want to stab ourselves in the head.

## 2 thoughts on “Why Deal or No Deal makes no sense”

1. Is the nature of the programme anything more that a promotion of the idea that securing that maximum amount of money for the least possible of effort is laudable?

• Yes. It also promotes the idea that the contestant is able to have some knowledge or control over which amount they choose.