“In the first of a new series, Ian Stewart, a professor of mathematics at Warwick University, takes a look at how we perceive luck and chance.
“A friend of mine won seven million on the Lottery,” said the chap next to me in the gym. “That’s the end of my chances. You can’t win if you know someone who has.”
There are as many urban myths about the National Lottery as there are legs on a millipede, but I’d not come across this one before. It set me wondering: why do people so readily believe this kind of thing?
Think about it. In order for the statement to be true, the Lotto machine has to somehow be influenced by your network of friends and acquaintances. It has to know whether any of them has won before, and then take steps to avoid your particular choice of numbers – which means that it also has to know what you have chosen. In fact, all 11 Lotto machines must know this, because the one used each week is itself chosen at random. Since a Lotto machine is an inanimate mechanical device, this doesn’t make a great deal of sense.
The maths is straightforward. Each week, the chance of any particular set of six numbers winning the jackpot is 1 in 13,983,816. That’s because there are that many possible combinations of numbers, and each is equally likely to occur. If not, the machine would be biased, and it is designed to avoid that. So it seems clear that the explanation for the myth must lie in human psychology, rather than probability theory. A possible reason is an unconscious belief in magic, here manifesting itself as luck. If you think that luck is a real thing that people possess, and it improves their chances, and if you think that there is only a certain amount of luck to go round — then perhaps your fortunate friend has used up all the luck in your neighbourhood. Which in this instance seems to be your social network.
Omigod. Can you tweet your luck away? Put your luck on Facebook for your so-called friends to steal? It’s a nightmare!”
Read more at The Telegraph (Thanks Tracey)
RE: Luck – I think there is a strong aspect to ‘luck’ and the perception of luck – if we allow ourselfves to see the more positive things in our life, than the more positive things around us show up more. This we then interpret as lucky as they may have continued but since we are looking for them, they appear more often?
However, I do have my lucky dice when I play games, my lucky car adornments and heck, don’t all guys have their pulling socks?
Ultimately it is in our own perceptions, but if there is something that allows more or less luck, then I’ve been good, and my lottery numbers are…
The situation described above is not really a myth, IMHO.
Although it is mathematically possible for several lottery winners to know each other (and I am sure there are small clusters within the general spread of winners) it is common sense that the more lottery winners you have in one area or group the less likely it is that the next winner will appear in that area or group. Since we mostly have 150 acquaintances and approx 30 close friends (numbers provided from the Top Of My Head.com), the man in the gym is reasoning that it has become less likely for him to win now that his group contains a winner.
This is not mathematically provable, or actually true, but it does describe the real distribution of winners that we actually see in real life, not in a hypothetical model.
Of course he is just as likely to win the lottery as anyone else and his ‘luck’ is no more real than phlogiston or ether.
However, after several thousand iterations of a random process, we find a fairly even (if slightly clumpy) distribution occurs nearly every time.
His assumption is based on that intuitive understanding: that he is less likely to be in the winning group if he is surrounded by winners.
Obviously his geographical location is arbitrary, as is his group of friends.
You could group people according to their initials – if lots of RAB’s won, I might feel less likely to win. Guess what? it is unlikely that all winners would have the same initials, although the system does not know our names. Unlikely, but not impossible.
Of all the possible distribution patterns of winners, the pattern of ‘all winners in the same place’ has only one set of possible precursor events.
The pattern of ‘winners distributed all over’ could be preceded by a vast number of possible events.
Therefore, it is more likely that winners would be distributed evenly as there are many pathways to that event.
Therefore the man is not actually wrong, although he is misguided in his interpretation.
Please prove me wrong, mathematicians and statisticians and actuaries!
I am sure you can.
Or at least send a link to somewhere that helps me to understand it better.
the lottery is a great example of the lengths we will go to in order to attract luck…& how lucky we feel when something good actually happens. i guess it just goes to show how unlucky we usually feel!
A have now had a short but fruitful correspondence with the very gracious Prof Ian Stewart who dismantled my illogic efficiently. Simply put, the system has no memory and all other conclusions must flow from that point. Obvious really. thank you Professor Stewart.
@Rob (first comment)
“it is common sense that the more lottery winners you have in one area or group the less likely it is that the next winner will appear in that area or group”
nope…
You probably think this because it is less likely for two people in a group to win than it is for just one of them too.
However, once one person has already won, it doesn’t affect the outcome of future events.
To better understand this, imagine you are flipping a coin twice.
It is more likely to get a head and a tail than it is to get two heads (or two tails.)
However, if you get heads the first time, the odds that the second toss will give heads is still 50%
You’re falling victim to something called the gambler’s fallacy, which is a well understood piece of bad logic.
The fact that humanity is still alive is soooo highly impropable~~…
Well that’s good to know… Not that any of my mates have won £7m on the lottery… It’s just Derren’s (roughly quoted) statemant that you’re more likely to die before the lottery starts than you are to win the lottery that prevents me shoving any more dosh on the lottery… I choose life.
Of course you are right. Just goes to show that common sense and probability are strange bedfellows… I shall think more and guess less. Very very interesting.
If anyone reading wants some extra luck, they can download some by clicking on [u]this link[/u]. (Sorry, I’m not 100% sure if BBCode will be accepted.)
Years ago I went through the last ten weeks or so on teletext and wrote down all the numbers that had come up and wrote down the ones that came up most. 41 etc. I never bought a ticket and not sure any number was there the following draw. I gave up after that. Perhaps I should gamble one of my precious pounds this year. Too many lottery choices last time I looked though, kind of positive I wouldn’t win.
It’s not that they ‘think’ the chances become lower, but suddenly the incomprehensible odds become real to them. They think, “Gosh, what are the odds that’ll happen round here AGAIN?” They see it as the odds of lightning striking twice in the same place, instead of one in the place they specify.