Making an offer you can't refuse...

[I am posting this excellent article by Adie as he is having technical problems with blogger]

So, we're 148 shows down, almost 6 months into the UK life of DOND, and already it seems certain that, like "Who Wants To Be A Millionaire" and "The Weakest Link", it's going to be a TV staple for years to come, and patterns are already emerging...

For instance, however good or bad a week the contestants have, the average win steadfastly refuses to budge from its level of just above £17,000 across the entire series. In fact, despite sterling performances this week from Linda (£24,000) and Gary (£29,999), this week's average win is just £16,250. This consistency definitely suggests that there is something in the way that the game is structured that steers wins towards this level.

A big part of this structure of course are the offers that The Banker makes, but how are those offers calculated? A huge part of the game's appeal is that the offers (at times) seem almost random - or at least to be emotionally driven - which is why despite never seeing or hearing him, that The Banker genuinely seems to have a tangible personality. But surely there must be certain given methodologies which contribute to each offer? Not being one to resist a challenge, I present my own list as follows:

1) THE MEAN VALUE: Aaron the bookie (29th March) made a lot of the mean value of the remaining boxes on the board as his principal way of determining how good or bad any offer was. There's much to commend this, but as a theory it is let down by the fact that the monetary values in the boxes are so disparate, with relatively enormous gaps between the top few boxes. At the start of any game, the average value of the boxes is £25,712, which immediately plummets to £15,032 without the £250,000 box, and to £10,783 without the £100,000 too. At the risk of stating the obvious, in many ways, DOND is always a "one box game", as the revelation of the £250,000 inevitably changes the whole outlook...

2) THE MID-POINT BOX: devastating in its simplicity! Just take the total number of boxes remaining, and pick the one halfway through by value as a starting point. Theoretically the player has a 50/50 chance of having more/less than that amount in their box, making this as good a method as any... in fact, a good rule of thumb in trying to guess any offer is to take the box one up from the halfway point, and pitch it slightly above or below that amount depending on the strength of the gameboard. I get to within a few hundred pounds about 75% of the time with this technique...

3) DIMINISHING RETURNS: It never feels like it, but "box-for-box," in general the offers tend to get less generous as the game progresses. Again very obviously, with each box the player opens, it's more information that The Banker has at his disposal, and unless The Player is doing well, then they're doing badly. The Banker also has the comfort of knowing that (to date) no-one ever deals in the first 3 rounds, so he can afford to be generous. I've pointed out in previous posts that almost 60% of players take home less money than the highest offer they received, ably demonstrating that the majority of players go "too far," with round 3 or 4 statistically being the best time to "Deal." Any player going beyond round 4 has effectively taken the decision that they're ready to go right to the endgame, with all the risks that implies... and finally,

4) WHO BLINKS FIRST: This is really where The Banker earns his money, in judging just how far a player is prepared to go to try and beat the odds. When he gets it right (and I'd put Micheal's £10,000 deal on Friday in this category), The Banker gets players to walk with far less money than they should according to the boxes left (notwithstanding the fact that Michael's decision turned out to be the right one!) That said, this can be turned to The Player's benefit... on Thursday, Gary was (arguably) the first player to really take advantage of The Banker's "emotional" component in getting his £29,999 win - I'm personally convinced that he would not have gotten that offer unless he had stated his (fake) target of £30,000 at the beginning of the show.

Without getting into the complexities of Game Theory [link to http://en.wikipedia.org/wiki/Game_theory], that's my quick 'n' dirty analysis of what goes into The Banker's offer-making process... we'll propbably never know for sure of course, but isn't that why we tune in day after day, because we really don't know what's going to happen next? And after all that, in case you're thinking that the average prize of £17,000 doesn't sound like all that much money, bear in mind that "The Weakest Link"'s biggest ever prize to date has been just £12,000*

Have a good week all you Fanatics out there, and 'til next time, "NO DEAL!"

* or so I'm informed - any corrections gladly received!