Let’s have a bit of fun. I realise that my idea of fun, in this instance, might differ somewhat from yours, but go with it.

In your head, perform the following calculation. Take no time over this, but instead merely make a best estimate of a rough figure within 5 seconds.

2 x 3 x 4 x 5 x 6 x 7 x 8

Got a rough estimate?

Great, now try this one, again allowing about 5 seconds for the working out:

8 x 7 x 6 x 5 x 4 x 3 x 2

Got a rough figure? Excellent.

Now, those readers that are perhaps more mathematically astute than the average might have spotted that the rule of commutation applies (the product is the same regardless of the order of the factors). Typically though, you might have instead estimated that the latter product was not only different, but in fact greater than the first. Of course, if you knew the rule and you still estimated different products, then shame on you. You might like to consider a course of self-flagellation in penance.

Try these speedy calculations out on a group of friends, who perhaps have nothing more pressing on their plates than removing lint from rather inconspicuous orifices about their person. You’ll likewise get an average product for the second sequence greater than the first.

This mistake in calculation is a classic example of anchoring, up to its naughty tricks in our little potato-shaped heads.

By anchoring, I mean we take an initial number (like taking the first 3 factors, 2 x 3 x 4 and coming up with about 20) and then we build on that number but remain so drawn to the initial estimate that we don’t go far enough. When we take the second sequence, we gather 8 x 7 x 6 to be around 400 and then we build on that number, but again we don’t deviate far enough from that initial estimate.

This explains why the estimates given are consistently lower than the actual product, and why the second estimate is consistently greater than the first. It’s how our lovely minds work.

Don’t Believe The Hype

Or propaganda, for that matter.

The same anchoring effect has repeatedly been used during the reporting of casualties of war by savvy propagandists. In fact, it was used quite famously during the Gulf war when reports of an air raid would describe the loss of a few or even a dozen Iraqi civilians. The more cynical of news-watchers may have suspected that the figures were somewhat under-estimated, but their own estimated figure still becomes anchored to the original quote. Perhaps we can add on another 20 to the count and be more in tune with reality? Try many tens of thousands of victims, as was revealed many months after the campaign.

Can you imagine the uproar that would have ensued if we had ever imagined that such was the case? Instead our own conservative estimates remained firmly anchored to those original reports.

Sized Up

When we are forced to make a spur-of-the-moment decision, we tend to use a kind of self-anchoring. We will bring forward our memories and experiences of the past to formulate an opinion on something and then compare that with what we are experiencing at the present moment. From this point forward, we can never fully remove ourselves from that original opinion that we formed. Revising the judgement at a later time will never fully undo the effects of the original judgement.

It is due to this kind of lop-sided thinking that you don’t much like the guy who, when you first met him, reminded you instantly of the guy who killed your cat when you were 6. He might be the most pleasant guy in the world, but there’s just something about him you don’t like.

What a nasty horrible thought, don’t you think?

Getting Your Own Back

It’s not all doom and gloom of course. Knowing how effective anchoring is gives you a valuable tool in your mental box.

You now understand just how important it is that someone’s first impression of you should be the greatest impression you could possibly present. Once they have formed an opinion of you, it will deviate little from that first impression over time. This works in your advantage, providing your first impression is a thoroughly positive one.

So, cast a very critical eye over your online social profiles, including your Facebook profile, Twitter profile, MySpace profile, etc. Make sure that you make any necessary tweaks so that what you are presenting is your very, very best, and that way any new visitors or friends that you make will forever hold you in great esteem.

Even if you do happen to list your favourite reading as The Daily Mail or your favourite TV program as Kilroy.

And so yet another opportunity for me to put forward my own opinion on the matter presented itself only to have it laughed at, silenced, and (partly) ridiculed. However, in this instance, I was absolutely right, and they were emphatically wrong. Being my usual reserved and sombre self, however, and realising the point didn’t really need pushing, I relented and shut the hell up.

After all, it’s only a game show.

I’m talking about the infuriatingly addictive game show, Deal or No Deal. (Well, infuriatingly addictive the first ten times you watch it, and infuriatingly predictable thereafter.)

As always, the ever-seductive “what-if” scenario was suggested. You must know the one? Surely you’ve been asked it before? It’s the one that goes, “Oh my God! What would you do if you were left with the 1p box and the £250,000 box still in play and the banker offered you the swap?”

Well, simple. Obviously…

Take the Swap

Why am I so adamant? Ok, I’ll give you my explanation. I am prepared, however, to receive a flood of comments disputing this explanation. That’s fine. I’m a big boy. I can handle it.

Here goes…

At the start of the show you’re offered a choice of one of the 22 boxes sealed by independent adjudicators, one of which contains the value of £250,000. So on making your random choice, the odds of you having chosen the box with the jackpot value in it are 1 in 22. With me so far? So, we’re agreed.

Now, regardless of what plays out between now and the final “reveal”, given that the big one isn’t revealed before this point, the odds of you having chosen the jackpot box are always going to be 1/22. Still agreed?

Knowing that this is the case (and it’s also the case that each of the remaining boxes also has 1/22 chance of containing the jackpot value), the total probability of the jackpot being in any other box is 21/22. This fact will also remain true until the final reveal, given that the jackpot isn’t revealed in the meantime (which is the scenario we are using).

During the course of the game, in order to reach the “nightmare” scenario of having the 1p box and the £250,000 box left in the game, you will have revealed randomly, and by pure chance, all but those two values.

The Final Reveal

Now here’s the important thing to take in. I assure you it’s absolutely true. Just because you have systematically removed twenty boxes from the game, the fact that your own box had (and has) a 1/22 chance of containing £250,000 hasn’t changed. And, for that matter, the fact that it has a 21/22 chance of not containing the £250,000 hasn’t changed. So where is the remaining probability?

It’s in the remaining box!

So, swap or no swap? Stick with the probability that the box you have has a 1/22 chance of the big prize? Or swap it for the box that has a 21/22 probability of containing the £250,000 prize?

Dur! No-brainer!

If you’re just not convinced, then you might like to check out the original Monty Hall problem.

Innocent Teaser

All very well, you say. Nice little teaser and something to argue endlessly with your friends and family about. But not really a big problem is it?

What’s clear from the resistance that this perfectly rational explanation receives is that our human tendency to stick to what we know, what feels right or, more technically, what we are anchored to, compels us to use our emotional rationalisation over our logical thinking.

Probably fine if you’re a poet, or an artist, or an international playboy. Less useful, perhaps, if you’re a juror, a scientist, or an international diplomat.