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Let's set aside the argument that computers have a pseudo-random number generator.

I'm interested in knowing if a lottery terminal generates each quick pick independently from all previous picks and draws each from an identical uniform distribution.

Why I'm doubtful of the above claim.

A colleague of mine relayed a story (I don't know his source) where he said that the lotteries are more interested in having multiple winners for a given jackpot prize than a single winner because it creates more publicity. So, people who ask for a quick pick are more likely to get numbers that were already picked.

matt_black
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Tim Reddy
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    Do you mind being even more specific? "In the United States, lotteries are run by 47 jurisdictions: 44 states plus the District of Columbia, Puerto Rico, and the U.S. Virgin Islands. In the US, lotteries are subject to the laws of each jurisdiction; there is no national lottery." http://en.wikipedia.org/wiki/Lotteries_in_the_United_States – Oddthinking Jan 06 '14 at 23:04
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    Except for knowing the exact algorithm used to generate quick picks, I'm not sure how you could (realistically) prove or disprove your colleague's theory. However, if it were true, it would decrease the chances of there being a winner in the first place, as there would be less total combinations in play. Furthermore, the greater the number of quick picks that are intentionally "grouped", the less likely it is for a Quick Pick to actually win the jackpot. So, if the goal is to have multiple winners, I don't think grouping the quick picks necessarily helps accomplish that. Finally, if you approa – TTT Jan 07 '14 at 02:48
  • @TTT: if you have the data of how many people won each prize level each week and how many were quick picks, you could check the distribution followed Poisson without viewing the exact algorithm. – Oddthinking Jan 07 '14 at 04:30
  • @Oddthinking: hmmm... are you sure that would suffice? Wouldn't you need to compare all the numbers of the ticket to know if jackpot groupings have occurred? By this I mean, even if the distribution doesn't match what you expect, perhaps that proves that it is rigged, but does it actually prove the grouping theory? – TTT Jan 07 '14 at 05:06
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    Is there a claim that Quick Picks are truly random (as opposed to generated by a cryptographic quality PRNG; or even a weaker PRNG)? Fankly, real randomness is demanding and expensive, while high quality pseudo-randomness is (relatively) cheap and easy. – dmckee --- ex-moderator kitten Jan 07 '14 at 05:14
  • @TTT: Agreed. It is an experiment that could only falsify the grouping theory. – Oddthinking Jan 07 '14 at 06:20
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    @dmckee: Covered by the first line. I am hoping we can avoid being distracted by the "pseudo" issue; it doesn't appear to be relevant. – Oddthinking Jan 07 '14 at 06:21
  • Actually the question is answerable with historic data from lotteries. The winning combinations are *public* information so it is easy to apply statistical tests to establish whether the distributions fit the claim in randomness. In the UK the national lottery even provides tools to help [here](http://www.national-lottery.co.uk/player/frequencyChecker.do?action=showAllForGame&gameType=lotto) for example. – matt_black Jan 20 '14 at 20:19
  • Though the records for quick picks might not be so accessible, but there should be some way to audit them. – matt_black Jan 20 '14 at 20:21
  • @matt_black Whether winning combinations are independently and uniformly distributed is a different question from whether quick-pick ticket selections are. –  Jan 20 '14 at 20:53
  • @Articuno Yes, my bad, commented too soon. However, some lotteries might publish audits and, if they don't, it would not take a large sample of users to pool their given numbers to run a decent statistical test. – matt_black Jan 20 '14 at 21:14
  • Here is a place to get a lot of "official" quick pick numbers to do some analysis on http://www.usamega.com/mega-millions-quickpicks.asp – Mark Jan 20 '14 at 22:13

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