Jade has done a lot of hard work and posted it for us to use, if we wish. With all due respect, Tucker Black, from this post, you don't seem to believe in "game theory" which is pure mathematics. in fact you utter these words:
"This is the superstition of "numbers chosen more frequently in the past are more likely to hit in the future" which is just as false as the superstition "numbers chosen less frequently in the past are due to hit in the future".
I have written lots of programs to simulate the lottery, not to try to make predictions (since it's impossible). I do this to get a probability distribution of winnings for buying n tickets. I never buy the tickets, I'm just curious to see how big n needs to be to reduce the probability of winning nothing below p, see what the median is, and the mode. The expected value is easy to calculate and does not require millions of simulations. The expected value (i.e., how much you win on average for one ticket) is very important. The lower the value, the more of your wager the state gets. Even if a game had an expected value of 100%, you can still lose (and there is no game like that with the exception of side bets at craps at some casinos in Las Vegas)."
Tucker Black, your statement is incorrect. Your focus on N as the number of tickets rather than on the numbers or draws themselves is the statistical flaw in your game. You use words like "superstition." This is a mathematics forum, not the other forums (which I am not able to comment on because I have not studied their methods). In mathematics, however, the statistical probability of the next draw number group can be deduced to a small group strictly from past draws if you have some idea of how to set up your statistical programs. Simple college statistics, if that. But to say that the only way to win is to buy 15 tickets with the MB number 1-15 is simply missing the point. If you have written programs "for fun" and they work, I suggest you get 5 dollars and go play the Pick 5 the next chance you get. When you have money on the line and a good statistical system to limit "bad" numbers, the odds of smaller wins (non-jackpots) become better than Blackjack or even Poker odds.
I am not being mean, I hope, and that is not my intention. Having some skin in the game will motivate you to develop winning programs. You seem to understand statistics but cannot apply them to lotto. Lotto is statistics, mathematics of draws and numbers as N. Jade is a superstar, sharing his knowledge with faith-filled and expectant lotto players. I say this sincerely, Tucker Black: if you think it is "impossible," that this is all "superstition," you have lost before you have even played. You should not play and waste your money with that mindset. The world is filled with people who need to see proof of any future event in order to believe it. Good luck with that theory playing lottery. Rich or poor, a person without faith is the poorest of the poor. Faith is more important than even knowing the next draw's best group of probable numbers.
To all Tucker Blacks: if you think lotto mathematics is "superstition" and "impossible," you will be correct in your personal draws; play quick picks or just play for the fun of it.
Make America great again. One draw at a time.