A question about lotto combinations. What is the correct answer?

Answer

Dear Dennis,

As a physics student I once got into an argument with my father about exactly this question… My father wanted to fill out a Lotto form and let me choose a combination. I said it didn’t matter, but he insisted. When I said the combination 1-2-3-4-5-6, he was angry that I didn’t want to be ‘serious’. However, as strange as it may seem, every opportunity has the exact same chance of being drawn, including 1-2-3-4-5-6.

The chance that a pre-specified combination of six different numbers between 1 and 45 will win at the next lottery drawing is less than one in eight million (about 0.000 012 %). The probability of combination 1-2-3-4-5-6 is indeed extremely small, but not smaller than for any other combination. All balls are exactly the same weight and size and the movement of the drum does not take into account what is written on those balls.

By the way: for the same reason, the chance that exactly the same combination will be drawn this week as last week is exactly as ‘great’ (extremely small) as any other combination.

What is special about 1-2-3-4-5-6 is that we see this combination as a special pattern. This allows us to describe the sequence in a compact way, such as ‘1 to 6’. The same goes for the pattern and the description ‘same as last time’. If you do not see a pattern in the six numbers, then you cannot describe that combination compactly, but only list the six numbers. However, whether you see a pattern in it or not, that doesn’t make the combination any more likely or unlikely.

It is true that the group of combinations with a special pattern is smaller than the group of combinations in which we see no pattern. (Although this will vary from person to person: what is meaningful to one person may not be to someone else. Think, for example, of birthdays and other special dates, telephone numbers, house numbers, etc.) So it is more likely that a combination was drawn. becomes what we see no pattern in. But that’s not because that particular combination is more likely, but simply because the group to which the combination belongs is larger.

It is a matter of human psychology that we (unconsciously) look for patterns in everything. This also influences our assessment of opportunities. You can hear a little more explanation about this in my lecture at the University of Flanders about the question of whether coincidence exists: https://www.youtube.com/watch?v=h6JglO8UDVk

There’s also a little explanation about it in my book Chance of Chocolate Cake in Chapter 7, under the heading “Law of the Chance of Water.” (Maybe they have it in the local library?)

Still, there is a good reason not to play the Lotto with the combination 1-2-3-4-5-6. There are more people who fill in ‘special’ combinations (consecutive numbers and other patterns in the grid). The chance of winning with this is not smaller, but if this combination is drawn, you have to share the pot with more people. That is why it is smarter to choose something else (and my father was somewhat right).

Regards,
Prof. dr. Sylvia