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same exact pick 3 numbers played in the exact same order, for eve and night what are the odds?
So for Tuesday 8/22/23 Georgia pick 3 numbers for the evening draw are 858, and for the night? 858, what are the odds of that happening, I would think it's very high .
Aug 23, 2023, 2:27 am - lottoman626 - Mathematics Forum

How many repeat combinations in Cash 5Reply
While there's no guarantee that there will be a certain number of repeats, the probability of it happening at least once in 8000 draws (for a 5/35 game) is 99.999...% or very nearly 100%. To see why, start with a small example with a simpler game. What is the likelihood of no repeats in Pick 3 played straight, over a period of 2 consecutive games? That would be just 999/1000, and so the probability of a repeat is 1 - 999/1000 = 1/1000 = 0.1%. The likelihood of no repeats in Pick 3 p
Sep 11, 2022, 12:51 pm - cottoneyedjoe - Mathematics Forum

Pseudo-random numbers from irrational numbers
Here is a Python script that can generate pseudo-random numbers from the decimal expansions of irrational numbers. It uses the 'decimal' module and the 'Decimal' function within the decimal module. The basic idea is to generate long decimal expansions of irrational numbers constructed from roots, exponents, logarithms, etc. Then chop the string into chunks of 3, 4 or 5 for Pick 3, Pick 4, or Quinto. You can play around with the code to customize it to your needs. https://sagecell.sagema
Oct 16, 2022, 9:31 pm - cottoneyedjoe - Mathematics Forum

Approximating chaotic systemsReply
I had found that time series over a mostly uniform distribution tends to return an average when trying to make a prediction. Had hopes for SARIMAX when studying python time series analysis, but the predictions always came out between 4.8 and 5.2 (for pick 3). Then when you see how predictions based on ARIMA are calculated, you realize it was the wrong tool to use My focus is shifting to classification, though I am not exactly sure what it will look like just yet.
Aug 25, 2023, 8:46 pm - hypersoniq - Mathematics Forum

Florida Fantasy 5 sums probabilityReply
It's not as simple as finding the convolution/sum of a distribution function. In this case, the distribution of the sum of the numbers on a random FL Fantasy 5 ticket is already known, call it P(X). The question is finding the probability that five i.i.d random variables X1, X2, X3, X4, and X5 whose underlying distribtution is P(X) are all distinct . P(X) itself is not a convolution of five discrete uniform distributions because a FL Fantasy 5 ticket must have five distinct numbers. Yo
Feb 3, 2023, 11:27 am - cottoneyedjoe - Mathematics Forum

Approximating chaotic systemsReply
I only recently started reading about PRNGs. I was surprised to learn that some PRNGs that are considered cryptographically secure aren't one large cycle in state space, but instead have some short cycles. That indicated to me that if the PRNG was seeded to start in those short cycles, the PRNG wouldn't be random enough. I'm aware of some satisfiability modulo theory libraries used to solve for the seed given PRNG output. But in those cases, you know the PRNG because it's in the code, and th
Aug 23, 2023, 11:21 am - Wavepack - Mathematics Forum

Arithmetic Complexity in Texas All or NothingReply
It's a really awful game in terms of odds vs returns The odds vs return in most pick 3 games are less than 50% and other games are even worse. The chances of a $2 All or Nothing ticket winning something is 22.22% or 1 out of 4.5 tickets. Though it could be $10, $50, $500 or quarter million, players should expect the minimum return of about $2 for every 5 tickets they purchase. Wouldn't call it an awful game but showing a profit playing the game might require winning the jackpot.
Jul 1, 2023, 2:52 pm - Stack47 - 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

Expected Value of Lottery Jackpot, Given You Are A WinnerReply
This is an interesting topic, nice write up. In the past I have run simulations to find the probability distribution of the number of jackpot winners (under the assumption every ticket is a quick pick to simplify things) varying the parameters of total number of combinations and number of tickets sold. For example, in a 5/39 game, which is common in many states, there are 575757 combinations (a more manageable number). If 575757 quick picks are sold, the likelihoods of 0, 1, 2, 3, and 4+ jac
Jul 19, 2022, 12:59 pm - cottoneyedjoe - Mathematics Forum

COUNTSReply
Some numbers may not hit for 30+ plus draws. 36 has currently been out for 42 draws. I don't think it's a good strategy to pick 2 or 3 numbers that have been out for say 20+ draws and start to key them. You might be chasing for awhile. And usually one will hit by itself. It's very rare to get both hitting at the same time. Now if you keep stats and are tracking and have statistics on each number or draws out. Then that could help. But randomness can still bite you in the butt. In the rolling cas
Nov 6, 2022, 2:58 pm - Cmoore50 - Mathematics Forum