How many combos in sequence for 5/36 matrix?Prev TopicNext Topic

• cottoneyedjoe

  

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  March 28, 2019
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  Sep 10, 2022, 11:45 am

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  In response to GiveFive

  Quote: Originally posted by GiveFive on Sep 7, 2022

  The above post is very likely the single best post I've ever seen on The Lottery Post.  Thanks very much for going the extra mile and giving me info on linear progressions that I hadn't even considered or even knew of. (Which is more the case... I wasn't a fan of math in school.  I knew it could be fascinating as Hell, but because I didn't want to be a good student, I basically didn't bother to study it. I'm the type of guy that got a 'C' without cracking a book.  I've often wondered what my grades would have been like if I decided not to be so lazy and be a good student.)  Now I'm old and gray and I've got a few regrets when it comes to my schooling. Coulda woulda shoulda.

  The reason why I decided to ask about the number of consecutive combo's is because I figured if there are a whole bunch of them, then I could tell people not to play them and by ignoring them because they never come out players could reduce the odds from 376,992 to 1 to whatever... 32 combo's doesn't do much with regard to lowering the over all odds.  BUT!! While the total of 144 other linear progressions doesn't reduce odds dramatically, it might pay to be smart and know enough not play those either because my guess is they haven't come out in Florida Fantasy5 very often either. But ya gotta know what those progressions actually look like to avoid playing them.

  I'm going to steal your excellent post and put it in The Florida Fantasy5 - Players thread.  I'll credit you as the expert that gave me that info.  Thanks again.  G5

  Thanks for the kind words and I'm glad you found this useful, G5. I have to disagree about your rationale for not playing them, though. The lottery is concerned with matching numbers, not patterns or abstract concepts such as the classification of a pattern. The combo 12-14-16-18-20 really is just as likely to be drawn as the "more randomish" (technical term ) combo 3-5-12-29-31.

  As a thought experiment, let's give the "more randomish" combo 3-5-12-29-31 its own classification: sets where the differences between numbers follow the pattern 2-7-17-2. Now there are only eight Florida Fantasy 5 combos in this new classification:

  • 1-3-10-27-29
  • 2-4-11-28-30
  • 3-5-12-29-31
  • 4-6-13-30-32
  • 5-7-14-31-33
  • 6-8-15-32-34
  • 7-9-16-33-35
  • 8-10-17-34-36

  Combos with this particular pattern of differences are more rare than combos classified as linear progressions, so with the same justification you could tell people not to play them. But every combo in Florida Fantasy Five has a pattern of differences that is shared by only a handful of other combos, making them all "rare" in their own particular way. 

  The only advantage in not playing linear progressions (or other similarly nice patterns) is when pari-mutuel payouts come into play. This is because, as you well know, tons of people play combos like 1-2-3-4-5, which means you'd have to split a sweet jackpot into lots of not-as-sweet payouts. I suppose that applies to most lotteries these days with their legally codified liability limits.

  * * * * * *

  As a side note, after I reread my comment about quadratic progressions, it got me thinking about how many there are. I wrote a script to generate them all, and there are at least 408. (I say at least because I could have missed something.) I will put pastebin link below in case I want to refer to it later...

  https://pastebin.com/VHBgwNJs
• ddude003

  

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  Sep 10, 2022, 8:44 pm

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  Statistics from here in Missouri Show Me Cash, which is a 5/39 game with 5115 historical draws, shows 1 odd/4 even is 13.4% and 4 odd/1 even at 15%...  Toss in 2% for all even and another 3.4% for all odd and you have the aprox tails of your typical standard deviation distribution curve...  How does that work out for the lotto games games you play???
• Orange71

  

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  Sep 30, 2022, 2:57 pm

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  The theoretical probabilities for a single draw are as follows:

  P(1 odd / 4 even) = 1360 / 10101 = 0.1346 = 13.46%

  P(4 odd / 1 even) = 1615 / 10101 = 0.1599 = 15.99%

  P(all even) = 68 / 3367 = 0.0201 = 2.01%

  P(all odd) = 272 / 10101 = 0.0269 = 2.69%

  A probabilities for a succession of draws will follow the Binomial Distribution. The standard deviation for a given event with probability P is sqrt[P*(1-P)/n] where n is the number of draws. If you're saying that all odd has 3.4% occurrence over 5115 draws, then we can calculate how many standard deviations that is away from the Expected Value (2.69%). P = 0.0269 and n = 5115. SD = 0.00226. EV + 3*SD therefore is 0.0337 or 3.37%. Thus, 3.4% is slightly above that.
• Orange71

  

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  Sep 30, 2022, 4:26 pm

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  Here are the probabilities for all possible outcomes. If the random variable x  is the number of odd numbers appearing in a single draw, then the Mean is 2.56 and the standard deviation is 1.06.