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In lotto game 7/39, combination of 7 numbers are drawn at random.

Should we trust 'lotto experts' and their lotto advice? For example, should we pick 4 of the higher and 3 out of the lower numbers (they claim that combinations like this win more often), or not to pick consecutive numbers because they rarely occur?

Is data and from the past games (conclusion drawn out of it) relevant for the future ones?

My thoughts (or pitfalls): Is there any point in looking for "greater justice" in a game like lotto, since it should be designed to be completely random? I cannot see any reason why combination [1,2,3,4,5,6,7] would be less likely to be winning combination than, say [2,5,9,17,21,33,38] (or any other, for that matter). Same goes for consecutive numbers, is there a reason to believe that any other sub sequence (1,2,3) is less probable than some other, say (5,9,17)?

deki_mg
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  • advices like "not to pick consecutive numbers because they rarely occur" are nonsense. See eg my answer here https://math.stackexchange.com/questions/467575/should-i-put-number-combinations-like-1111111-onto-my-lottery-ticket/467581#467581 – leonbloy May 14 '17 at 02:46
  • @leonbloy, I think your intuition for this question is wrong. In your example, you compared the probability of a number with all the same digits ($P(A)$) with a number with different digits ($P(B)$). Obviously $P(A)$ has a more likely chance than $P(B)$, but in this case, individual combinations have the same probability. – Toby Mak May 14 '17 at 02:52
  • @TobyMak I don't get you. The "expert" is say don't pick numbers (1,2,3,4,5,6,7) because consecutive numbers occur rarely. – leonbloy May 14 '17 at 02:55
  • @leonbloy Sorry, I was thinking about the higher and lower numbers example. For that example, the events have the same probability, but for your example, consecutive numbers and non-consecutive numbers have the same probability. – Toby Mak May 14 '17 at 02:57

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Lotteries are by definition, drawn at random, so there is an equal chance of each of your combinations match the actual drawn numbers.

As a result of this, higher numbers and lower numbers have an equal chance of occurring, so these 'lotto experts' are wrong. Even if a combination is more likely to occur in the short-term, there is an extremely likely chance close to $1$ that these will have been outweighed by other numbers in the long-term.

Hope this cleared some misconceptions about the definition and consequences of a random event. This misconception is also closely related to the gambler's fallacy, which I suggest you to look at.

Toby Mak
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  • Lotteries may be random (historically some have been fixed) but there are reasons to choose your numbers carefully. In many lotteries the prize pool for the jackpot is shared between all winners. In this case it is wise to pick numbers that no one else has, so don't pick 1,2,3,4,5,6,7. But the most reliable way to make money from a lottery is to operate it. – Angina Seng May 14 '17 at 03:17