Pick 3 Repeat ProbabilityPrev Topic Next Topic

KyngeRycharde

Bemidji MN
United States
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January 13, 2004
114 Posts
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Apr 25, 2020, 1:06 am

Greetings everyone:

Assuming a number that is drawn has three unique digits, the probability that at least one number will repeat is 65.7%, and if the number is a double, the probability is 48.8%.

But, I got to wondering, what is the probability that EXACTLY one number would repeat?

Because of the situation with COVID-19, and with plenty of time to kill, I sat down for a couple of hours, and tried to work it out, just to have something to do. I don't know if this information would be of any help, but I will post it in the hopes that it will.

Assuming that the last draw consisted of three different numbers (i.e. 123), the probability that...

exactly one number would repeat is 44.1%.

there are no repeating numbers is 34.3%.

exactly two of the three numbers would repeat is 18.9%.

all three numbers would repeat is 2.7%.

Assuming that the last draw was a double (i.e. 112), the probability that...

there are no repeating numbers is 51.2%.

exactly one number would repeat is 38.4%.

both numbers repeat is 10.4%.

It would appear that repeating just one digit per number line has the best chance.

Kindest regards,

Kynge

"Announcing your plans is a good way to hear God laugh"
cottoneyedjoe

United States
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March 28, 2019
1,633 Posts
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Apr 28, 2020, 12:46 am
Quote: Originally posted by KyngeRycharde on Apr 25, 2020
Greetings everyone:

Assuming a number that is drawn has three unique digits, the probability that at least one number will repeat is 65.7%, and if the number is a double, the probability is 48.8%.

But, I got to wondering, what is the probability that EXACTLY one number would repeat?

Because of the situation with COVID-19, and with plenty of time to kill, I sat down for a couple of hours, and tried to work it out, just to have something to do. I don't know if this information would be of any help, but I will post it in the hopes that it will.

Assuming that the last draw consisted of three different numbers (i.e. 123), the probability that...

exactly one number would repeat is 44.1%.

there are no repeating numbers is 34.3%.

exactly two of the three numbers would repeat is 18.9%.

all three numbers would repeat is 2.7%.

Assuming that the last draw was a double (i.e. 112), the probability that...

there are no repeating numbers is 51.2%.

exactly one number would repeat is 38.4%.

both numbers repeat is 10.4%.

It would appear that repeating just one digit per number line has the best chance.

Kindest regards,

Kynge
Pretty cool, Kynge Rycharde. I wrote a script to generate the overall percentages for all Pick3 combos, be they singles, doubles, or triples. I got
```
0 digits repeating: 39.249%
```
```
1 digit repeating: 47.79%
```
```
2 digits repeating: 12.447%
```
```
3 digits repeating: 0.514%
```
```
avg: 0.74226 repeating digits
```
KyngeRycharde

Bemidji MN
United States
Member #3,340
January 13, 2004
114 Posts
Offline

Apr 28, 2020, 10:21 am

Thanks for posting the info. It would appear that this pretty much confirms that one should include one digit from the last draw when selecting a number to play. This would result, I would think, in playing anywhere from 3-9 lines, depending on where the possible repeating digit is placed in a matrix---first, second or third position.

Kynge

"Announcing your plans is a good way to hear God laugh"
cottoneyedjoe

United States
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March 28, 2019
1,633 Posts
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Apr 29, 2020, 1:44 am

Just to be thorough...

Pick 1
0 digits repeating: 90%
1 digit repeating: 10%
avg: 0.1 repeating digits

Pick 2
0 digits repeating: 65.7%
1 digit repeating: 32.4%
2 digits repeating: 1.9%
avg: 0.362 repeating digits

Pick 3
0 digits repeating: 39.249%
1 digit repeating: 47.790%
2 digits repeating: 12.447%
3 digits repeating: 0.514%
avg: 0.74226 repeating digits

Pick 4
0 digits repeating: 19.55025%
1 digit repeating: 45.60840%
2 digits repeating: 29.29212%
3 digits repeating: 5.37336%
4 digits repeating: 0.17587%
avg: 1.210162 repeating digits

Pick 5 (Quinto)
0 digits repeating: 8.3376369%
1 digit repeating: 32.0150610%
2 digits repeating: 39.2688405%
3 digits repeating: 17.7302520%
4 digits repeating: 2.5768890%
5 digits repeating: 0.0713206%
avg: 1.74407657 repeating digits

Pick 6 (Sexto?)
0 digits repeating: 2.965752657%
1 digit repeating: 17.339083884%
2 digits repeating: 35.357784714%
3 digits repeating: 30.574593180%
4 digits repeating: 10.944392175%
5 digits repeating: 1.345578840%
6 digits repeating: 0.032814550%
avg: 2.30480783052 repeating digits
lottologix

United States
Member #139,773
March 3, 2013
605 Posts
Offline

Apr 29, 2020, 5:17 am

Quote: Originally posted by KyngeRycharde on Apr 25, 2020
Greetings everyone:

Assuming a number that is drawn has three unique digits, the probability that at least one number will repeat is 65.7%, and if the number is a double, the probability is 48.8%.

But, I got to wondering, what is the probability that EXACTLY one number would repeat?

Because of the situation with COVID-19, and with plenty of time to kill, I sat down for a couple of hours, and tried to work it out, just to have something to do. I don't know if this information would be of any help, but I will post it in the hopes that it will.

Assuming that the last draw consisted of three different numbers (i.e. 123), the probability that...

exactly one number would repeat is 44.1%.

there are no repeating numbers is 34.3%.

exactly two of the three numbers would repeat is 18.9%.

all three numbers would repeat is 2.7%.

Assuming that the last draw was a double (i.e. 112), the probability that...

there are no repeating numbers is 51.2%.

exactly one number would repeat is 38.4%.

both numbers repeat is 10.4%.

It would appear that repeating just one digit per number line has the best chance.

Kindest regards,

Kynge

I see what you're saying. In my backtests I have found these percentages to have
a range but fit the general percents over a range of draws. For example.........
In pick 3 mixed numbers come out about 70ish percent of the time. Doubles around 20
ish percent. Triples in the neighbourhood of 10ish percent. If you look at this at
say over 730 draws you will see the overall percents kinda fit most of the time.
But while the percents do workout.In actual game play you could wind up waiting out
a string of games with no repeats or spotty repeats. We can say 1 number from the
last draw will repeat a reasonable amount of the time as a general rule of thumb.
But what is that numbers correlation, if any at all to the other 2 numbers you need
to make a winning combination? Some would say its all random. However some numbers
or patterns do come out more often than others which is the basis of most systems,
methods, or workouts. We are looking for the ideas that have a more definite bias
toward the winning set to tilt the odds in our favor in the next draw or set of
draws. Often when you combine ideas or methods together they don't workout like you
think they would. For example... Lets say you do a frequency count of all the sums
that came out in the last year of your pick 3 game. Whether you separate the sums
by mixed, double,or triple numbers or just count all of the sums together, most of
the time the sums of 9 thru 18 will generally be in the highest frequency count of
all 27 sums in the pick 3 game. Then lets do a frequency count of all of the boxed
number sets which generally range from 0 to 12 times a year. Say we find that the
boxed number frequency count shows the highest frequency repeating counts are 3 to
6. We would actually play numbers that have a frequency count of 2 to 5 as when
the numbers do come out their frequency count changes to the next highest number.
Now we are only playing numbers that sum up between 9 and 18 that have a frequency
count of between 2 and 5. While this makes for a much smaller group of numbers to
play in the next draw. Lets go a one step more and select only numbers that contain
1 number from the last draw. This further shrinks the group of numbers to play that
will likely have a winning set. Or so we think... The sum set of 9 to 18 show they
come out around 60ish percent of the time. The box frequency count shows 3 to 6 hit
around 50ish percent of the time, and the one number hitting in the next draw shows
up about 44ish percent of the time. If you backtest all 3 ideas combined for say
730 draws you would find that it only hits around 30ish percent of the time, I
found usually less. So while this method may seem to work it will not have positive
returns over time. Consistency is the tough part of the pick games.
Hopefully this helps.
dr san

bgonÃ§alves
Brasil
Member #92,560
June 9, 2010
3,779 Posts
Offline

Apr 29, 2020, 7:13 am

hello cottoney, great job on the odds percentages,
can you calculate the value of the probabilities of the pick3 positions? example
478 = last draw
726 = next
repeated a digit, but not in the same position,
so the question for pick3, calculate the probability of pick3 of a digit not repeating in the same position as the last draw? please
we could create a filter at the next not repeat the position
cottoneyedjoe

United States
Member #197,030
March 28, 2019
1,633 Posts
Offline

Apr 29, 2020, 11:41 am

Quote: Originally posted by lottologix on Apr 29, 2020
I see what you're saying. In my backtests I have found these percentages to have
a range but fit the general percents over a range of draws. For example.........
In pick 3 mixed numbers come out about 70ish percent of the time. Doubles around 20
ish percent. Triples in the neighbourhood of 10ish percent. If you look at this at
say over 730 draws you will see the overall percents kinda fit most of the time.
But while the percents do workout.In actual game play you could wind up waiting out
a string of games with no repeats or spotty repeats. We can say 1 number from the
last draw will repeat a reasonable amount of the time as a general rule of thumb.
But what is that numbers correlation, if any at all to the other 2 numbers you need
to make a winning combination? Some would say its all random. However some numbers
or patterns do come out more often than others which is the basis of most systems,
methods, or workouts. We are looking for the ideas that have a more definite bias
toward the winning set to tilt the odds in our favor in the next draw or set of
draws. Often when you combine ideas or methods together they don't workout like you
think they would. For example... Lets say you do a frequency count of all the sums
that came out in the last year of your pick 3 game. Whether you separate the sums
by mixed, double,or triple numbers or just count all of the sums together, most of
the time the sums of 9 thru 18 will generally be in the highest frequency count of
all 27 sums in the pick 3 game. Then lets do a frequency count of all of the boxed
number sets which generally range from 0 to 12 times a year. Say we find that the
boxed number frequency count shows the highest frequency repeating counts are 3 to
6. We would actually play numbers that have a frequency count of 2 to 5 as when
the numbers do come out their frequency count changes to the next highest number.
Now we are only playing numbers that sum up between 9 and 18 that have a frequency
count of between 2 and 5. While this makes for a much smaller group of numbers to
play in the next draw. Lets go a one step more and select only numbers that contain
1 number from the last draw. This further shrinks the group of numbers to play that
will likely have a winning set. Or so we think... The sum set of 9 to 18 show they
come out around 60ish percent of the time. The box frequency count shows 3 to 6 hit
around 50ish percent of the time, and the one number hitting in the next draw shows
up about 44ish percent of the time. If you backtest all 3 ideas combined for say
730 draws you would find that it only hits around 30ish percent of the time, I
found usually less. So while this method may seem to work it will not have positive
returns over time. Consistency is the tough part of the pick games.
Hopefully this helps.

You're correct that this won't help you pick winning numbers, but then again, nobody was promoting this probability analysis as a system or method to pick lottery numbers.

These math findings are of general interest, and this is the mathematics forum. I like that Todd has provided a place for people to discuss purely mathematical topics without the expectation that everything be in service of answering the question "how will this help me pick winning lottery numbers?" Some things are interesting in their own right whether or not they are applicable to predicting numbers.
cottoneyedjoe

United States
Member #197,030
March 28, 2019
1,633 Posts
Offline

Apr 29, 2020, 12:02 pm

Quote: Originally posted by dr san on Apr 29, 2020
hello cottoney, great job on the odds percentages,
can you calculate the value of the probabilities of the pick3 positions? example
478 = last draw
726 = next
repeated a digit, but not in the same position,
so the question for pick3, calculate the probability of pick3 of a digit not repeating in the same position as the last draw? please
we could create a filter at the next not repeat the position

Thank you dr san. The probabilities I worked out are for repeats in any position -- same position and different position. I didn't break it down further than that. If you want a more granular analysis of repeats in pick 3, you would have to work out the probabilities of 9 outcomes:

0 digits repeating
1 digit repeating (same pos.)
1 digit repeating (diff. pos.)
2 digits repeating (both diff. pos.)
2 digits repeating (1 same pos., 1 diff. pos.)
2 digits repeating (both same pos.)
3 digits repeating (all diff. pos.)
3 digits repeating (1 same pos., 2 diff. pos.)
3 digits repeating (all same pos.)
dr san

bgonÃ§alves
Brasil
Member #92,560
June 9, 2010
3,779 Posts
Offline

Apr 29, 2020, 1:49 pm

ok, good job, don't repeat the same
position from the last draw we can create a filter, since when you repeat in position, you can use direct, we can also see the probabilities of repeating and not repeating even / odd patterns = 0,2,4,6,8
odd = 1,3,5,7,9
ex = 456 = last
263 = next
default for valley = 0
odd = 1
last draw = 456 = 010
last 263 = 001
repeated the even pattern in the 1st position,
then we can see in excel the repetition of the digit
and also standards, even / odd
lottologix

United States
Member #139,773
March 3, 2013
605 Posts
Offline

Apr 29, 2020, 2:05 pm

Quote: Originally posted by cottoneyedjoe on Apr 29, 2020
You're correct that this won't help you pick winning numbers, but then again, nobody was promoting this probability analysis as a system or method to pick lottery numbers.

These math findings are of general interest, and this is the mathematics forum. I like that Todd has provided a place for people to discuss purely mathematical topics without the expectation that everything be in service of answering the question "how will this help me pick winning lottery numbers?" Some things are interesting in their own right whether or not they are applicable to predicting numbers.

I do agree with you. I find probability very interesting in its own right. However
being we are on lottery post I also think alot of people are approaching the idea
of probability with that low hanging fruit in mind "how will this help me pick winning lottery numbers?".
In my post I was trying to point out that I find it very interesting how the idea
of repeat probability sort of points to patterns in numbers and how it can have many
rabbit holes in this train of thought. Which could lead to other interesting ideas about
probability weather or not it has any applicability to predicting numbers or not.

bgonÃ§alves
Brasil
Member #92,560
June 9, 2010
3,779 Posts
Offline

Apr 29, 2020, 2:32 pm

repeat table or not at 100%
repeat pattern = worth 0			0
do not repeat voucher = 1			1
defaults are odd / even
always from last to next
the list is an example I will put lots of draws on pick3, the macro has automatic
0	0	0
0	0	1
0	1	0
0	1	1
1	0	0
1	0	1
1	1	0
1	1	1

dr san

bgonÃ§alves
Brasil
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June 9, 2010
3,779 Posts
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Apr 29, 2020, 2:46 pm

hello= cottoney=

http://www.mediafire.com/file/adg00wmhoyuxs1z/3_padroes_repetidos.xlsx/file
dr san

bgonÃ§alves
Brasil
Member #92,560
June 9, 2010
3,779 Posts
Offline

Apr 29, 2020, 3:05 pm

hello cotoney, this planilia already has the formula, you can place new drawings, it will do automatically, it is
select and drag, you can place sweepstakes from any American state, exchange them and put new ones, cotoney, well now you need to find a way to see the patterns delayed in a certain number of sweepstakes starting from the last one.
ex = the default 101 is delayed, that is, to see the frequency of the patterns, can you put this feature? please
cottoneyedjoe

United States
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March 28, 2019
1,633 Posts
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Apr 29, 2020, 5:53 pm

Sanny, I'm not downloading your spreadsheets, making drawings, or working on your "planilias." Best of luck with your project.

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