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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

COUNTSReply
Hi Cmoore, Something is drawing me back to the lottery, I've put it down for months and haven't been on the site for a while. I saw your post and want to ask have ever tried just using two or three that are due and letting the system pick the other two or three numbers? I was talking with a friend and she does this for the pick 4 and she has had excellent results (largest is 25k multiple slip runs). So that got me think about giving it a try.
Nov 3, 2022, 12:00 am - alchemist7 - Mathematics Forum

Box odds questionReply
Of course for a straight hit the odds are 1 in 10,000, but we are talking about people who actually play pick 4. Box odds are not the same, I actually prefer to play 50/50 and for my 4538 pick in Maryland I at least get $100 for a box hit, and if I beat the 1/24 odds I also get $2500. You can always play a combo if your state has it. But a $1 combo will cost your $24 if it is a 24 way number.
Jul 20, 2023, 3:37 pm - kdsjeter - 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

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

Box odds question
In Pick 4 there are 715 different box combinations 210 singles (ex: 1234) 360 doubles (ex: 1123) 45 Double Pairs (Ex: 1122) 90 Triples (Ex: 1112) 10 Quads (Ex: 1111) My question is, if I'm playing just 2 boxes, say 1122 and 1234, then do they both have the same 1/715 box odds? Or is the double pair combo odds different since its type of combination has 45 boxes while the other has 210?
Jul 10, 2023, 3:28 pm - ScoobyDue - 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

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

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

Counting problem challenge - 6/54 Lotto
Here's a fun counting problem (at least fun to me). Suppose we have a Pick 6 from 54 lotto. (This happens to be the Texas Lotto game.) Calculate the maximum number of tickets (call it N) that could be generated such that no more than any 2 out of the 6 numbers are duplicated across tickets. Example: 5 8 9 12 46 52 and 5 8 13 17 25 36 meets this criterion. So does 5 8 9 12 46 52 and 4 8 11 15 20 22. P.S. I have not yet worked out the solution myself. The reason I picked no more than 2/6 is t
Mar 3, 2023, 12:41 pm - Orange71 - Mathematics Forum