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lottery and math

Topic closed. 7 replies. Last post 4 years ago by jamella724.

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macon
United States
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October 3, 2009
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Posted: September 5, 2012, 7:41 am - IP Logged

for the last several games of mega millions and powerball i have played the same exact numbers and each time i play, this maybe a dumb question/topic, but i am going to ask anyway, i am only 2-3 numbers away on each of my numbers for being in the money in fact, if i had went up or down by no more than 2-3 numbers i would have had 5 numbers at least once  4 numbers at least 2 times in both megamillions and powerball so i would like some  help developing a system based on the set numbers i play can i please get some help thank you my set numbers are 5-19-29-42-56 and 5-19-29-46-52 mega/powerball is 7 thank youBig Smile

    savagegoose's avatar - ProfilePho
    adelaide sa
    Australia
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    April 11, 2006
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    Posted: September 5, 2012, 8:14 am - IP Logged

    the reason you see all those numbers  withing 1 or 2 of your pick is there are so many more numbers available withing 1 or 2 of your number. than just your number.

     

    ie say you select 1 numbber out of the 59 to match. ythats a 1 in 59 chance. but if you say wityhin 2 of my number, thats 2 up and 2 down plus yours, or 5 in 59  chance  one will be hit.  much more likely. thats why theyre always appearing. if you where to start buying all those 5  options,  for ea number you select the cost soon sky rockets.

     

    5 x 5 x 5 x 5 x 5.

    jus1 1 away up or down, gives 3 x3x3x3 x3 meaning 240+ game combos.

     

    but this place will explain the math better than i can

    http://www.khanacademy.org/math/probability

    2014 = -1016; 2015= -1409; 2016 JAN = -106; FEB= -81; MAR= -131; APR= - 87: MAY= -91; JUN= -39; JUL=-134; AUG= -124; SEP = -123; OCT= -84  NOV=- 73 TOT= -3498

    keno historic = -2291 ; 2015= -603; 2016= JAN=-32, FEB= +12 , MAR= -86, APR = -77. MAY= -48, JUN= -29, JUL=-71; AUG = -52; SEPT= -43; OCT = +56 NOV = -33 TOT= -3297

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      macon
      United States
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      Posted: September 5, 2012, 9:16 am - IP Logged

      i understand what you are saying but there should be an easy mathamatical  way since most of the time most numbers don't repeat the very next game sometimes its four games before a number repeats any help would be apreciated thank you for your response savagegooseBig Smile

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        July 25, 2012
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        Posted: September 5, 2012, 8:41 pm - IP Logged

        for the last several games of mega millions and powerball i have played the same exact numbers and each time i play, this maybe a dumb question/topic, but i am going to ask anyway, i am only 2-3 numbers away on each of my numbers for being in the money in fact, if i had went up or down by no more than 2-3 numbers i would have had 5 numbers at least once  4 numbers at least 2 times in both megamillions and powerball so i would like some  help developing a system based on the set numbers i play can i please get some help thank you my set numbers are 5-19-29-42-56 and 5-19-29-46-52 mega/powerball is 7 thank youBig Smile

        I find that there are two types of players.

        One type is best typified by a fool that posted an elaborate "mathematical" sequence of calculator functions that magically determines which of several numbers to choose.  His methodology is nothing more than a "deterministic" process for selecting random numbers.  But he believes the sequence is the key to success.

        If you are of that ilk, I have nothing to say that will interest you.  Find some tea and count the leaves.

        -----

        The other type truly understands the mathematics of these games.  Therefore, there are no "systems" that truly improve your chances.  There are only "systems" that make us humans feel better about our choices.

        Consider the Mega Millions game.  Each combination of 5 regular numbers and 1 Mega number has a 1-in-175,711,536 chance of winning the jackpot.  And each combination of numbers has about a 1-in-39.89 chance [1] of winning __something__, albeit most of the time that is by matching just the Mega number, which I believe has the lowest payout.

        And there is absolutely nothing you can do to improve those chances for an individual  combination.  The only thing that you can do is to purchase a lot of different combination.

        As for your observation that most of the time you are "2-3 numbers away [...from...] being in the money", surely you don't believe that the selection process knows your numbers and chooses 2-3 numbers away from them.

        So the obvious answer is:  that is just a coincidence.  All you have done in your mind is increase the number of combinations that you are considering possible outcomes.

        Let me illustrate.  If we consider "poker" combinations of numbers, more than 49% of the possible Mega Millions regular-number combinations -- 1,876,800 of 3,819,816 [2] -- will form a pair and 3 singles; that is, 2 numbers from one decade, and 3 each from different decades.  For example, 1-2-11-22-33.

        So if you choose a combination with that form, you might think that you have improved your chances significantly:  1-in-1,876,800 instead of 1-in-175,711,536.

        But that is only if the lottery-selected numbers form a pair and 3 singles.  There is a 1,876-800-in-175,711,536 chance of that.

        So the __conditional__ probability is 1,876-800/175,711,536 that the lottery-selected numbers will form a pair and 3 singles times 1/876,800 that it will match yours.  The 1,876,800s cancel out, giving the result of -- drum roll! -- 1/175,711,536.  QED.

        Nevertheless, it might feel good to limit your choices to a pair and 3 singles -- or 2 pair and a single; together, they represent more than 71% of the possible Mega Millions regular-number combinations.  That way, 71% of the time, you can say that the lottery-selected numbers matched your pattern, so you were "this close" to winning. ;-)

        You can apply the same kind of analysis to every "system" for "filtering" your choices.  But the mathematics might be overwhelming and sometimes intractable.

        For more complex "systems", I often resort to writing programs that exhaustively generate all of the combinations and count the occurences of specific patterns.  Computers are so fast and memory is so large these days, it actually does not take long to analyze 175+ million combinations.

        I hope this helps to give you some perspective.

         

        -----

        [1] About 1-in-39.89 is exactly 4,405,086 in 175,711,536 combinations.  2,349,060 in 4,405,086 combinations match only the Mega number.

        [2] The Excel formula for determining the number combinations that form a pair and 3 singles is:

        =COMBIN(7,2)*(9*COMBIN(4,2)*10^2+COMBIN(4,3)*10^3)
        +COMBIN(9,2)*(7*COMBIN(4,2)*10^2+COMBIN(4,3)*10^3)
        +4*COMBIN(10,2)*(7*9*3*10+7*COMBIN(3,2)*10^2+9*COMBIN(3,2)*10^2+10^3)

        Ostensibly, it computes the number ways of chosing a pair from one decade times the number of ways of choosing just one each from 3 of the remaining 5 decades.

        The formula is complicated by the fact that not all "decades" truly contain 10 numbers.  In particular, the units "decade" has only 9 numbers, 1 through 9.  And the 50s "decade" has only 7 numbers, 50 through 56.

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          macon
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          Posted: September 6, 2012, 12:24 am - IP Logged

          there it goes again one off 3 of f powerball

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            July 25, 2012
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            Posted: September 6, 2012, 2:46 am - IP Logged

            I find that there are two types of players.

            One type is best typified by a fool that posted an elaborate "mathematical" sequence of calculator functions that magically determines which of several numbers to choose.  His methodology is nothing more than a "deterministic" process for selecting random numbers.  But he believes the sequence is the key to success.

            If you are of that ilk, I have nothing to say that will interest you.  Find some tea and count the leaves.

            -----

            The other type truly understands the mathematics of these games.  Therefore, there are no "systems" that truly improve your chances.  There are only "systems" that make us humans feel better about our choices.

            Consider the Mega Millions game.  Each combination of 5 regular numbers and 1 Mega number has a 1-in-175,711,536 chance of winning the jackpot.  And each combination of numbers has about a 1-in-39.89 chance [1] of winning __something__, albeit most of the time that is by matching just the Mega number, which I believe has the lowest payout.

            And there is absolutely nothing you can do to improve those chances for an individual  combination.  The only thing that you can do is to purchase a lot of different combination.

            As for your observation that most of the time you are "2-3 numbers away [...from...] being in the money", surely you don't believe that the selection process knows your numbers and chooses 2-3 numbers away from them.

            So the obvious answer is:  that is just a coincidence.  All you have done in your mind is increase the number of combinations that you are considering possible outcomes.

            Let me illustrate.  If we consider "poker" combinations of numbers, more than 49% of the possible Mega Millions regular-number combinations -- 1,876,800 of 3,819,816 [2] -- will form a pair and 3 singles; that is, 2 numbers from one decade, and 3 each from different decades.  For example, 1-2-11-22-33.

            So if you choose a combination with that form, you might think that you have improved your chances significantly:  1-in-1,876,800 instead of 1-in-175,711,536.

            But that is only if the lottery-selected numbers form a pair and 3 singles.  There is a 1,876-800-in-175,711,536 chance of that.

            So the __conditional__ probability is 1,876-800/175,711,536 that the lottery-selected numbers will form a pair and 3 singles times 1/876,800 that it will match yours.  The 1,876,800s cancel out, giving the result of -- drum roll! -- 1/175,711,536.  QED.

            Nevertheless, it might feel good to limit your choices to a pair and 3 singles -- or 2 pair and a single; together, they represent more than 71% of the possible Mega Millions regular-number combinations.  That way, 71% of the time, you can say that the lottery-selected numbers matched your pattern, so you were "this close" to winning. ;-)

            You can apply the same kind of analysis to every "system" for "filtering" your choices.  But the mathematics might be overwhelming and sometimes intractable.

            For more complex "systems", I often resort to writing programs that exhaustively generate all of the combinations and count the occurences of specific patterns.  Computers are so fast and memory is so large these days, it actually does not take long to analyze 175+ million combinations.

            I hope this helps to give you some perspective.

             

            -----

            [1] About 1-in-39.89 is exactly 4,405,086 in 175,711,536 combinations.  2,349,060 in 4,405,086 combinations match only the Mega number.

            [2] The Excel formula for determining the number combinations that form a pair and 3 singles is:

            =COMBIN(7,2)*(9*COMBIN(4,2)*10^2+COMBIN(4,3)*10^3)
            +COMBIN(9,2)*(7*COMBIN(4,2)*10^2+COMBIN(4,3)*10^3)
            +4*COMBIN(10,2)*(7*9*3*10+7*COMBIN(3,2)*10^2+9*COMBIN(3,2)*10^2+10^3)

            Ostensibly, it computes the number ways of chosing a pair from one decade times the number of ways of choosing just one each from 3 of the remaining 5 decades.

            The formula is complicated by the fact that not all "decades" truly contain 10 numbers.  In particular, the units "decade" has only 9 numbers, 1 through 9.  And the 50s "decade" has only 7 numbers, 50 through 56.

            I wrote:  ``So the __conditional__ probability is 1,876-800/175,711,536 that the lottery-selected numbers will form a pair and 3 singles times 1/876,800 that it will match yours.  The 1,876,800s cancel out, giving the result of -- drum roll! -- 1/175,711,536.  QED.``

            Sorry about the typos.  I was pushed for time.  I hope the point was still clear.  But in case it wasn't, this is what I __should__ have written.  (We are long-past the window of time that permits me to edit the posting.)

            ``So the __conditional__ probability is 1,876,800/175,711,536 that the lottery-selected numbers will form a pair and 3 singles times 1/1,876,800 that it will match yours.  The 1,876,800s cancel out, giving the result of -- drum roll! -- 1/175,711,536.  QED.``

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              Posted: September 6, 2012, 4:23 am - IP Logged

              i understand what you are saying but there should be an easy mathamatical  way since most of the time most numbers don't repeat the very next game sometimes its four games before a number repeats any help would be apreciated thank you for your response savagegooseBig Smile

              Well, I believe the mathematics is quite complicated for combinations of numbers.  But we can illustrate the mathematics by looking at the probability of repeating the Mega number.  It is determined by the geometric distribution [1].

              For the Mega Millions lottery, the probability of repeating the most recent Mega number in the next drawing is 1/46.  The probability of repeating it in the second drawing and not before is (1/46)*(1-1/46).  The probability of repeating it in the third drawing and not before is (1/46)*(1-1/46)^2 [2].

              In general, the probability of repeating a Mega number in n-th drawing and not before is (1/46)*(1-1/46)^(n-1).

              If we calculate that for n=1,2,3,..., we find that we can expect that the most recent Mega number will appear again 14 to 63 drawings later and not before, with a mean of 46.  The mean is the weighted average.  Statistical theory tells us it is 1/p, where p is 1/46.

              That does not mean it cannot appear in fewer or in more drawings later.  It just means that the middle two quartiles (50%) is 14 to 63.

              In fact, an analysis of the first 742 Mega Millions drawings [3] shows that the Mega number has repeated 11 to 58 drawings later and not before.  Pretty close the theoretical expectation.

              So my "system" would be:  randomly choose among the Mega numbers selected 14 to 63 drawings earlier. 

              As for combinations of regular numbers, I have found empirically that the lottery-selected numbers match at most 3 of any previous drawings about 62% of the time; and they match at most 2 of any previous drawings about 34% of the time.

              Moreover, 50% of the time, at least 1 number matches a number from 1 to 4 drawings earlier; at least 2 match numbers from 6 to 25 drawings earlier; and at least 3 match numbers from 46 to 225 drawings earlier.

              Those statistics and a couple others would factor into my "system" of "filtering" random combinations of my own.

              As I noted earlier, I cannot compute those statistics mathematically.  (Perhaps someone else could; it is just beyond my skill level.)  Instead, they are based on an analysis of the first 742 Mega Millions drawings. 

              And again, I want to reiterate that these "filtering" heuristics do not change the probability of any one combination being "in the money"; that is about 1-in-39.89 for each combination.

              They just satisfy our human perception of numerical patterns; and they make us feel better about our choice(s).

              I hope that is helpful.  Good luck!

               

              -----

              [1] In a previous explanation, I mistaken referred to the binomial distribution.

              [2] The operator "^" means "to the power of".  For example, 5^3 = 5*5*5.

              [3] The first 742 Mega Millions drawings are 6/24/2005 through 7/31/2012.  I'm a little behind. :-)

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                Texas
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                September 4, 2012
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                Posted: September 7, 2012, 8:13 am - IP Logged

                Others are still confused on how Mathematics can help them out with Picking the right combination of numbers.  Luck or not, with Math help or not, it is proven that Math somehow give us idea on what numbers to choose and the probability that it will win.