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Pick 4 Math Help?

Topic closed. 31 replies. Last post 11 years ago by Badger.

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Badger's avatar - adu50016 NorthAmericanBadger.jpg
Wisconsin
United States
Member #1303
March 27, 2003
1508 Posts
Offline
Posted: June 6, 2006, 5:29 pm - IP Logged

Data for the Pick 3 is available easily in many places. But I've become a lot keener on playing Pick 4, and the various breakdowns don't seem as readily available.

So if any of you are into P4 I'd appeciate you reading this post and correcting me if anything that follows is incorrect.

In terms of BOXED combinations for P4, I'm coming up with

210 single combos

360 doubles combos

45 "double" doubles combos

90 triples combos

10 Quads

That's a total of 715 possible boxed P4 combos.

Now, I'm trying to figure the math on something and here it is.....in Wisconsin, the boxed combo 0246 has skipped over 3,000 drawings. That seems an awful lot to me, even though the singles combos account for only 30% of all the possible combos. The thing has not hit in any of its permutations in over eight years !

So I'm wondering...how often, statistically, should any particular "singles" combo hit in a Pick 4? Anyone out there that knows the math?

============

How can you tell if a politician is lying?

Answer: His lips are moving.

    johnph77's avatar - avatar
    CA
    United States
    Member #2987
    December 10, 2003
    832 Posts
    Offline
    Posted: June 7, 2006, 3:17 am - IP Logged

    With 24 permutations possible for any given singles combination the odds of that combination hitting in any form is 24::1000, or 1::41.67.

    I'd have to pound out a probabilities spreadsheet to determine the odds on that specific occurance you cite, but time is a little restricted for me right now.

    gl

    j

    Blessed Saint Leibowitz, keep 'em dreamin' down there..... 

    Next week's convention for Psychics and Prognosticators has been cancelled due to unforeseen circumstances.

     =^.^=

      Badger's avatar - adu50016 NorthAmericanBadger.jpg
      Wisconsin
      United States
      Member #1303
      March 27, 2003
      1508 Posts
      Offline
      Posted: June 7, 2006, 6:53 am - IP Logged

      With 24 permutations possible for any given singles combination the odds of that combination hitting in any form is 24::1000, or 1::41.67.

      I'd have to pound out a probabilities spreadsheet to determine the odds on that specific occurance you cite, but time is a little restricted for me right now.

      gl

      j

      That's okay, john. I appreciate the information you have given. Thanks.

      ============

      How can you tell if a politician is lying?

      Answer: His lips are moving.

        SirMetro's avatar - center
        East of Atlanta
        United States
        Member #6191
        August 11, 2004
        1389 Posts
        Offline
        Posted: June 7, 2006, 9:10 am - IP Logged

        Take in consideration there are 55 Pairs. In combination with Paurth's Hot/Cold Counter, you could very well narrow in on the pair you think is most likely to come and combine it with the 55 pairs ($13.75 cost online, if you play online, 27.50 if you don't). Look in the Pick4 Forum at the Idea that TnT has presented. From my viewpoint, it's working very well. Also, when tracking numbers, instead of hunting ALL 4, hunt down the 3 most likely ABCx (let x = 0 thru 9). This gets you down to 10 sets instead of 55.

        Good Luck

        Sir Metro

          Thoth's avatar - binary
          Findlay, Ohio
          United States
          Member #4855
          May 28, 2004
          400 Posts
          Offline
          Posted: June 7, 2006, 10:55 am - IP Logged

          Data for the Pick 3 is available easily in many places. But I've become a lot keener on playing Pick 4, and the various breakdowns don't seem as readily available.

          So if any of you are into P4 I'd appeciate you reading this post and correcting me if anything that follows is incorrect.

          In terms of BOXED combinations for P4, I'm coming up with

          210 single combos

          360 doubles combos

          45 "double" doubles combos

          90 triples combos

          10 Quads

          That's a total of 715 possible boxed P4 combos.

          Now, I'm trying to figure the math on something and here it is.....in Wisconsin, the boxed combo 0246 has skipped over 3,000 drawings. That seems an awful lot to me, even though the singles combos account for only 30% of all the possible combos. The thing has not hit in any of its permutations in over eight years !

          So I'm wondering...how often, statistically, should any particular "singles" combo hit in a Pick 4? Anyone out there that knows the math?

          Badger,

          There are 24 different ways that 0246 can be drawn out of the 10,000 possible permutations that are possible for each drawing in the Pick 4.  This equates to odds of 24 in 10,000 or 1 in 416.666 when reduced.

          Below is the percentage of chance that a no-match boxed Pick 4 combo will be drawn within a measured amount of consecutive games.  These figures are very accurate:

          50% = 289 games

          75% = 577 games

          85% = 790 games

          90% = 959 games

          95% = 1247 games

          99% = 1917 games

          99.5% = 2205 games

          99.9% = 2875 games

          99.95% = 3164 games

          99.99% = 3834 games

          Statistically, you could expect to see any no-match ("single") drawn once for about every 417 games.  However, all numbers cannot perform statistically perfect like this—otherwise, each no-match combo would have to be drawn once within every 417 games, which is nothing short of being astronomically improbable.

          Heres a little analogy on the probability of 0246 (boxed) not being drawn for 3,000 games:  Suppose you take 210 quarters and write one of the 210 boxed no-match combos on the heads side of each quarter.  All 210 quarters would each contain a different combo, thus using up all 210 possibilities.  Now suppose you give one quarter to 210 diferent people and they begin flipping.  Each flip represents 289 consecutive games.... and when the quarter lands - it's either on head (number side up), which is a winner, or it's tails, which is a loser.

          Now assume that all 210 people each flip their quarter 10 consecutive times and while doing so record their results as heads or tails or wins or losses.  When the flipping is all completed there is going to be 210 strings of win-lose outcomes for the ten cosecutive flips that each quarter performed.  Remember that each flip is a representation of a 50% chance that a combo will be drawn within 289 consecutive Pick 4 games.

          If 0246 is out 3,000 consecutive games then 3,000 ÷ 289 =  10.38 flips.....

          You can compare the probability of your number not being drawn for 3,000 games to a quarter being flipped 10.38 times on tails.  Most states Pick 3 and Pick 4 have a few numbers out that far - Ohio's 0-2-3 straight just hit 13 flips without a "heads".

          ~Probability=Odds in Motion~

            Thoth's avatar - binary
            Findlay, Ohio
            United States
            Member #4855
            May 28, 2004
            400 Posts
            Offline
            Posted: June 7, 2006, 11:51 am - IP Logged

            Oh, and heres a few other probabilities for that analogy...

            The total amount of outcomes for 10 consecutive 50% chances (whether it be quarters or Pick 3 & 4 numbers) can be expressed as 2^10, which equals 1,024 possible outcomes.  Each of those outcomes is really a combination of wins and losses.  The probability for a number to lose all 10 chances is 1 in 1,024, which is also the same chance that a number will win all ten chances!

            LLLLLLLLLL OR WWWWWWWWWW

            In the analogy, there were 210 quarters/numbers being flipped for ten trials (or 50% chances).  Out of the 1,024 possible outcomes, how many different outcomes will the 210 quarters/numbers produce as a whole?  There should be right around 189 different outcomes, which means that 21 of the 210 will be assorted repeats of the others.  Supposing that 189 of the 1,024 outcomes do occur for the 10 flips (or 50% chances), then there should be an 18.45% (189÷1,024) chance that at least one number will make it 10 flips without a win.  This is calculated similar to one number being drawn in keno (P=1/4) where 25% of the possibilities are drawn giving you a 1 in 4 chance that your digit could be one of them.

            Of course the 18.45% probability is for ANY combo in general, not a specific combo, which is 1 in 1,024.

            ~Probability=Odds in Motion~

              Badger's avatar - adu50016 NorthAmericanBadger.jpg
              Wisconsin
              United States
              Member #1303
              March 27, 2003
              1508 Posts
              Offline
              Posted: June 7, 2006, 7:27 pm - IP Logged

              Take in consideration there are 55 Pairs. In combination with Paurth's Hot/Cold Counter, you could very well narrow in on the pair you think is most likely to come and combine it with the 55 pairs ($13.75 cost online, if you play online, 27.50 if you don't). Look in the Pick4 Forum at the Idea that TnT has presented. From my viewpoint, it's working very well. Also, when tracking numbers, instead of hunting ALL 4, hunt down the 3 most likely ABCx (let x = 0 thru 9). This gets you down to 10 sets instead of 55.

              Good Luck

              Sir Metro

              AHA ! Hadn't thought of that last one. Thanks !

              ============

              How can you tell if a politician is lying?

              Answer: His lips are moving.

                Badger's avatar - adu50016 NorthAmericanBadger.jpg
                Wisconsin
                United States
                Member #1303
                March 27, 2003
                1508 Posts
                Offline
                Posted: June 7, 2006, 7:31 pm - IP Logged

                Data for the Pick 3 is available easily in many places. But I've become a lot keener on playing Pick 4, and the various breakdowns don't seem as readily available.

                So if any of you are into P4 I'd appeciate you reading this post and correcting me if anything that follows is incorrect.

                In terms of BOXED combinations for P4, I'm coming up with

                210 single combos

                360 doubles combos

                45 "double" doubles combos

                90 triples combos

                10 Quads

                That's a total of 715 possible boxed P4 combos.

                Now, I'm trying to figure the math on something and here it is.....in Wisconsin, the boxed combo 0246 has skipped over 3,000 drawings. That seems an awful lot to me, even though the singles combos account for only 30% of all the possible combos. The thing has not hit in any of its permutations in over eight years !

                So I'm wondering...how often, statistically, should any particular "singles" combo hit in a Pick 4? Anyone out there that knows the math?

                Badger,

                There are 24 different ways that 0246 can be drawn out of the 10,000 possible permutations that are possible for each drawing in the Pick 4.  This equates to odds of 24 in 10,000 or 1 in 416.666 when reduced.

                Below is the percentage of chance that a no-match boxed Pick 4 combo will be drawn within a measured amount of consecutive games.  These figures are very accurate:

                50% = 289 games

                75% = 577 games

                85% = 790 games

                90% = 959 games

                95% = 1247 games

                99% = 1917 games

                99.5% = 2205 games

                99.9% = 2875 games

                99.95% = 3164 games

                99.99% = 3834 games

                Statistically, you could expect to see any no-match ("single") drawn once for about every 417 games.  However, all numbers cannot perform statistically perfect like this—otherwise, each no-match combo would have to be drawn once within every 417 games, which is nothing short of being astronomically improbable.

                Heres a little analogy on the probability of 0246 (boxed) not being drawn for 3,000 games:  Suppose you take 210 quarters and write one of the 210 boxed no-match combos on the heads side of each quarter.  All 210 quarters would each contain a different combo, thus using up all 210 possibilities.  Now suppose you give one quarter to 210 diferent people and they begin flipping.  Each flip represents 289 consecutive games.... and when the quarter lands - it's either on head (number side up), which is a winner, or it's tails, which is a loser.

                Now assume that all 210 people each flip their quarter 10 consecutive times and while doing so record their results as heads or tails or wins or losses.  When the flipping is all completed there is going to be 210 strings of win-lose outcomes for the ten cosecutive flips that each quarter performed.  Remember that each flip is a representation of a 50% chance that a combo will be drawn within 289 consecutive Pick 4 games.

                If 0246 is out 3,000 consecutive games then 3,000 ÷ 289 =  10.38 flips.....

                You can compare the probability of your number not being drawn for 3,000 games to a quarter being flipped 10.38 times on tails.  Most states Pick 3 and Pick 4 have a few numbers out that far - Ohio's 0-2-3 straight just hit 13 flips without a "heads".

                Well thank you, Thoth !  I like the figures. That 0246 combo in WI is pretty ripe and ready, as I had suspected. It's been out just over 3,000 drawings. I'm keeping your figures, above, in hard copy for future reference. Thanks a lot !

                ============

                How can you tell if a politician is lying?

                Answer: His lips are moving.

                  Thoth's avatar - binary
                  Findlay, Ohio
                  United States
                  Member #4855
                  May 28, 2004
                  400 Posts
                  Offline
                  Posted: June 8, 2006, 1:17 am - IP Logged

                  Your welcome...and ya, it does seem pretty ripe

                  ~Probability=Odds in Motion~

                    johnph77's avatar - avatar
                    CA
                    United States
                    Member #2987
                    December 10, 2003
                    832 Posts
                    Offline
                    Posted: June 9, 2006, 1:23 am - IP Logged

                    All -

                    You're absolutely correct, Thoth - the odds of that permutation hitting are 1::416.67, not 41.67 as I had originally posted. I moved a decimal point. Sorry and apologies to those affected.

                    gl

                    j

                    Blessed Saint Leibowitz, keep 'em dreamin' down there..... 

                    Next week's convention for Psychics and Prognosticators has been cancelled due to unforeseen circumstances.

                     =^.^=

                      Bryan's avatar - Lottery-002.jpg
                      Mid-Missouri
                      United States
                      Member #644
                      August 31, 2002
                      4271 Posts
                      Offline
                      Posted: June 9, 2006, 2:48 am - IP Logged

                      Hey Badger,

                      If you were after the math you got your answer, but if you think that combo is ripe for the pickin' have you taken into consideration the method of drawing has changed? Didn't everything go to computerized drawings some time back? If so, I wouldn't keep any data before the change was made. It would be like mixing apples and oranges.

                      Best of Luck,

                      Bryan  :) 

                        Badger's avatar - adu50016 NorthAmericanBadger.jpg
                        Wisconsin
                        United States
                        Member #1303
                        March 27, 2003
                        1508 Posts
                        Offline
                        Posted: June 9, 2006, 6:35 am - IP Logged

                        Hey Badger,

                        If you were after the math you got your answer, but if you think that combo is ripe for the pickin' have you taken into consideration the method of drawing has changed? Didn't everything go to computerized drawings some time back? If so, I wouldn't keep any data before the change was made. It would be like mixing apples and oranges.

                        Best of Luck,

                        Bryan  :) 

                        Hi Bryan,

                        Yeah, a couple years (a year and a half?) they went to RNG. But in spite of that, and I do know the debate offered on LP about machines vs RNG, I have found very little difference in hitting states where they use RNG vs states still using machines. I do prefer to play the machine states, but that is mostly because there are fewer of them, and I use this for a method of reducing the number of states that I have to examine.

                        I know there is likely more potential for fraud possible by someone in an RNG's state Lottery Commission, but really....I've hit just as "easily" (not that any of them are "easy") in RNG states in both P3 and P4 as I have in machine states. So, to me at least, whether a state runs an RNG or not just doesn't bother me any more. The short-term patterns show up in both, and both end up adhering to long term statisical patterns as well.

                        Mostly, success in the Daily Games seems to be a matter of picking the "right" day and state. ANd there doesn't seem to be a method for that.

                        ============

                        How can you tell if a politician is lying?

                        Answer: His lips are moving.

                          doodoohead's avatar - bioresonance therapy.jpg

                          United States
                          Member #2392
                          September 27, 2003
                          273 Posts
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                          Posted: June 9, 2006, 7:07 am - IP Logged

                           My simple way of thinking says this. SINGLE numbers only appear 50% of the time and therefore all the expected hit rates listed above would be off by at least that amount. 50% Yes?

                                 When is a single number late?

                                                                  210 singles x 24 = 5,040 

                           

                          “If what you take for granted is wrong,  that makes you rethink some other things you know.”

                            Thoth's avatar - binary
                            Findlay, Ohio
                            United States
                            Member #4855
                            May 28, 2004
                            400 Posts
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                            Posted: June 10, 2006, 11:17 pm - IP Logged

                             My simple way of thinking says this. SINGLE numbers only appear 50% of the time and therefore all the expected hit rates listed above would be off by at least that amount. 50% Yes?

                                   When is a single number late?

                                                                    210 singles x 24 = 5,040 

                             

                            ...All of the percentages and the amount of games required to obtain them are all very accurate.  The calculations don't need to account for the "50% frequency" because it's the per-game chance of a no-matched boxed Pick 4 number (24/10,000) that is used to calculate all the figures.

                            As for when a single number is late: I like to think that a single number (in boxed form) is late after 2,511 consecutive games without having been drawn—heres why:

                            The odds for a single to be drawn are 24 in 10,000 or 24 ÷ 10,000, which equals .0024 or .24%.  At 2,510.44 consecutive games, there is a 99.76% chance that any single combo you choose to play should have been drawn in boxed form.  Because the probability for the single to come up within 2,510.44 games is 99.76%, the reverse of that figure (100%-99.76%) is .24%.  Heres where I like to think that a combo is mathematically late or due...when the long-term probability for it to NOT HAVE been drawn is worse than its original odds.  The chance that a single WILL NOT be drawn within 2,511 games is .239675%, which is worse than the .24% chance that it has to actually be drawn during any game.

                               

                            ~Probability=Odds in Motion~

                              derek7's avatar - speedykat
                              IL
                              United States
                              Member #34578
                              March 4, 2006
                              198 Posts
                              Offline
                              Posted: June 10, 2006, 11:36 pm - IP Logged

                              Hey Badger,

                              If you were after the math you got your answer, but if you think that combo is ripe for the pickin' have you taken into consideration the method of drawing has changed? Didn't everything go to computerized drawings some time back? If so, I wouldn't keep any data before the change was made. It would be like mixing apples and oranges.

                              Best of Luck,

                              Bryan  :) 

                              Hi Bryan,

                              Yeah, a couple years (a year and a half?) they went to RNG. But in spite of that, and I do know the debate offered on LP about machines vs RNG, I have found very little difference in hitting states where they use RNG vs states still using machines. I do prefer to play the machine states, but that is mostly because there are fewer of them, and I use this for a method of reducing the number of states that I have to examine.

                              I know there is likely more potential for fraud possible by someone in an RNG's state Lottery Commission, but really....I've hit just as "easily" (not that any of them are "easy") in RNG states in both P3 and P4 as I have in machine states. So, to me at least, whether a state runs an RNG or not just doesn't bother me any more. The short-term patterns show up in both, and both end up adhering to long term statisical patterns as well.

                              Mostly, success in the Daily Games seems to be a matter of picking the "right" day and state. ANd there doesn't seem to be a method for that.

                              Hey,

                              Do you know exactly when they went to RNG...?

                              Anyone...?

                              /Derek7