To enter the UK national lottery, you select six numbers. I always feel that I must choose at random, yet the odds would be the same if I always chose the numbers 1 to 6. Why do I feel this way?
As you acknowledge, the set of six numbers 1, 2, 3, 4, 5, 6 is neither more nor less likely to win than any other, but while the machine selecting the winning numbers does not prefer particular combinations, the same is not true of humans. We have brains adapted to make sense of the world by looking for patterns, and for us the set 15, 18, 23, 31, 37, 49, which was drawn one week, does not seem to possess any significant pattern to distinguish it from the numbers selected on previous weeks.
Our brains cope with a large number of individuals by stripping them of their individuality, so we regard all sets of numbers which lack an obvious pattern as being essentially similar, and do not differentiate between them. Any set that does possess an obvious pattern feels like an unlikely candidate for winning because we perceive it as distinctive, special and 鈥� by perverse logic 鈥� unlikely to be drawn.
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鈥淎ny set of numbers that shows an obvious pattern feels like an unlikely lottery winner鈥�
Despite the fact that 1, 2, 3, 4, 5, 6 is no less likely to win than any other set of numbers, if you鈥檙e hoping to win big money, this might not be the best set to choose. I have seen estimates that if all six were ever to come up together, the jackpot would have to be shared between as many as 10,000 people because these people have also seen through the meaninglessness of the patterns we like to impose on random numbers. What they have not realised is that there are a large number of like-minded people with whom they will have to share their winnings.
In this respect your instinct to choose numbers 鈥渁t random鈥� may yet have some rational justification. Probably the best tactic is to choose numbers that other people shun 鈥� see for some advice.
Strangely, selecting 1, 2, 3, 4, 5, 6 for the 鈥淟otto鈥� draw on the date of the edition in which this question was printed would have won 拢10 for three matching numbers 鈥� the first time this set would have won anything for at least the past 50 draws.
Stephe Ellis, York, UK
There are around 14 million ways of selecting six numbers from 49, and although each of these ways has the same probability of occurring there are far more sequences that look radom, such as 4, 16, 27, 35, 48, 49, than ordered ones like 1, 2, 3, 4, 5, 6. So, if you had to bet on a random sequence or an ordered sequence being drawn, then the money is with the random sequences every time.
Steven Winfield, Cambridge, UK