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Tails You Win: The Science Of Chance

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David Spiegelhalter David Spiegelhalter | 10:00 UK time, Wednesday, 17 October 2012

Chance, risk, uncertainty, luck - call it what you will - affects every part of our lives.

And so when BBC Four commissioned our programme Tails You Win: The Science Of Chance there was a huge range of possible themes to explore, from gambling to natural disasters, extreme sports to collapsing economies, coincidences to lotteries.

We ended up touching on all of these since they all, at least to some extent, can be handled using numbers.

Of course people's feelings about chance and risk are vital, as my guts told me when I was waiting to do a skydive.

David Spiegelhalter in Tails You Win: The Science of Chance

David Spiegelhalter in Tails You Win: The Science of Chance

But I am a statistician in the Faculty of Mathematics in Cambridge and so I think numbers are cool and when someone says something is 'risky', I immediately ask 'how risky?'

The programme shows how we try and answer that question, although the producers would not let me use all the equations. Meanies.

But they did let me talk about the fundamental ideas of chance itself. Does it exist as part of the external world? Or is it just a way of saying we don't know - our personal ignorance?

These are wonderfully tricky questions that a seven-year-old can ask and the biggest brains can't agree on.

My personal tendency is towards the 'ignorance' interpretation and I certainly believe that any probabilities we put on future events are a product of our judgment and don't really exist 'out there'.

But in the end all these fancy ideas don't make much difference, we still need to decide whether to spend our pension lump-sum on a huge motorbike or save it for our old age, go for a jog or slump on the sofa, buy a premium bond or a lottery ticket.

As the programme shows I love trying to compare the risks of different choices and so, for example, the theory of gambling fascinates me.

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What affects our chances of living to 100?

But in practice I don't get a huge thrill from actually risking my money and I know I would lose in the long run, and so my online betting account is kept for academic demonstrations only (honest).

The programme is not intended to make people more cautious or more risk-taking, but maybe to ask 'what are the chances?' and try to get an answer.

David Spiegelhalter is the Winton Professor for the Public Understanding of Risk at Cambridge University and presenter of Tails You Win: The Science of Chance.

Tails You Win: The Science of Chance is on Thursday, 18 October at 9pm on BBC Four. For further programme times, please see the upcoming broadcasts page.

More on Tails You Win: The Science of Chance
Professor David Spiegelhalter's articles on The Guardian.
Read David's lecture If you can calculate risk you can make better judgments.
More on David's website Understanding Uncertainty.

Comments made by writers on the BBC TV blog are their own opinions and not necessarily those of the BBC.


  • Comment number 1.

    Nice site!! I like BBC

  • Comment number 2.

    Now that David has said 123456 has as much chance of winning the lottery as any other combination, how many people will pick that this weekend? If it comes up they'll have to share the Jackpot with many other people

  • Comment number 3.

    hi. i was just wondering if any one other than me thought this was a coinsidence or a remarkable pattern of events.My dad born feb 3rd ,my ex wife born feb 3rd and my eldest child born feb 3rd.

  • Comment number 4.

    gmorrell - it's remarkable, and it's a coincidence. The odds of them three sharing a birthday are about 100000 to 1. But let's add in other people close to you - parents, siblings, friends, neighbours. Once we reach 22 people, the chance of two sharing a birthday is nearly 50/50, or evens.

  • Comment number 5.

    As I understnd it, the central issue when dealing with the nature of uncertainty is whether or not it has an objective existence. This is not simply an academic or philosophical question since it bears upon how one might attempt to quantify uncertainty. For example, when one uses the Monte Carlo method to formulate predictions one makes a number of assumptions, such as assuming one understands the form of variability upon which the modelled uncertainty is predicated. In reality, such assumptions may themselves be subject to uncertainties that invalidate the methodology. And it is in the nature of such second order uncertainties that they may not immediately manifest themselves. If one takes as a starting point that all uncertainty is an artefact of personal (or collective) ignorance, then one has to be prepared to accept that this uncertainty is so profound that one can never be certain how uncertain one is; in which case, no amount of Monte Carlo simulation is going to bale you out. I think a useful thread for this blog could address the strengths and weaknesses of the Monte Carlo approach and debate whether or not the method is often used inappropriately, for example when modelling project outturn uncertainties that would be much better analysed using Bayesian techniques.

  • Comment number 6.

    I'll confess maths isn't my strong point... I found this programme very interesting but something I wonder about is to what extent chance is influenced by people's unconcious which affects our behaviour. For example, if you wake up on the 'wrong side of bed' and your day gets off to a bad start, do you sometimes find that your own negativity sparks more unfortunate events throughout the day. Is it in your mind (ie more irritable, more aware of annoying events), is it because your behaviour is affected by your own negativity or is it coincidence e.g. 'bad luck happens in threes'? On the flip side, the saying 'success breeds success' seems to ring true too, so, perhaps chance isn't completely out of our control?!

  • Comment number 7.

    123456 has the same chance of winning the lottery jackpot as any other permutation ..... well, of course it does. The same holds true for ABCDEF if capital and small letters are on the 49 balls ..... or ,.:;'! if punctuation marks are on the 49 balls. The lottery (and games like Sudoku) use numbers purely as SYMBOLS instead of having a property such as quantity or rank etc. The public are fooled and say nonsensical things such as, "I was very close, I had 22 and 23 would have won!"

    'Coincidence' could have been better defined. People say after an event, "Wow! look what happened - that must be a millions to 1 chance!" Well ... yes ... of course it was ... ALL unplanned events in life are usually 'millions to one' coincidences.
    Uneducated brains attach significance where NONE exists; this is well exploited by a myriad of charlatans.
    123456 appears to have 'significance' and ,.:;'! appears to have no 'significance' ... yet in the context of symbols on balls they are absolutely identical 'coincidences'.

  • Comment number 8.

    In reply to gmorrell and ChorleyPie, you both understandably but inappropriately used the adjective 'remarkable'; if something has a chance of happening, and it happens, it is not remarkable.
    Events can only be described as remarkable if they apparently break the laws of physics (which include the laws of statistics).
    For example, if a die were rolled 6000 times and yielded 1500 sixes (with of course 500 ones), then this would appear 'remarkable'. However, any statistician would conclude with near 100% certainty that, without examining or x-raying, the die is 'loaded', i.e. biased.

  • Comment number 9.

    My definition of remarkable is "I might make a remark about it", so that birthday combination is remarkable to me.

    j_s_p, my gut feeling is that positive thoughts bring positive results (although not on their own). The world-record sprinter Michael Johnson said whenever he had a negative thought he always deliberately overrode it with a positive thought.

    However, maybe it makes no difference. It could be we only remember the unusual days when we have three positive or three negative incidents, and we forget the days when we only have one or two of each. So when we look back in our memories, we only remember the unusually good or bad days, and we think all days were like that.

  • Comment number 10.

    This comment was removed because the moderators found it broke the house rules. Explain.

  • Comment number 11.

    These are great points for discussion.

    r0naharm0ny describes nicely why a real ‘coincidence’ is not only an unlikely concatenation of events, but that has ‘significance’ than others to the observer (and if anyone wants to share their own coincidence, they could got to our site https://cambridgecoincidences.org%29

    gmorrell has 3 close family members with the same birthdays - this is around a 1 in 135000 chance and is very surprising for your family, but remarkably common in the country! And it must make it easy to remember birthdays.

    Mr_Plebian's raises some very important, and slightly technical, issues which I would have loved to have included but the producers said everyone would switch off! As we described it in the programme, Monte Carlo assumes known probabilities and generates multiple possible futures. But it has been extended to deal with uncertain probabilities: first the probabilities get generated from their (Bayesian) distribution, and then a future is simulated. This generates more appropriate uncertainty, but even then does not of course allow for uncertainty about the underlying model. As the Bank of England interview illustrated one should always allow a little bit of probability for the unexpected! [I apologise if this is utterly incomprehensible to most people – presumably that’s why I was not allowed to include it]

    J_s_p rightly identifies that our culture, beliefs and and emotions hugely influence our attitude to risk and uncertainty. We deliberately left this vital aspect out of the programme - just not enough time and another programme (or series!) would be needed.

    And ChorleyPie, 123456 is apparently the most common choice of lottery numbers anyway, so if it ever comes up there will be a lot of jackpot winners.

  • Comment number 12.

    This quantative analysis includes no qualitative moderators. Although implicit in the conversational aspects, that is not explicitly stated ? For example, if a coin could be tossed in a perfect vacuum by a perfect coin placement and flipping machine, it should come up with a million heads in a row. The references to the frequency distribution histogram are, in my opinion, the most interesting aspect of this cleverly presented programme. Mathematics is a symbolic reference system, and like Astrology ( sorry that may be contentious to others in the same breath as Maths ) or Poetry, can potentially describe the world we occupy in many interesting, unusual and revealing ways. However, these descriptions of the world are just that. Decriptions. Not the actual world or universe itself. The main problem is that any symbolic reference system will never ( and I hate saying never :o) be able to completely describe the true nature of reality. It can contine to allude to it for ever, but each revelation will always raise the question or spectre of the next hidden aspect. For example, should the "origin" of the universe be neatly decribed in Mathematics, the next question to answer is, what occured "before". There is the known, the unknown and the unknowable, in essence. I love programmes of this nature, because they remind me of the unquenchable thirst for true knowledge. And the need to think outside the box. All the words I use here are symbolic references comprised of individual characters, but will not fully describe all my thoughts and feelings, although I hope the learned Professor and others will understand pretty much all of it. Shakespeare, Einstein, Tesla, Eastern mystics, Shaman, Wizards and Holy men where or are seekers of knowledge of the world we live in and mostly shared that with us all. Thankyou for sharing your expertise with us, Professor David Spiegelhalter, the world is a richer place for it and the very reason guys like yourself should carry on the good work. All the best, Steve

  • Comment number 13.

    My previous, and actually first post ever, was a bit off Professor David's programme subject, more a general comment about Mathematics. I just want to add a brief moderator to my post. Thanks to the brilliance of the guy who so effectively solved the famous three body gravitational problem, space probes can successfully navigate our solar system. A fantastic example of Maths doing it's stuff, and an example of a symbolic reference system in harmony with natural laws. I think I just contradicted my first post, somewhat :o) never mind. Anyway, perhaps these blogs are a bit like an open brainstorming session. I'll not patronise the Professor with further plaudits. I do, however highly praise the BBC for providing a platform for friendly academics, and allowing interested parties to add their comments to any particular forum. The BBC needs a bit of praise these days as, despite so much adverse current press, they really are one of this countries great institutions.

  • Comment number 14.

    Sorry, previous link to our coincidence site included the final bracket - it is https://understandinguncertainty.org/coincidences

    Thanks again for the comments. steven96663's points would take an essay to answer - I was pleased BBC4 encouraged us to include some challenging ideas about whether chance really existed 'out there'. Left up to me, I probably would have included a long discussion about the role of mathematical models, which are simplified and always inadequate attempts at building a map of reality, but can be very useful. But most people would have turned off rapidly, and so fortunately I was over-ruled!

  • Comment number 15.

    1 What did your maths say about the frequency of meeting poeple you know while on holiday, especially when abroad? Important for me to know if you reply to these messages.
    2 A challenge for you - What are the mathematical chances of a beaurocracy corrupting over time, like the church, goverment etc where there is little movement within office?
    3 if we assume that chance is a part of the fabric of reality it would mean that as yet we know very little and may never get to know. Also it would mean that if it is possible to know more then we have a long way to go and must embrace some very radical ideas before we can begin to make sense of it. By tadicalI mean David Deutsch ideas.


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