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Comment by zh3 | Hacker News Reader

I like to tell people who play the lottery they should go for 1 2 3 4 5 6 as it's just as likely to come up.

That is not a good strategy. That pattern is just as likely to come up. However, should it come up, you are almost guaranteed to split the pot.

The best strategy is to not play. The second best strategy is to minimize the chance of splitting the pot.

But it's bad advice compared to a random selection because these are all numbers with meaning for people. Many people who enter lotteries use meaningful numbers such as days of birth. So 1 2 3 4 5 6 is just as likely as any set of numbers to come up but if you do win you're more likely to be sharing the jackpot with other people who chose the same set.

But does it really matter? If you selected another number on that basis and then 1 2 3 4 5 6 won, you would still be kicking yourself as splitting the pot is better than no pot at all.

You have the same chance of hitting right combination if you enter 12345 or a random number chosen by a wall of lava lamps. But you have lower expected return since more people will use 12345 than your particular random number.

Expected return being size of the pot you can win multiplied by probability of winning. It's the first number that is lower when everybody has the same bright idea at once.

It does really matter. It's certainly better to have x% chance to win y, than x% change to win z, for z < y. Psychologically, if you assume you lose (and you're "kicking yourself") then avoid betting on popular sets, because it's better to miss a chance to win $100 000 (10 way split) that you would get by betting on a popular set, than to miss a chance to win $1 000 000 that you would get by betting on a unique set.

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