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In the national lottery 6 balls are drawn with numbers 1 to 49 on them. My father could never believe that the numbers 1,2,3,4,5 and 6 had exactly the same odds to come out as any other set of six you defined (e.g. 3,11,24,34,35,47).

Is there a name for this kind of bias or confusion with numbers?

Should I be asking on this on the Math or English stackexchange ..

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    Innumeracy comes to mind.
    – Hot Licks
    Commented Aug 6, 2019 at 12:11
  • An interesting read: onlinelibrary.wiley.com/doi/full/10.1111/tops.12345
    – marcellothearcane
    Commented Aug 6, 2019 at 13:07
  • Although non-gamblers may also be confused here, this is a sop for lottery gamblers (my father 'sort of realised' the real argument involved. But pushed it away.) They realise that the odds against 1,2,3,4,5 and 6 coming up are enormous. So they confuse 'it's more likely that a random-looking set of numbers turns up' with 'it's more likely that a particular random-looking set of numbers turns up'. Blinding themselves with science.
    – Edwin Ashworth
    Commented Aug 6, 2019 at 14:03
  • While it's true that, everything being equal, the chances of rolling a 1 on a die is exactly the same on the first roll as on the thousandth roll, if you've actually rolled ones 999 times in a row, logic would dictate that the die is weighted, or something else is going on, rather than that you've just encountered something highly unlikely. As such, the more times a 1 is rolled, despite the theoretical odds remaining the same, the more you can reasonably conclude that "something is wrong" in the practical world and that a 1 is more likely in that one specific case.
    – Jason Bassford
    Commented Aug 6, 2019 at 16:09

2 Answers 2

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Representativeness heuristic or bias (Holtgraves & Skeel, 1992):

a tendency to judge the probability of an event based on the extent to which the event is similar to the parent population; the more similar the event is to the population, the higher the perceived probability that it comes from that population.

A study done by Krawczyk and Rachubik (2019) seems to confirm this bias. People that choose to stick with random-looking combinations, even when offered a reward for switching, justify their choice by "more random numbers" (50% of the people) and "higher probability" (16% of the people).

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  • What are the 'the inevitable "streaks" or "clusters" arising in small samples from random distributions' involved here? {1,2,3,4,5,6} is an artificially chosen set, not a winning selection that has turned up as far as I know. Like {3,11,24,34,35,47}.
    – Edwin Ashworth
    Commented Aug 6, 2019 at 17:51
  • @EdwinAshworth I think that's more to do with the situation where you roll 6 6s in a row and people think the die must be loaded. The representative heuristic does seem relevant though, i.e. whenever the lottery numbers are announced they look random, so the parent population consists of sets of numbers with no apparent order, so the probability of any given non-ordered set is perceived to be higher than the probability of any given ordered set.
    – user339660
    Commented Aug 7, 2019 at 3:24
  • &@Minty I can see that {1,2,3,4,5,6} fulfills the 'clustering rather than nicely spread throughout the population' requirement of the clustering illusion. But the clustering illusion only involves (mis)interpreting observed results displaying clustering, as far as I can see. Not pre-rejecting as purely random possible future non-random-seeming results.
    – Edwin Ashworth
    Commented Aug 7, 2019 at 12:07
  • But there's another factor: I feel {1,2,3,4,5,6} might feel to some (hedge, hedge, hedge – I taught maths to not-quite-uni level, so never let my heart rule my head. Except on the last Thursday in the month) a lot less likely winning set than say {31,32,33,34,35,36}. Is this (a) my misapprehension, or (b) 'familiarity (1,2,3,4,5,6 ... come on, now) breeds contempt', 'too easy to be right – life's never so simple', ''too easy to be right – anybody can guess that' ...?
    – Edwin Ashworth
    Commented Aug 7, 2019 at 12:08
  • I'm also not quite happy with the clustering illusion. Should I delete that part of the answer?
    – Boondoggle
    Commented Aug 7, 2019 at 19:18
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Apophenia

Apophenia is the spontaneous perception of connections and meaningfulness of unrelated phenomena.

Source: Skeptic's Dictionary

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  • I'm not completely happy with this, because it doesn't signify patterns such as 1 2 3 4 5 6 having any precedence.
    – marcellothearcane
    Commented Aug 6, 2019 at 12:42
  • Not really precise enough. Hot Licks put 'Innumeracy comes to mind' as a comment.
    – Edwin Ashworth
    Commented Aug 7, 2019 at 12:15

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