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Math or Data help please

Topic closed. 30 replies. Last post 4 years ago by SergeM.

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Posted: May 1, 2013, 10:46 am - IP Logged

 Hi adobea78 !  Speaking of doubles... LOL   Right? 

  How about a philosophical focus on that doubles question up there.

 

   I had a sister that worked very hard getting her degree in philosophy.

  Boy, was she was surprised at the end of her fourth year when her college had "career day".....and none of the big Philosophy Companies even showed up!   LOL

Wind, I understand and get all  pertaining to  stats, probabilities etc, but be mindful that all these concepts  started with assumptions and logic, hence mathematical formulas!. I am not discarding  these concepts, I am trying to understand randomness, probability(very fluid concept). The Brain is not just a data reservoir, our perception is limitness, thanks for the sarcasm about your sister, nice ad hominen!.

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    The Quantum Master
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    Posted: May 1, 2013, 2:28 pm - IP Logged

                  We are looking for some help for a Doubles Trap in Pick 3.        What is the best strategy math wise....and perhaps backed up with some data.   

     

     

                         question:            What is the most effective Window of Oportunity to catch a double play.....any double? 

     

                  Here is a pretty effective day to day strategy suggestion over in the Systems forum.... http://www.lotterypost.com/thread/259964

                           

                       We need to check our ......3 day window suggestion.  The current KILL Zone suggestion is the 8th. 9th and 10th. day window.

             

                                                               This is the current 3 day play window..... then STOP Play after the 10th. day.

     

     Note: This is more a Multi state strategy ......and so

        Out of the approx 69 p3 games going on right now......only 5 state games have reached the 3 day Window of opportunity....and only one that has gone past it so far. Only 4 games are in the current Kill Zone right now. This is about the average at any given time. 

    Before we get started.

    There are a few posts we made that may help understand the timing of your plays as it relates to the Reoccurrence of Doubles.

    They are:

    Discharging Reoccurrence Distribution

    Potential Reoccurrence Probability

    Potential Occurrence Probability

    First and Second Order Work Equations

     

    Also, for reference, when we write about Draw Difference it is similar to the common terms: Skip, Hit.

    The Draw Difference is how many draws between events.

    If an event happens at draw X and then reoccurs at draw Y, the Draw Difference is Y minus X.

    In a mathematical expression, Δd = Y - X .

    Continues...

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      Posted: May 1, 2013, 3:08 pm - IP Logged

      If we look at the expected and the actual distributions of the Draw Differences for my state's lottery MN Daily 3, we can see how the Discharging Reoccurrence Distribution equation looks compared to the actual observations.

      We will use the past year's drawings from 2012-05-01 to 2013-04-30 in this example.

      The basic equation is y = (d / μ2) e-(Δd / μ) , where y is the approximate expected frequency, d is the total number of draws, Δd is the draw difference, and μ is the average rate of reoccurrence.

      In this case, d = 365 and μ = 1000 / 270 ≈ 3.7; 1000 being the total number of all combos and 270 being the total number of doubles possible.

      Continues...

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        The Quantum Master
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        Posted: May 1, 2013, 3:15 pm - IP Logged

        Below is a graph of the calculated approximation and the actual observation.

         

         

        The actual tends to follow the calcualtion, dimishing in frequency with increasing Draw Difference between events.

        Continues...

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          The Quantum Master
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          Posted: May 1, 2013, 3:40 pm - IP Logged

          The Draw Difference distribution is related to the Potential Reoccurrence Probability.

          The basic equation is y = e-(Δd / μ).

          This shows the draw relative probability of the event reoccurring again.

          For the Doubles, we can see the probability of a Double happening again is pretty high just after is has happened and begins to dimish as more draws go by.

          About 48% of all doubles will reoccur within the next 3 draws.

           

           

          Continues...

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            The Quantum Master
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            Posted: May 1, 2013, 3:53 pm - IP Logged

            Now, getting to the other observations of the 8, 9, and 10 Draw Differences.

            We need to expand this a little bit.

            There are two different routes to follow.

            The first is the expansion into the First and Second Order Work Equations, and possibly higher order work equations we have not posted here.

            The second is the examination of the sub components that make up a Double, sub components meaning the different kinds of Double possible and how it relates to the overall Doubles observation.

            Continues...

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              Posted: May 1, 2013, 4:11 pm - IP Logged

              We have thought about this question, too.

              "When is the optimal time to play knowing when something has just happened?"

              Well, it does look like the optimal time is just after when the event has occurred.

              However, there is another aspect of the event happening again, it's the Potential Occurrence Probability.

              This just simply means how long does it take, just after the event occurred, for it to happen again.

              The Occurrence Probability is complement the Reoccurrence Probability.

              The Reoccurrence can be thought of as what's the chance it will happen at a given draw difference, possibly now, since it last happened.

              The have different meanings, but they are tied to each other.

              Both of these probabilities add up to exactly 1.

              Continues...

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                Posted: May 1, 2013, 4:44 pm - IP Logged

                Before we move on, let's work on the Draw Difference.

                The Draw Difference is just how many draws between events.

                If we saw that an event happened at these draws: {3, 9, 18, 21, 37}, then the Draw Difference is: {9 - 3, 18 - 9, 21 - 18, 37 - 21} or {6, 9, 3, 16}.

                To get to the next draw, if we say we are looking for someting to happen again, then we would add our estimated Draw Difference to the last time we knew when it happend to get the next approximate draw we need to play.

                Let's say we saw in our doubles data that it last happened on draw 1928 and we estimate to happen again 7 draws later, then the next draw to look for it is 1928 + 7 or 1935.

                Now, whatever that translates into a date, you'd have to figure out due to the fact that draws can happen on certain days for different lotteries.

                Continues...

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                  Posted: May 1, 2013, 5:45 pm - IP Logged

                  The First and Second Order Work Equations were derived from the Potential Occurrence Probability and Reoccurrence Probability.

                  Each Work Equation has its complement and is used to derive the next order level.

                  The equations were setup to balance the possibility of an event happening at a given instant and how long it will be from the last time it happened.

                  Each is also based on the Draw Difference.

                  We can plug in some values like we did in the Potential Reoccurrence Probability and see how they relate to each other.

                  Below we can see the Reoccurrence Probability is high just after the event, then diminish as more draws go by.

                  The First Order Work Equation starts at about the same as the Reoccurrence Prrobability, goes up to a max at 3 draws later, then diminishes with increasing draw difference.

                  The Second Order Work Equation again starts at about the same level, then drops quickly and returns to a maximum at 7 draws later; it then diminishes after that.

                  Individually these give their own optimized maximum and can be used to approximate a draw difference to play doubles.

                  However, we can combined them to give a more complete out look on optimization.

                   

                  Continues...

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                    Posted: May 1, 2013, 6:03 pm - IP Logged

                    We combined the individual probabilities by summing them and then do a Normalization of the curve to get it fit between a value of 0 to 1.

                    Below we can see how the combined probability curve looks.

                    It starts high at the beginning, does a little bounce at about 3 draws later, goes high again at about 6 draws later then begins to fall off to 0.

                    We can also see that at about 10 draws later from the previous event the probability drops below 0.5.

                    This may also explain the beyond 10th draws later STOP play reasoning, but there is more and more that can be optimized.


                     

                    Continues...

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                      Posted: May 1, 2013, 6:23 pm - IP Logged

                      Let's carry the Work Equations out to 20 levels.

                      When we do that, the curve looks a little less like a curve, or at least at this sample rate.

                      Below is the graph and shows the erratic nature of including more levels.

                      If we set a threshold of 0.75 as a limit and anything above that threshold is playable, then we can see the play times happen at {1, 2, 3, 4, 5, 6, 10, 11} draws later after the last event.

                      If we use the previous post as an example, then with a threshold of 0.75, the draw differences become {1, 5, 6} for the playable draws after the last event.

                       

                      Continues...

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                        Posted: May 1, 2013, 6:51 pm - IP Logged

                        We have made a graph showing a few more levels above the First and Second Order Work Equations to see how the increasing levels become very erratic at the beginning then smooth out.

                        This is what we can do when the sample rate is increased between draws.

                        Out at 20 levels, the Work Equation is extremely erratic near 1 draw difference from the last event.


                         

                        Continues...

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                          Posted: May 1, 2013, 7:25 pm - IP Logged

                          Next we can look at the sub components.

                          The sub components for a Double are the three different ways a double can happen.

                          These are: XXN, XNX and NXX, where X is the doubled number, N is some other number and X ≠ N.

                          If we divide these up and look at the individual draw differences for this event, the average rate of reoccurrence is 1000 / 90 = 100 / 9 ≈ 11.1 .

                          We can apply this average rate to the same Potential Reoccurrence Distribution to see how this looks and compare it to the overall Doubles.

                          The graph below shows the expected frequency for both the overall Doubles and the individual Doubles.



                          The current frequency scale doesn't show it very well, we can change it to a Natural Log Scale to see how these distributions converge at a Draw Difference of 12.

                          Below we can see that after a difference of 12 draws later after the last event there is a less than 1 expected frequency.

                          Doesn't mean it can't happen, just means that for one years worth of draws there is very little happening beyond 12 draws.

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                            The Quantum Master
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                            Posted: May 1, 2013, 9:13 pm - IP Logged

                            Here are the reoccurrence probability and first 4 work equations.

                            We would like to post the others beyond 4, but they are Huge.

                            Reoccurrence Probability

                            First Order Work Equation

                             

                            Second Order Work Equation

                             

                            Third Order Work Equation

                             

                            Fourth Order Work Equation

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                              Posted: May 1, 2013, 9:40 pm - IP Logged

                              To find higher Work Equations, use the following:

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