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I'm not sure about other countries, but in NZ one ticket has 4 or more rows, one row has 6 numbers - let's not play Powerball here

Say last week I won division 5 on one of the row (that is to match 4 numbers out of 6). Let's assume the odd to win that division is 1 out of 100.

If I continue to play the same row this week, would the following probabilities to win that row again decrease?

  • Win the same division, different sets of winning numbers
  • Win the same division, exactly the same set of numners
  • Win any division

I'm thinking: because each draw is independent, the odd should be the same. But obviously the odd of one row winning twice in a row is much smaller than to win only one, right?

Max
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2 Answers2

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The a priori probability of a given selection of numbers coming up twice in a row is certainly less than the probability of the selection coming up once.

However, if a particular selection has just been drawn, the probability of that selection occurring next time is the same as the probability for any other selection. The lotto balls have no "memory" and do not "know" how they turned out last time.

David
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  • That still sounds like a paradox to me. Could you offer an explanation? I think I must have misunderstood something. – Max Nov 04 '14 at 05:08
  • Why exactly does it sound like a paradox to you? – David Nov 04 '14 at 05:26
  • Your first sentence is "the probability [...] [for] twice in a row is less than [...] once". I understand that as: the winning row has less probability to win again than a row that has not won before.

    But later you said the probability for that to occur next time (the second time) is the same.

    So is it less than, or the same?

     – Max Nov 04 '14 at 07:57
  • The point is that we are talking about two situations: two consecutive identical draws in the future, and a future draw which is identical to a past one. These are completely different, because probability has nothing to say about known past events. – David Nov 04 '14 at 08:52
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If you win once, that does not increase/decrease your probability of winning again. For example, if you toss a coin till a head comes, these are the some possibilities: P(H)=1/2, P(TH)=1/4, P(TTH)=1/8, ...

This means that whether you get a head or not, your chance of getting another head in a minimum no. of chances is the same. If you have not got a single head yet, the probability of getting 2 heads in a fixed no. of chances is less than that of 1 head.

The same may not be said about simple computer RNGs, which have a slightly less probability if getting the same no. on the immediate next time.

ghosts_in_the_code
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