Back to the Bar

So what do all those weird figures on the commentary and DoND Stat-o-matic actually mean? Here's a quick guide.

Please note that statistics give an objective view of the board at any given time and suggests whether it's worth dealing or no dealing based on "average" luck. They certainly can't work out which box has the quarter million in, and whilst we can always advise people to take the deal given the odds there will always be those who go against the odds and beat them.

Fair Deal value (FD):
Deal or No Deal is primarily a game of probability and calculated (or not!) risk. But how do you measure elements of risk when it means different things to different people? This is where utility theory comes in. Different amounts of money mean different things to different people, and with more money on the line, the less likely it is you will risk it on gaining possibly substantially more - sure, £50k is lovely. But if you knew you could double it up or lose it all on a coin flip, would you do it? The threat of losing £50k is a much bigger consideration to you than the idea of winning £100k. Just because something is twice as much doesn't neccessarily make it twice as good. And the banker knows this.

So how do we measure how much we think the board is worth at any given time given everyone's different utility definitions? Arbitrarily. We use a formula called the "root-square-mean" - find the mean of the square roots of all the values left on the board (thereby reducing the relative weighting of the really big numbers) and then square it out again to give a figure. At the beginning of the game, using our system, we would consider a fair offer with no box opened to be £9,215. This is some way beneath the mean value of £25,712 but seeing as the median is only £875, represents the premium the big boxes have over the game. We reckon a fair value for a board with just 1p and £250,000 on it is £62,525. For entertainment purposes, The Banker often overpays the final offer.

You can play around with fair values and utility curves with David J Bodycombe's patented Deal or No Deal Excel Stats Machine.

Note: Iain Weaver has begun experimenting with the Fair Deal formula, by taking the current root-mean and then multiplying it to the 0.5271th power. This gives an opening Fair Deal value of £10,000 dead.

Sure, the Fair Deal gives a decent indication of how much we think the board is worth, but that's not the same as deciding as to whether the board is "good". Bipolarised boards carry a far higher risk than boards with the top and bottom cut off.

Absolute Balance:
Devised by Gizensha, simply each of the twenty-two cash values are given a weighting from -11 for the 1p to +11 for the £250,000, ignoring zero. The balance is all the weights added together. This gives a (very) basic indication of how "good" the board is - the higher the better. You might have £250,000 left, but with nothing but low numbers you would be right to be scared.

Significant Balance:
A tool to help decide whether to deal or not, based on observations on how we believe top contestant Trevor Walker (episode 23) was calling the shots. Again, each of the 22 values are weighted. Iain Weaver writes (NB: value of £100 box changed from 0 to -1 on Gizensha's suggestion that it makes the opening weight 0):

"1p, 10p, 50p = -2
£1, £5, £10, £50, £100= -1
£250 to £10,000 = 0
£15,000, £20,000, £35,000, £50,000 = +1
£75,000, £100,000 = +2
£250,000 = +3

Work out two figures: the sum of the weights (which starts out at 0, and increases if the small prizes go faster than the big), and the sum of the positive weights (starts at 11 and falls.)

From a quick run through archived commentaries, it appears that Trevor's been recommending "no deal" when (positive weight) / (number of boxes) > 0.5, and/or the total weight is greater than 0."

Volatility

A measure of how much power the highest value on the board has at any given moment, measured by (top value)/(sum of all the other values). The higher the volatility rating, the more you can expect the bank offer to collapse if you hit it during the next round. Suggested by Mister Al.

Comparative Banker Generosity

It's been noticed that the Banker tends towards averages of the mean for each offer at each stage, as of Episode 286 (and based on the previous fifty games):

• Offer of 17: 26% of the mean (previously 19%, 19%)
• Offer of 14: 43% of the mean (previously 30%, 35%)
• Offer of 11: 51% of the mean (previously 38%, 45%)
• Offer of 8: 56% of the mean (previously 40%, 45%)
• Offer of 5: 58% of the mean (previously 47%, 53%)
• Offer of 2: 71% of the mean (previously 66%, 71%)

We can also see how the offers compare to the Fair Deal value:

• Offer of 17: 70% of the FD
• Offer of 14: 116% of the FD
• Offer of 11: 133% of the FD
• Offer of 8: 136% of the FD
• Offer of 5: 134% of the FD
• Offer of 2: 112% of the FD

The generosity factor is the proportion of the actual offer in comparison to the benchmark offer. For example, if the benchmark suggests the bank will offer £5,000 and the bank offers £6,500, this gets a generosity rating of 1.3, the actual offer is effectively 1.3 times more generous than the expected offer given recent banker behaviour. If, the offer is £4,000, that's a generosity factor of 0.8. A number less than 1 suggests a comparatively stingy offer, above 1 a comparatively generous one. This also gives us a decent benchmark to pitch the hypothetical post deal offers against. Work out the benchmark figure, then divide the offer by the benchmark to get your Comparative Benker Generousity Figure.

After the game, the geometric mean of all the banker's offers is taken to suggest how stingy or generous the bank has been all game. From this, perhaps we can work out how the bank read the player's utility... or not!

The benchmark figures are subject to change if and when significant long term changes in bank behaviour are noted. Thanks Mister Al!

Pairwise stats

Using a mystical formula (so as to not give The Banker any ideas), Iain Weaver can often be found analysing the respectability of the offers post game. It is based on the odds that any two given boxes will end up as the final two.

Scoring a game:
We like giving things numbers at Bother's Bar so another one of the punters, David, has come up with a way to determine whether the player or banker had the best of it and by how much. We do not count hypothetical swapped boxes, just the box that has actually been sold.

• If the final deal is equal to the maximum bank offer AND the final deal is greater than the box value, it is a Outright Player win. (100-0 Player)
• If the player keeps the box and it ends up being higher than the maximum bank offer, it is also a Outright Player win (100-0 Player)
• If the player takes ANY deal and it is lower than the box value, it is a Outright Banker win (100-0 Banker)
• If the player keeps the box and it turns out to be lower than the maximum bank offer, it is an Outright Banker win (100-0 Banker)
• If a player takes a deal that is greater than the box value BUT is lower than the maximum value the bank had or would have offered, is is split based on the amount of the deal versus the amount of the maximum value on percentage. Whoever had more than 50% gets a Technical win (e.g so if you had a 1K box, you took a deal at 20K but because of picks you could have gotten a max 30K deal, it's a Technical win for you (67-33: You took an offer that was 67% of the peak offer but was still better than the box))

FAQs:

• How do they pick their boxes?
  The boxes are mixed and sealed by an independent adjudicator before everyone enters the studio. The players then pick their box number by drawing numbered ping-pong balls.
• How does The Banker come up with the offers?
  Banker's software throws up a lower and higher cash sum based on the values left on the board. The Banker then puts his own spin on the proceedings by picking a figure between the two boundaries. Factors such as the attitude of the player and who is having the better run of luck are all considerations. Producer Glenn Hugill says "I don't pretend to know how he operates but I believe there is a range which is considered to mathematically cover the financial risk. However if the banker wishes to gamble or indeed play safe he can accordingly pitch his offer anywhere below or above it."
• Who is The Banker?
  We reckon it's top series producer and modern day gameshow saviour (or something) Glenn Hugill. His biography suggests "geek", and the way he threw himself into hosting and producing The Mole suggests that acting up the slightly shady character is Clearly Something He Enjoys Doing (And Is Good At). This said, we qualify this by saying that we don't have any concrete proof for this whatsoever. Recent auditionees were being told that there are several bankers - frankly we don't believe them.
• Do the players know when they're about to be selected?
  We don't think they do. However, we're fairly confident that flashing the names up at the top of the show is an act of misdirection and that the production team are well aware who is going to play each episode. It's a pretty safe bet you'll be on box opening duties for between 20-30 shows, which is two-three weeks of recording time. At the time of writing, Endemol provide the hotel and all expenses. Players can bring (and are actively encouraged to bring!) along partners and friends to sit in the audience, but they must share the hotel room. Producer Glenn Hugill: "No it's not random. For some reason the Radio Times said it was, but that didn't come from us. It's always been a selection otherwise we can't guarantee people that they will play within a reasonable time period/have people in the audience etc. The players for each week are selected on Monday and confirmed in threes each weekday morning."