Many years ago I was asked to help write software to assist lottery players in "selecting their numbers". I was very careful not to make statements like "better chance of winning" or "improved odds" because mathematically speaking, it is impossible to change the probability of any particular event happening.
That said, it is not at all difficult to put together wheels and other systems that change the probability of a win and the pattern of what might be won, but ultimately, the expected amount won will always be the same.
For example: A simple 5 of 6 combo wheel looks like this:
A B C D E
A B C D F
A B C E F
A B D E F
A C D E F
B C D E F
You simply set A B C D E and F to the values of your 6 favorite numbers, and if any 5 of the 6 numbers occur in the draw, you are guaranteed to win a Match 5. The cost is 6 times a single ticket, and the probability of matching is 6 times better than a regular ticket. If you match 4 or 3 (and there are prizes for that) you will win multiple Match 4 and Match 3 prizes.
Sounds pretty good.
However, if you buy 6 Quick Picks, your overall expected likelihood of winning and the amount you will win, over time at least, will be exactly the same. The actual prize amounts will vary slightly, but there is no difference to the expected total return over a long period of time. In fact, even the variation between the expected value and what might happen in 99% of cases (a statistical confidence interval) will get smaller the more you play. Ultimately, if the game pays 50% ... you will win 50%.
This is especially true of numbers games like Pick 3 or Pick 4, where the odds are not all that large, and a heavy player is expected to have a few top prize wins in a lifetime of play. The more you play, the more likely you are to return 50% (or whatever the game is designed to payout ... some lottery games I have seen pay out as much as 65%, and I am sure there are some that are higher).
Every system I have ever seen (and I have seen a great many) has this same aspect when looked at purely from a mathematical perspective.
So, is there any way to improve the odds?
The only one I have ever been able to come up with is Jackpot Chasing, and there are two parts to it. Of course, this will only work on games with rolling Jackpots, but it does not really matter if it is a small game with a Jackpot in the $10,000 range, or a big game like Powerball or Mega Millions. If you want to improve your expected return, the only way this can be done (in my opinion) is as follows:
1. Don't make any wagers when the Jackpot value is low.
Look at the odds of winning the game. If they are 100,000 to 1 and the Jackpot is $25,000, then you only expect to get 25% back from the Jackpot. Assuming another 30% in lower tier prizes, the expected return for a wager is only 55%. Wait (in this case) until the Jackpot is around $70,000 or higher before wagering. If you normally wager $10 per draw, and you do not wager on 10 draws prior to the Jackpot reaching this level, you can wager $100 on the enriched Jackpot, and all 100 wagers have a 100% expected return (much better than the 50% or so when the Jackpot is low).
2. Make your wager on unpopular numbers.
One of the unfortunate aspects of high jackpots is that often they are shared by more than one player. Of course, this could happen when the Jackpot is low, but low Jackpots usually do not have as many sales, so the probability of splitting the Jackpot is also lower. When the Jackpot is high, the probability of a split increases. To offset this, it is advantageous for players to select uncommonly selected numbers. While the prevalence of Quick Pick plays makes it harder to find absolutely unpopular numbers, it is nevertheless still advantageous to avoid those numbers that are commonly played by the general populous. Any number between 1 and 12 tends to be selected rather frequently, then numbers between 13 and 31. These are the numbers corresponding to birthdays. Multiples of 7 and 8 are also common selections. And for some reason, numbers ending in 0 (multiples of 10) tend to be selected less often than other numbers.
If your lottery offers a chart of what numbers are selected most often by the players, it could be helpful in selecting uncommon combinations as well.
This system is not going to make you rich. There are no implied promises here. It is just the most advantageous way I can think of to play the lotteries. I do not know if it qualifies as a "secret", but anyone who is interested is welcome to try it out. If you are interested in more specific information about a game you would like to play, let me know and I will try to work out what a good Jackpot level might be.
Also, there is one "caveat" to this approach.
Caveat: If high Jackpots result in extremely high sales, such that the ticket pool is overly saturated, the actual expected return can drop based upon the high probability of a multiple win (the Jackpot is most likely going to be shared). In a game like this, the maximum return occurs before the Jackpot brings the expected return to 100% or higher. In such games, it is better to play when the Jackpot is slightly lower than desired, but this also results in a lower expected return (under 100%). If you are interested in such a game, this approach will be better than a fist full of Quick Picks on every draw, but it is still going to result in less that a 100% expected return.
Enjoy and have fun!