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.
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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.
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[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.