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Minimal parameter system approximation
Given the last N lotto draws, D i i = 1..N, determine the IFS (iterative function system), x i+1 = f(x i ), D i = g(x i ), which generates Di with minimal B f , B f = number of bits needed to specify the parameters in f(x) and g(x). f(x) and g(x) can be any combination of any operators. If you restrict f(x) and g(x) to be linear, then this is equivalent to finding the minimal state discrete linear system which duplicates the output. I conjecture that this minimal parameter iterative func
Sep 8, 2023, 10:19 am - Wavepack - Mathematics Forum

Nature of Randomness in Mechanical Systems
I recommend reading the book Dynamics of Gambling: Origins of Randomness in Mechanical Systems if you want a good understanding of exactly how randomness arises in coin flipping, dice throwing, and the roulette wheel. In particular, Chapter 5, entitled Nature of Randomness in Mechanical Systems The authors model mechanical systems in high detail to allow them to calculate the bounds on initial condition uncertainties needed to allow correct prediction. They do not model a lotto bal
Jan 14, 2024, 2:27 pm - Wavepack - Mathematics Forum

Nature of Randomness in Mechanical SystemsReply
The notion that collisions of balls in a lotto machine can be predicted such that some advantage can be gained in a fair game is utterly nonsensical. It defies all logic and reason. Now, if there were to be fraud, such that certain balls intentionally had heavier weights, that's a different story. However, I have never heard of that been shown to happen in any State-run lottery, ever.
Feb 5, 2024, 8:38 pm - Orange71 - Mathematics Forum

Shuffling and Mixing
Lotto ball machines work well to randomize ball picks because of their mixing properties. A closely related problem is how many shuffles are sufficient to randomize a deck of cards. The following curve is pulled from an AMS (American Mathematic Society) post on this topic. A link to the post is given below. https://www.ams.org/publicoutreach/feature-column/fcarc-shuffle d is a measure of how close the pdf (probability distribution function) of the card ordering is from uni
Dec 24, 2023, 5:01 pm - Wavepack - Mathematics Forum

Megamillions number frequency - probability puzzle
In Megamillions there are 70 numbers in the main lotto pool (not counting the Megaball). 5 numbers are drawn from this pool in each game. Consider 50 random game draws. What is the probability that at least one number (ball) will (a) never occur in the 50 draws, and (b) occur in at least 10 game draws?
Nov 17, 2023, 1:46 pm - Orange71 - Mathematics Forum

Approximating chaotic systemsReply
What is the minimum number of past lotto draws to use for prediction? My data is up to 1530 draws. This is for a 5/39 game.
Oct 10, 2023, 8:47 am - Cmoore50 - Mathematics Forum

Approximating chaotic systemsReply
Chaotic systems are a subset of nonlinear systems. The following Nonlinear Dynamics video series by Prof. Liz Bradley , a course funded by the Santa Fe Institute, is worth a watch for better understanding nonlinear systems and practical issues when characterizing them. https://www.youtube.com/playlist?list=PLF0b3ThojznQ9xUDm-EbgFAnzdbeDVuSz During the course, she mentions a Nonlinear Time Series Analysis book, which is also worth looking at. The author of that book gave a talk wher
Sep 19, 2023, 8:16 am - Wavepack - Mathematics Forum

My fascination -The first digitReply
Please explain what this contest means. You're picking a single white ball from 1 to 69, correct? (That presumably corresponds to the Powerball lotto.) Then, your pick is compared to actual (5) lotto winning number results. Correct? Do you win if your pick is any of the 5 actual drawn numbers or only the first one? You were a 12-time winner in 2022, and you are an 8-time winner this year so far, is that correct? How many draws is that in both cases? Let's get the parameters down
Aug 19, 2023, 10:32 am - Orange71 - Mathematics Forum

Craps Pass Line SimulationReply
Thanks cottoneyedjoe. I may adapt this for a lotto game, like Powerball or Megamillions, just for the fun of it (and to see how much money a player is likely to lose over a lifetime, even with a modest weekly expenditure). If I do, I'll post it here. I'll also check out that crypto PRNG package.
Jul 31, 2023, 7:13 pm - Orange71 - Mathematics Forum

Mega Millions Just The JackpotReply
There are numerous famous cases of PRNGs not being properly seeded, or the PRNG being weak. Any cryptographic algorithm based on those weak PRNGs can then be cracked in reasonable time. Windows had a weak PRNG for a long while. In the lotto world, a bad PRNG or PRNG seeding would result in excess repeats and pick biases.
Jul 19, 2023, 8:29 pm - Wavepack - Mathematics Forum