Have you ever put together a historical listing of all the combos drawn in your states Pick 3 game and wondered why there are so many combinations that have never hit? Have you ever noticed how some combos hit with a much higher frequency than others? Have you ever wondered just how long it will take for all of the 1,000 pick 3 straights to be drawn in your states game? The answers to these questions can be found within the laws of probability.
Believe it or not, the laws of probability actually dictate the long term performance of the game. The projected long term outcome for EVERY Pick 3 game IS highly predictable. In essence, every Pick 3 game in the country is identical with respects to how the randomness within each game operates. There is a very real and distinct timeline that all Pick 3 games follow. I like to call this timeline the Matrix Completion Cycle. Many trackers and game analyzers prefer to gather statistical data and derive approximated probabilities or expected results from them. I like to do just the opposite...first I calculate the probability, then I watch the stats verify them like magic.
So, how long will it take for every Pick 3 number to be drawn in your state? Heres a formula that dictates the answer: log(1-MP)/log(1-p). This is saliu's formula with the "DC" replaced with "MP". The formula doesnt really change any but the logic in it does slightly. The MP is used to denote the "Matix Percentage"...which is any percentage of the matrix entered as a decimal. So 50% is .5 and 75% is .75 etc. Now, since the game is random and nothing can truly be predicted with absolute certainty, do not enter 100% (1.00)! You can, however, enter 99.99% (.9999)...or as many nines as you like. The "P" in the formula is the decimal probability for each straight combo in the matrix. In Pick 3, each straight combo represents 1 in 1,000, so the P is 1/1000, which equals 1÷1000 = .001.
Simply put, this formula will tell you how many consecutive games must take place before you can expect to see a specific percentage of the matrix drawn! As an example, if you wanted to know how many games it takes to get to the point where 750 of the 1000 possible straights are drawn, you would run the formula as: log(1-.75)/log(1-.001). The formula then spits out the number 1385.601. Which means 1385.601 consecutive games or 1386 when rounded. The number of trials this formula spits out for any percentage entered into it is extremely accurate! Take a look at the first 1386 games in your state and count how many DIFFERENT Pick 3 straight were drawn. It will be very, very close to 750!
I labeled this post as the Matrix Completion Cycle. The word "completion" can be paralelled to the term "100%", which I just said to never use in the formula, so I should probably clarify what i mean here little better. The matrix is completed when all 1,000 combos are drawn. To project all 1,000 combos would imply 100% of the matrix. Since we can't honestly use 100%, the next best thing will have to do, which in this case is the 99.9% mark. Of the 1,000 combos in the matrix, 99.9% equates to 999 combos. The number of games given by the formula is accurate, but is better to treat the figures as close approximations. Most state will not measure up perfectly...meaning that the actual amount of different numbers drawn will normally be slightly over or slightly under the calculated expected result, but I assure you, they will be very close! Since there is a minor fluctuation in the actual results, many times the one last combo (or last few combos) will hit before or soon after the 99.9% mark...which is 6,905 consecutive games. It's usually those last one or two combos that many see as the great anomalous stinkers that seemingly defy the odds.
The first of the three graphs below illustrates the expected percent of matrix to be drawn within a givin number of games. Notice how the line crosses the 50% mark at 693 games. It only take 693 games to have very close to 500 of the 1,000 pick 3 combinations drawn. The odd part is, you usually wont see the the last of the other 500 non-hitters until sometime between games 6,237 and 7,623, which is the 99.81% to 99.95% range! This is the range where most states Pick 3 matrices are completed!
Rather than using percents, the next chart shows the actual amount of combos drawn within the listed consecutive number of games. I used the entire histories of Indiana, West Virginia and Georgia. Notice how closely each state follows the expected result!. Note: the ending points on the graph indicate that all three states completed their cycles on game 6237. This is not really the case, all three states had the their last combo drawn between games 5544 and 6237, but this would have requred alot more work to illustrate on the graph. Other than that, the data points are all valid and accurate.
The last graph shows the amounts as percentages. Here again, it's amazing how closely the six listed states follow the calculated and expected result! Each of the states follows so closely that it becomes difficult to discern one line from another. If we added the three states from the graph above, they would follow along just as well.
For each of the nine states, here are the actual drawing# that their cycle or matrix was completed in as well as the combo the hit:
STATE | GAME | COMBO |
OH | 8118 | 157 |
PA | 7623 | 214 |
NJ | 6092 | 453 |
MD | 6371 | 720 |
IL | 5883 | 698 |
MI | 8044 | 486 |
WV | 6132 | 516 |
GA | 5712 | 848 |
IN | 5973 | 063 |
There is much more to discuss regarding this data, I'll post more before the weekends through.