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Deal or no Deal Box 23

In the article deal_or_no_deal_uk_tv_show there is a good description of the Deal or no deal game show on British TV. The article you are reading now describes a recent change to the format of the program that was made at the start of January 2014. The change was the introduction of a new box - Box 23

Box 23

Box 23 is not selected by any of the contestants at the start of the game - instead it is positioned in prominent view at the side of the studio awaiting the end of the game (i.e at the point when all other boxes have been opened). The amount of money won by the player has been decided by this point and in the old format of the show, that is the amount of money they go away with.

However, in the new format, every contestant is given the opportunity to open box 23. They have to buy the box for the amount of money they have just won in the game in order to do so.

Box 23 may contain one of the following

  • Double
  • +£10000
  • Money back
  • Half
  • Nothing

So, for example, if the player has just won £3000 in the game, the possible results if the player decides to purchase box 23 are

  • £6000
  • £13000
  • £3000
  • £1500
  • £0

Opinion

In my view, box 23 adds an interesting additional aspect to the game, but I do not agree with the way it has been introduced. Noel is at pains to point out in every show that the content of box 23 has been selected at random by the independent adjudicator. I have no evidence to suggest that this is not the case, but I remain suspicious, particularly since in the first outing of this format the content was +£10000 which is arguably the best result for scenarios where the contestant is likely to choose to buy box 23.

However, leaving this aside, I still think having a single box with 5 possible contents destroys the purity of the game.

In the old format, it was possible for each and every player playing the game to walk away with the maximum prize, irrespective of what they may have selected as their own box. This is because at the end of the game, when the position of 2 boxes remaining is reached and the player has not dealt, if the £250,000 box is still in play the player is automatically offered the swap (meaning in effect that they can open either box and win the contents).

Of course, there is no way at any stage to have any idea of what is contained in any of the boxes despite the mythologies of the game (curse of the newbie, death box etc). But notwithstanding this, it is still the direct consequence of the player's own choices what prize he or she eventually wins. This is the appeal of the game. As viewers we can empathize with how the player feels as the game develops. We cheer when the 1p is discovered and we groan if £250,000 is discarded. If the player eventually wins a good prize we also feel good, and if it all goes wrong we also feel a tiny part of their pain.

But box 23 spoils this. If the player chooses to buy box 23 (and let's face it, what player that has ended up with a blue would not?) then the final outcome is now determined - it was determined even before the start of the show

How much better would it be to have 5 boxes instead - box 23 to box 27. Each of these boxes could contain one of the options listed above, and the player would have to choose which box they wanted. The outcome is now back in the hands of the player - if the player decides to buy the extra box then in every game the best and worst outcomes are possible. This means that in principal, each and every time a player takes the walk of wealth, a win of £500,000 is a possibility. The purity of the game is restored.

So come on Channel4, how about it? We love Deal or no deal, and we love it because it is the players themselves that are the arbitrators of their success or downfall, not the independant adjudicator. Give us boxes 23 to 27, and I, for one, will be happy.

Possible future developments

As mentioned above, box 23 can be purchased for the amount of money that the player has won in the game. If they have won £5000 that is the cost of purchasing the box.

At least, that is all that has been presented to date. I am writing this article only a short time after this new format has been introduced, so it is early days yet. However, it occurs to me that there is another opportunity here for the banker to play with players mind by offering them box 23 for only a certain percentage of their winnings

Obviously, the more money the player has won in the first place, the less appealing box 23 becomes. If you have won £250000 then there is only 1 option out of 5 that significantly improves your winnings whereas there are 2 options that can cost you a lot of money - so it doesn't look like a good bet. It is a completely different situation if you have only won 10p - you effectively have nothing to lose, and there is the 1 in 5 possibility of winning a very nice £10000 (and 10p). I think everyone will buy the box in that circumstance.

But what would happen if the banker says to the player that has won £250000, “You can purchase box 23 for £200000”. That would start to get interesting. The player could then go away with

  • £260000
  • £450000
  • £250000
  • £150000
  • £50000

This would give the player a lot more to think about. The banker is a clever man. I am sure he would be able to come up with a purchase value for box 23 in every game that would give the player a difficult choice

And that's the point of the game isn't it?

Notes on Psychology

In article Numerical Analysis of Deal or no Deal I had a close look at the mathematics of the game, using a computer analysis. As part of this analysis I used the computer program to work out expected outcomes for some situations from real life games.

Have a read of Numerical Analysis of Deal or no Deal if you have time; it is quite a long article. One of the main things that I have done is to predict the range of offers that the Banker is likely to make at the next round. In one particular game (Wally’s game) the prediction for 2 box based on the remaining boxes at 5 box was as follows

wally2.jpg

Wally had been offered £9000 for his box at this point. Looking at the chart we see that there is a 30% chance that the next offer will be very low (sub £1000), a 20% of a similar offer to the current £9000, a 40% chance of offers in the £12000 to £16000 range and a 1 in 10 chance of a tantalising £43000

It occurred to me at the time that this chart of outcomes is not so very different to the Box 23 outcomes if you deal in the main game at £9000. The Box 23 distribution looks like this

box23_9000.jpg

If anything the box 23 distribution for a £9000 win in the main game looks slightly better than the main game distribution predicted for Wally’s game. There is only a 20% chance of a sub £1000 win and the 40% block at £18000 - £19000 is better than the 40% at £12000 to £16000 in Wally’s game. The main difference is the absence of the possibility of the very big win – but bear in mind that there is only a 1 in 10 chance of that happening.

Wally did not really hesitate to say No Deal in his game, and I think a large number of other players would do the same. However, from my experience of watching player’s reactions to box 23, I can say with a high degree of confidence that there will be very few, if any, players that would take the risk on box 23 with £9000 at stake. It is intriguing that this should be the case, even though the evidence suggests there is not much difference in potential outcomes between the two situations.

My view is that something happens to the player’s attitude in between the normal end of the game and the opening of box 23. It is as though the main game win has become more concrete in the player’s mind. It is now real, and it belongs to them, hence the reluctance to risk losing it all in the gamble of box 23.


Television


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