JustMaybe & winoneday,
Sorry for the delay, but life in general and my sleeping disorder issue put me out of commission for a little while.
Everything below refers to the 5 white balls of PowerBall, the PowerBall is not considered as it just multiplies everything by 26.
The list I am playing from comes from a wheel that I have developed over the past 18 months or so. I never really documented the start date and I had about 2 months of inactivity, so 18 months total is about right.
The wheel generator took all 864,501 combinations of 4 numbers from 1 to 69 and compressed them down to a 100% coverage of 4 numbers in 186,146 playable lines of 5 numbers. Which is much better than the 864,501 total of 4 number combinations, don't you think?. And yes, every number from 1 to 69 is used in the generated playable lines with a variance of most used minus least used = 53. Not *exactly* balanced for all 69 numbers, but it is not bad at all for the number of playable lines produced.
For this exercise I am working from a reverse point of view. Instead of trying to find 4 number hits (or 5) by picking numbers to play, I am working on finding ways to reduce the ways to miss 4 number hits. And, also providing a better shot at getting a 5 number hit from just playing combinations in the list.
For a single 5 number ticket played out of the list that is now 186,145 ways, and occasionally two 4 number hits are there (See 04/12/2025 below) leaving 186,144 ways to miss a 4 number hit. I kind of relate this to "Fishing for 4 number hits in a much smaller pond".
For every 5 number ticket in the entire realm of 11,238,513 5 number combinations, there are only 320 ways to hit 4 numbers. That is 4 numbers plus 1 each of the 65 remaining minus the 5 used balls, or (5*65)-5 = 320. So, 11,238,513-320 = 11,238,193 ways to miss a 4 number hit on each ticket. I prefer 186,145 ways to miss a 4 number hit.
This seems pretty wild to me and I have argued with and questioned Copilot in different ways for several hours over a period of time. Usually, if I say "Are you really, really sure?" I can get a different answer but not this time, as much as I tried. If the 320 number and resulting calculation is wrong, please provide a proof and I will have learned something new. I do not mind being corrected if the correction is true.
Overall, the list has a 1 in 65 chance of having a five number hit. It will always have one 4 number hit and there are only 65 numbers left to make a 5 number combination. And that happens from time to time. If there is no 5 number hit, there will always be five 4 number hits in the list and I have seen as high as seven 4 number hits. It all depends on the numbers in the list and the numbers drawn.
As for 5 number hits occasionally happening,here are the results of the backtesting I have done:
Total Since 10/7/2015 - 1,242 Draws
25 Straight - 1.86% 5 Ball Hits
22 Number Substitution - 1.64% 5 Ball Hits
47 Total 5 ball hits
*Number substitution statistics will vary according to how you arrange your substitutions.
Since 01/01/2025 - 102 Draws- 2.94% 5 Ball Hits
Straight: 102 Draws- 2.94%
04/12/2025 16 22 44 45 53
Hit 5 1
Hit 4 1
Hit 3 340
06/23/2025 5 25 42 44 65
Hit 5 1
Hit 4 0
Hit 3 342
07/02/2025 7 19 21 54 63
Hit 5 1
Hit 4 0
Hit 3 335
Number Substitution: 102 Draws- 2.94% 5 Ball Hits
01/15/2025 8 41 52 53 58
Hit 5 1
Hit 4 1
Hit 3 343
03/26/2025 5 20 29 39 53
Hit 5 1
Hit 4 1
Hit 3 343
08/23/2025 11 14 34 47 51
Hit 5 1
Hit 4 0
Hit 3 344
So far this year the list is exceeding the expectation of 1.66%.
And, this is an *HONEST* backtest. The wheel generator had no access to past winning combinations and therefore was not *influenced* by them while calculating. The playable combinations were produced "blind" as a mathematical function of number distribution.
Also, I can play from the list either of two ways. One way is a straight 1 to 1 use of the combinations as they were generated for the list. Or, I can use a number substitution method like the list=5 and I play=37 throughout all 69 numbers like a decoder wheel for kids) whichever I prefer at the moment. The substitution method does keep the integrity of the list producing 1 or more 4 number hits intact.
Now that I believe I have explained what I am doing, I have a question for all of you: Which of the 186,146 playable lines do I play?
You are all excused now so you can go to the emergency room and get your ribs taped up that you broke while laughing so hard at me...
Best wishes to all!
