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# How many repeat combinations in Cash 5Prev TopicNext Topic

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• Connecticut
United States
Member #182,319
June 12, 2017
321 Posts
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The Connecticut Cash 5 game is a 5/35 game meaning that there are
324632 5 number combinations of those 35 numbers.  In over 8000 draws
how many times would any sequence be repeated.

I know there are some real sharp Math people on this site and could figure
out how many combinations would be repeated.

• Florida - West Coast
United States
Member #92,605
June 10, 2010
6,679 Posts
Online

Quote: Originally posted by Geodesic on Sep 11, 2022

The Connecticut Cash 5 game is a 5/35 game meaning that there are
324632 5 number combinations of those 35 numbers.  In over 8000 draws
how many times would any sequence be repeated.

I know there are some real sharp Math people on this site and could figure
out how many combinations would be repeated.

93 times in the more than 8100 drawings of CT Cash5 have two sets of five numbers been drawn twice.

There have been three times in Cash5 where a set of five numbers has been drawn THREE times.  They are 1 17 27 28 34 which was drawn on  7/31/2003, 2/28/2015 &  7/21/2021.   2 18 26 28 30 was drawn on 4/1/2001,  4/4/2008 & 1/23/2020.  21 22 25 28 30 was drawn on 8/19/2014, 8/24/2018 & 11/15/2018.

While it may surprise you to have learned there have been 93 times in CT Cash5 where the same set of five numbers has been drawn twice, it's a fairly common thing to happen.  New York's Take (5/36 matrix) has 74 sets of five numbers drawn twice and one set of five drawn three times.  Massachusetts Mass Cash had one set of five drawn three times and 60 times has an identical set of five numbers been drawn twice.  In Florida Fantasy5  (a 5/36 matrix  and I'm located in Florida) there have been 68 out of 7,727 drawings held since July 16, 2001 where a set of five numbers was drawn twice.  There haven't been any Fantasy5 drawings were the same set of five numbers was drawn three times.

A few years ago I looked at all the state lottery's that have a Pick5 game. I looked at Michigan, California, and Georgia just to name a few. All of the  states with a Pick5 game had the same thing happen many times.  Most think it shouldn't happen, but it does and more than people think it does. I've no idea why it happens and to date I've never heard a good explanation why it does.  I just know that it happens.

In case you're wondering why I know this, it's because I have commercially available lottery software on my laptop. G5

Play Smart!

• United States
Member #197,030
March 28, 2019
1,661 Posts
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Quote: Originally posted by Geodesic on Sep 11, 2022

The Connecticut Cash 5 game is a 5/35 game meaning that there are
324632 5 number combinations of those 35 numbers.  In over 8000 draws
how many times would any sequence be repeated.

I know there are some real sharp Math people on this site and could figure
out how many combinations would be repeated.

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 played straight, over a period of 3 consecutive games is (999/1000) x (998/1000), so the probability of at least one repeat is 1 - (999/1000)(998/1000) ≈ 0.3%. Getting a little more likely to see a repeat.

The likelihood of no repeats in Pick 3 played straight, over a period of 4 consecutive games is (999/1000) x (998/1000) x (997/1000), so the probability of at least one repeat is 1 - (999/1000)x(998/1000)(997/1000) ≈ 0.6%.

The likelihood of no repeats in Pick 3 played straight, over a period of 20 consecutive games is (999/1000) x (998/1000) x (997/1000) x ... x (981/1000), so the probability of at least one repeat is 1 - (999/1000)x(998/1000)x(997/1000)x...x(981/1000) ≈ 17.4%.

The likelihood of no repeats in Pick 3 played straight, over a period of 50 consecutive games is (999/1000) x (998/1000) x (997/1000) x ... x (951/1000), so the probability of at least one repeat is 1 - (999/1000)x(998/1000)x(997/1000)x...x(951/1000) ≈ 71.2%.

The more consecutive games you analyze, assuming each game's outcome is independent of the previous, the more likely it is you see at least one repeat. To analyze a different game with more combos, it's a simple change of numerators and denominators. For CT Cash 5 over a period of 8000 games, the number you're looking at is

1 - (324631/324632)x(324630/324632)x(324629/324632)x...x(316631/324632) = 99.9999999...%

There's a practically 100% chance you'll see a repeat in CT Cash 5 over that many draws.

• Missouri
United States
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August 9, 2020
336 Posts
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1 17 27 28 34 looks like a perfect GH pick...

• Connecticut
United States
Member #182,319
June 12, 2017
321 Posts
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Thank you G5 for the totally amazing stats. I'm blown away.

"I have commercially available lottery software on my laptop."

Care to elaborate on the name of the software?
You must have one heck of a database to feed that software.

Cottoneyedjoe,   You explained in a way that made sense to this old man
the certainty of repeat numbers in the Cash5 game.  Thank you :)

• Florida - West Coast
United States
Member #92,605
June 10, 2010
6,679 Posts
Online

Quote: Originally posted by Geodesic on Sep 11, 2022

Thank you G5 for the totally amazing stats. I'm blown away.

"I have commercially available lottery software on my laptop."

Care to elaborate on the name of the software?
You must have one heck of a database to feed that software.

Cottoneyedjoe,   You explained in a way that made sense to this old man
the certainty of repeat numbers in the Cash5 game.  Thank you :)

My software is Gail Howard's Smart Luck.  Google Smart Luck and it comes to the top of the search list.  As far as Howard's software goes it's simply the software I chose to buy. It's no worse nor any better than any other.  They all do pretty much the same thing. I enjoy using it... studying the numbers and learning about things like the repeating sets of five numbers is kind of my hobby. The thing about repeating sets of five numbers is that without software it's completely invisible to anybody.  There are many other things the software revealed to me, things you just cant see or know without it, and I find that interesting/fun. Some of the things it reveals to you might help you win a prize, but there are other individual weird stats that are totally meaningless. Knowing those stats wont help me win a jackpot but they're fun to know.

In Florida Fantasy5 my software told me that only once in more than 7,700 drawings has any number skipped 64 consecutive drawings. (it's #4)  I saw another number approaching 60 drawings skipped, so I knew that it would hit soon because that record of 64 drawings skipped is very hard to break.  So I told a guy I know to play that number because it was going to hit soon, but I didn't tell him why I knew it. He also didn't know that I had software on my laptop.  It blew him away when that number hit the very next drawing.  I never told him him how I knew or that I have software.

The big thing I tell people about software is this - My experience with lottery software is that I've won many more small prizes with it (as compared to my lottery playing friends that don't have it) but I've never won a jackpot using it. (I have never won a jackpot without it either)  To win a jackpot with software you'll still need a healthy dose of good luck too.

And to Cottoneyedjoe - THANK YOU!  No one has ever provided me with what I thought was a reasonable explanation of why there have been so many repeat combo's of five numbers drawn until your post.   People said things to me like "It's the law of big numbers" without any type of explanation of what The law of big numbers actually is.  G5

Play Smart!

• Connecticut
United States
Member #182,319
June 12, 2017
321 Posts
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Combination number, Lexicographic order number or just the Index number.

G5, your Lottery Post Member Number is 92,605 so converted it to a 5/35 set

92,605 = 3-5-8-10-14

Who knows,  it just might be lucky

Have fun finding out more hidden stats.

• Florida - West Coast
United States
Member #92,605
June 10, 2010
6,679 Posts
Online

Quote: Originally posted by cottoneyedjoe on Sep 11, 2022

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 played straight, over a period of 3 consecutive games is (999/1000) x (998/1000), so the probability of at least one repeat is 1 - (999/1000)(998/1000) ≈ 0.3%. Getting a little more likely to see a repeat.

The likelihood of no repeats in Pick 3 played straight, over a period of 4 consecutive games is (999/1000) x (998/1000) x (997/1000), so the probability of at least one repeat is 1 - (999/1000)x(998/1000)(997/1000) ≈ 0.6%.

The likelihood of no repeats in Pick 3 played straight, over a period of 20 consecutive games is (999/1000) x (998/1000) x (997/1000) x ... x (981/1000), so the probability of at least one repeat is 1 - (999/1000)x(998/1000)x(997/1000)x...x(981/1000) ≈ 17.4%.

The likelihood of no repeats in Pick 3 played straight, over a period of 50 consecutive games is (999/1000) x (998/1000) x (997/1000) x ... x (951/1000), so the probability of at least one repeat is 1 - (999/1000)x(998/1000)x(997/1000)x...x(951/1000) ≈ 71.2%.

The more consecutive games you analyze, assuming each game's outcome is independent of the previous, the more likely it is you see at least one repeat. To analyze a different game with more combos, it's a simple change of numerators and denominators. For CT Cash 5 over a period of 8000 games, the number you're looking at is

1 - (324631/324632)x(324630/324632)x(324629/324632)x...x(316631/324632) = 99.9999999...%

There's a practically 100% chance you'll see a repeat in CT Cash 5 over that many draws.

I'm sure Cottoneyedjoe's explanation (above) is accurate/correct.

Here's what I think is the most interesting thing about it.  It took only 688 drawings for the same set of five CT Cash5 numbers to be drawn twice.

The first Cash5 drawing was held on 4/14/2000.  On 9/16/2001 the 511th draw was held and this combo was drawn ======> 1 10 12 15 34.

One hundred and seventy seven Cash5 draws later that same combo was drawn for the second time on 3/2/2002 - the 688th drawing of CT Cash5.  So the game was just 1.88 years old when it happened for the very first time.  G5

Play Smart!

• Missouri
United States
Member #208,879
August 9, 2020
336 Posts
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Connecticut Cash 5 Draw Method is a Mechanical Lottery Ball Machine...  A glitch in the matrix perhaps...

• Florida - West Coast
United States
Member #92,605
June 10, 2010
6,679 Posts
Online

Quote: Originally posted by ddude003 on Sep 14, 2022

Connecticut Cash 5 Draw Method is a Mechanical Lottery Ball Machine...  A glitch in the matrix perhaps...

Nah.   No matter if  a RNG or ball and drum machine is used, the same thing happens in Pick5 games all over the USA.  The same glitch would have to be in each and every states method.

You're in Mizzou... which has a a 5/39 game.  Although I don't know if it's a RNG or ball and drum, since 9/8/2008  Show Me The Cash has had it happen 20 times in 5119 drawings. Last time it happened was on 9/17/2021 when this combo was drawn ====>  5 6 17 27 31  G5

Play Smart!

• Missouri
United States
Member #208,879
August 9, 2020
336 Posts
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Mo is RNG...  Always looking for an opportunity to learn GiveFive...  Did you use your GH Smart Luck software to come up with those stats?  I use GH SL AG to double check some things about my own software...  Would you mind saying what feature(s) you use to come up with the 20 times???

• Texas
United States
Member #200,559
August 28, 2019
160 Posts
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cottoneyedjoe, agree. It's virtually inevitable to have at least one repeat occur.

If we want to consider the unconditional probability that any particular combination will occur at least twice, we'd use this equation:

where r = number of draws of interest, e.g. 8000 in this case, and N = number of combinations for the game, e.g. 324631 in the 5/35 game case. In the case of r=8000 and N=324631, then, P=0.0003 or 0.03%.

• Florida - West Coast
United States
Member #92,605
June 10, 2010
6,679 Posts
Online

Quote: Originally posted by ddude003 on Sep 14, 2022

Mo is RNG...  Always looking for an opportunity to learn GiveFive...  Did you use your GH Smart Luck software to come up with those stats?  I use GH SL AG to double check some things about my own software...  Would you mind saying what feature(s) you use to come up with the 20 times???

Yup... I have/use GH SL AG.

In The Drop Down Menu from the main screen select/click Option 9.  (Companion Pairs)  Then click on Option C, "Quints".  G5

Play Smart!

• Missouri
United States
Member #208,879
August 9, 2020
336 Posts
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Quote: Originally posted by GiveFive on Sep 15, 2022

Yup... I have/use GH SL AG.

In The Drop Down Menu from the main screen select/click Option 9.  (Companion Pairs)  Then click on Option C, "Quints".  G5

Thank you !!!

• Texas
United States
Member #200,559
August 28, 2019
160 Posts
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If we were to ask what the probability distribution is for subsequent number of draws until a repeat of particular combination (or sequence), it would be this:

Again, r is the number of draws until the repeat (1,2,3,...), N is the number of combinations and P is the cumulative probability that a repeat of a combination / sequence will occur on or before the r-th subsequent draw. We can then solve for r as follows:

r is generally not going to be an integer, so we would need to round it.

For N=324632, here are the r results for various values selected:

The 63.2121125% value is the Mean. Its value is N, in our case 324632. An interesting point here is that as N approaches ∞, the Mean probability value (P) approaches 1-1/e (in decimal form). For example, in the Powerball and Megamillions lotteries, N~300 million, and the Mean value is incrementally closer to 1-1/e than the 5/35 game example.

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