Going on is making a big assumption that the red in the box is the £250k.

Given that the banker would probably be very generous on the £75k/blue and £100k/blue finishes (as much as £30k and £40k respectively), there could be an argument that even if you think that the £75k or £100k is the box, then it would be worth the gamble but then it's a 50/50 chance that the other box is a red also making the offer higher than the £60k you've just turned down.

You also have to factor into account that the swap would be guaranteed so the banker might be trying to double bluff you.

Risking £60k on something I know the probability of one thing, risking it on the basis of reading the mind of the production team is another thing altogether.

The only risk to Alphonso was the blue/250k finish with guaranteed swap. But if you decide to play on the assumption that no one would make a £60k offer on a blue then just need the guts to finish what you started.

You see it still boils down to the fact that on five box no one would have made a £60k offer if they knew the box was blue. No one. As Spock says the most probable explantion is the most logical and likely one (something like that). Man should have thought it through and stopped worrying about double bluffs and such rubbish. You don't double bluff over £60k. You double bluff over a few thousand.

Except the Banker has already double-bluffed over twice as much as £60k. When Em played in a Summer Special game in 2008 she had a final pair of £250,000 vs. 10p. The Banker had seen in her box and knew she had 10p. So why did he offer her £120,000?

Unfortunately for Em she'd already dealt, but nonetheless it's proof that the Banker will sometimes adopt some unusual tactics when he's looked in a player's box. So the £60k offer to Alphonso was by no means a clear cut signal that the £250k was on the table.

So say he had the £1 in the box, and he offers 50p. Clear indication to everyone that there is a blue in the box. Now say by chance that he leaves the £250k in the wings, oops, instant swap guarranteed and he wins £250k.

They gotta be careful and explore all finalities.

You're assuming that the £60k offer implies that the only red that could be in the box is the £250k and that's a big assumption - the banker only said there was a red in the box.

If the £75k was in the box, the potential offers at 2-box would probably have been £30k, £30k, £87k and £150k (average is about £75k - above the £60k offered)

If the £100k was in the box, the potential offers at 2-box would probably have been £40k, £40k, £87k and £170k (average of £84k).

Assuming the £250k is in the box is not a logical conclusion statistically.

Simon

If at five box you believed there was a red in the box then the minimum was always £75k. Forget about the other offers. You would need to see the game to the end. By taking the 60k you are being ultra cautious at a time when in fact you have the best odds to actually be really bold. In this case it was a no brainer.

I get that - if I had seen a blue in the box I would have offered £10k and then taken my chances he would have eliminated the 250k which was the most likely outcome!

I get that - if I had seen a blue in the box I would have offered £10k and then taken my chances he would have eliminated the 250k which was the most likely outcome!

Right. Let's say you're the Banker. You believe the player is very confident in reading you, and you see a blue on Alphonso's final five. You offer him £60,000, or even more.

The player, as you expect, goes "he wouldn't offer that if I had a blue on the table", and hence says No Deal.

You now have a 25% chance of each of the following: all-blue, blue/£75k, blue/£100k, and blue/£250k. Either way, you've won: you can either get him out for less, or make another inflated offer confident in the belief he will continue to have faith in what turns out to be an incorrect assumption. Only the swap can deny you, and he won't swap, because he believes the blue is on the wings and not on the table.

That's how the double bluff can help.

For what it is worth, Matilde Bombardini and Francesco Trebbi - two economists of Italian origin working at North American universities - used the Italian version, where the Banker always knows where the money is, to study risk-aversion at varying stakes. While it was not the focus of their study, they found a positive but not especially strong correlation between offer generosity and what was in the box. Most interestingly, they illustrated (by means of mathematical arguments some way beyond my capabilities) that "optimal strategy to minimize the payout to the contestant is to make a constant offer, irrespective of the content of the box held by the contestant." I'm not in a position to argue with their workings

Even if I believed there was a minimum of £75k in the box, there's a 50% chance the other box will be a blue and if the banker offered close to the mean (say £35k on a £75k/blue finish), then I'm taking the offer without the presence of a meaningful backup.

I think we'll have to agree to disagree here - I play the stats of the game - not the psychology of the production team.

To be fair if I was the banker there I'd offer £100 knowing the £250,000 was there. I'd then offer say £1,000 on the end and leave it to the player to decide whether to swap or not.

Because i'm evil

I remember one show where the Banker offered £1.50 when he knew £15k was in the box.

It's too simplistic to think the banker will ALWAYS offer a huge amount if he sees the quarter of a million in the box. He has mixed his play up plenty of times in the same situation. In my opinion it depends on how they view the player, and even whether they want them to win a good amount or not, and the flow of the game afterwards.

Now that's harsh.

There have been far worse decisions - think of Richard...