Monday, October 1, 2012

Introducing the Lottery Probability Surface

In an effort to help players find a financially feasible strategy for playing the lottery, we discovered an important organization inherent in all lottery games.  By reducing all the combinations of a particular game into individual sum and range buckets, and then totaling those occurrences, have identified each game's "probability surface".

The surface is constructed using the only the primary white balls and not the bonus balls.  One axis of the surface consist of the Sum of all the balls.  And, the second axis is defined by subtracting the last ball from the first ball (the X and Y axis are interchangeable).

Doing this, for Pick 3 and 4 games which allow all selection for replacement, the resulting surface is that of a diamond. The reason for this pattern is that the last ball may be less than, equal to, or greater than the first ball, thus allowing the Range to progress from negative to positive values.  The illustration below is a 3-D view of the Pick 4 probability surface.

Pick 4 Lottery Probability Surface (3-D)
3-D Image of Pick 4 Lottery Probability Surface

For those games which do not have replacement (such as Mega Millions, Powerball, Lotto 649, Texas 2 Step, etc), we ignore the order drawn and sort the numbers from lowest to highest value. Doing this, we define a shape that is trapezoidal in shape. The illustration below is a 3-D view of the Texas 2 Step probability surface. This shape similar to that of Powerball, Mega Millions, etc. However, its scale is more condensed.

Texas 2 Step Lottery Probability Surface (3-D)
Texas 2 Step Lottery Probability Surface (3-D)

During the coming months, we will publish the probability surface characteristics for each of the lottery games that we cover.  In addition, we will be adding new analytic pages to our website summarizing the historical data of each game.

Our first application using this new discovery will be the Pick 4 games. We are well into the development of studying the New Jersey Pick 4 and hope to release this in the next few weeks. Following that, we will apply the same template to analyzing the Pick 4 games which we can easily obtain the complete drawing histories (California, Texas, North Carolina).

JL ..........

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