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Approximating chaotic systemsReply
I don't know if this will help or not, but in both MM and PB they do two test draws that you don't get to see. So your numbers could have come up in the test draws. The winning numbers that come up are in past draws even the powerball or mega number. So pick 25-30 numbers and 5-10 bonus numbers from the past draws and pick from that pool of numbers and you have a better chance of winning, or you can just Quick Pick.
Oct 10, 2023, 4:02 pm - Down - Mathematics Forum

Math challenge - Mega Millions white ball range
There are 70 white (main) balls in Mega Millions. The player chooses 5 balls from 1 to 70 (or opts for a Quick Pick to randomly choose the same). Define R (for range) as max ball - min ball + 1 . For example, if the player chooses the balls {1, 2, 3, 4, 5}, then R = 5. Now consider the case where the balls are chosen randomly, such as a Quick Pick or lottery drawing for the winning numbers. R is now a random variable, and the set of all possible values of R is {1, 2, 3, ... , 70}. Suppose th
Apr 29, 2023, 11:17 am - Orange71 - Mathematics Forum

Chances of 1,2 or three winners in PowerballReply
The Lottos really should publish the repeat distribution, and number of plays per customer transaction, so that that P(x) could be better estimated. Also, their quick pick PRNG repeat distribution should be published. That would expose any problems with the PRNG and its seeding.
Jul 19, 2023, 8:22 pm - Wavepack - Mathematics Forum

Mega Millions Just The JackpotReply
Interesting that the EVJ peaks. What assumptions did you make on repeat ticket picks? The PRNG (pseudo-random number generator) used in the Lotto ticket generating machines have not been been openly published, which is concerning. If those PRNGs are not seeded with enough bits of entropy (randomness), or the PRNG has a weakness, then the PRNG will not have a uniform pick probability, resulting in more repeats than expected from the quick picks.
Jul 19, 2023, 8:07 pm - Wavepack - Mathematics Forum

Chances of 1,2 or three winners in PowerballReply
OK. My local TV news in TX says the cash value of the $1 Billion PowerBall Jackpot after income taxes is $325 million. (You would instantly become an evil 1%-er.) The probability of a single random ticket winning is 1 in 292201338. Nobody knows how many tickets will be bought before the fact, but 350M might be a reasonable (very rough) estimate based on history. If everybody bought a Quick Pick, the Expected Value of the cash after-tax Jackpot (per the Binomial Distribution) would be about $189
Jul 19, 2023, 8:05 pm - Orange71 - Mathematics Forum