5/50 Combinations

[maureen1038]

Hello everybody.

I wonder if anybody can help me calculate the number of certain types of combinations in a 5/50 draw (eg Euromillions Main Numbers).

I am curious to know:-

(i) how many of the 2,118,760 combinations contain one, and only one, pair of consecutive numbers;

(ii) how many combos contain exactly 2 pairs of consecutive numbers;

(iii) how many combos contain exactly 3 pairs of consecutive numbers; and

(iv) how many combos contain exactly 4 pairs of consecutive numbers.

I think the answer to (iv) is 46, but I am getting into a dreadful muddle trying to find the others.

Btw, I am a pencil-and-paper person. I do not understand Excel or Macros etc.

 

[PAB]

A very warm welcome to the Forum maureen1038 .

Hello everybody.

I wonder if anybody can help me calculate the number of certain types of combinations in a 5/50 draw (eg Euromillions Main Numbers).

I am curious to know:-

(i) how many of the 2,118,760 combinations contain one, and only one, pair of consecutive numbers;
(ii) how many combos contain exactly 2 pairs of consecutive numbers;
(iii) how many combos contain exactly 3 pairs of consecutive numbers; and
(iv) how many combos contain exactly 4 pairs of consecutive numbers.

I think the answer to (iv) is 46, but I am getting into a dreadful muddle trying to find the others.

BTW, I am a pencil-and-paper person. I do not understand Excel or Macros etc.

I will calculate these figures for you hopefully later on this evening and post the results.
It would be useful for other members if you were to edit your profile and put your location, this will help with answers to questions that you post in the future.

Regards,
PAB


-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-
12:45, restate my assumptions.
(1) Mathematics is the language of nature.
(2) Everything around us can be represented and understood through numbers.
(3) If you graph the numbers of any system, patterns emerge. Therefore, there are patterns, everywhere in nature.

 

[maureen1038]

Thank you for your swift reply, PAB; and thank you for the welcome.

I live in North Devon, England; and I shall now try to edit my profile.

 

[PAB]

Hi maureen1038,

Here are the total combinations for the different Consecutive Numbers...

0 Consecutive = 1,370,754 combinations.
2 Consecutive = 698,280 combinations.
3 Consecutive = 47,610 combinations.
4 Consecutive = 2,070 combinations.
5 Consecutive = 46 combinations.
Total = 2,118,760 combinations.

I hope this helps!

Regards,
PAB


-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-
12:45, restate my assumptions.
(1) Mathematics is the language of nature.
(2) Everything around us can be represented and understood through numbers.
(3) If you graph the numbers of any system, patterns emerge. Therefore, there are patterns, everywhere in nature.

 

[maureen1038]

Hi PAB

Thanks very much for calculating these quantities for me.

Best wishes

Maureen

 

[PAB]

You're very welcome Maureen, I hope you can put the data to good use and win the big one!

Regards,
PAB


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12:45, restate my assumptions.
(1) Mathematics is the language of nature.
(2) Everything around us can be represented and understood through numbers.
(3) If you graph the numbers of any system, patterns emerge. Therefore, there are patterns, everywhere in nature.

 

[Bertil]

5/50

Those numbers are very interesting and motivated me to test the last 26 numbers drawn in PowerBall. I found only 6. I grant you the PB is a 5/59
game but wonder what would be the theoretical value for 1 pair and what
would be the standard deviation?
Would it be 4.7% for 5/50 since its frequency is 33%?

Bertil

 

[PAB]

Hi Bertil,

Those numbers are very interesting and motivated me to test the last 26 numbers drawn in PowerBall. I found only 6. I grant you the PB is a 5/59 game but wonder what would be the theoretical value for 1 pair and what would be the standard deviation?
Would it be 4.7% for 5/50 since its frequency is 33%?

I assume when you say I found only 6 you mean 6 Single Consecutives?

Here are the statistics for your PowerBall of C(59, 5)...

0 Consecutive = 3,478,761 combinations which = 69.4865%
2 Consecutive = 1,442,925 combinations which = 28.8217%
3 Consecutive = 81,675 combinations which = 1.6314%
4 Consecutive = 2,970 combinations which = 0.0593%
5 Consecutive = 55 combinations which = 0.0011%
Total = 5,006,386 combinations which = 100.0000%

I had to use four decimal places for the percentages because otherwise the 5 Consecutives would have shown 0.00%.
How did you actually come up with the STDEV figures out of interest?

Regards,
PAB


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12:45, restate my assumptions.
(1) Mathematics is the language of nature.
(2) Everything around us can be represented and understood through numbers.
(3) If you graph the numbers of any system, patterns emerge. Therefore, there are patterns, everywhere in nature.

 

[Bertil]

5/50

Having only a rudimentary understanding of statistics I assume that
variance can be calculated with the binomial formula np(1-p).
It usually applies to games of chance.

Bertil

 

[PAB]

Hi Bertil,

Having only a rudimentary understanding of statistics I assume that variance can be calculated with the binomial formula np(1-p).

(1) Was my assumption I assume when you say I found only 6 you mean 6 Single Consecutives? correct?
(2) Were the statistical results I posted what you were after or any good, although I posted them all for you?
(3) Can you post the actual Calculation/Formula that you used as well as the Data that you used that you to arrive at the Would it be 4.7% for 5/50 since its frequency is 33%? please?

Regards,
PAB


-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-
12:45, restate my assumptions.
(1) Mathematics is the language of nature.
(2) Everything around us can be represented and understood through numbers.
(3) If you graph the numbers of any system, patterns emerge. Therefore, there are patterns, everywhere in nature.

 

[Bertil]

5/50

PAB,
Your calculation looks like what I wanted.
My calculation for variance should have been 100x0.33x0.67=4.7% .

In the case of the PowerBall game it should have been 26x0.288x0.712=5.33
or a std.dev. =2.31 from an expected 7.49 in 26 draws.

Feel free to disagree with my calculation.

Bertil

 

[PAB]

Hi Bertil,

My calculation for variance should have been 100x0.33x0.67=4.7% .
In the case of the PowerBall game it should have been 26x0.288x0.712=5.33 or a std.dev. =2.31 from an expected 7.49 in 26 draws.

I missed the fact that your analysis was done on a reduced selection of 26 actual draws.
As far as standard deviation is concerned, I think that Frank is better suited to calculating the figures for you more than myself.
My understanding of what you are calculating is that you don't have a definitive standard deviation value on which to base your reduced selection of 26 draws on. If you were to calculate another standard deviation range using a different 26 draws then that result will be different to the first.

I hope this helps!

Regards,
PAB


-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-
12:45, restate my assumptions.
(1) Mathematics is the language of nature.
(2) Everything around us can be represented and understood through numbers.
(3) If you graph the numbers of any system, patterns emerge. Therefore, there are patterns, everywhere in nature.

 

[Bertil]

There is an alternative way of looking at 'consecutive' numbers., viz. as pairs. Look at 1-2-3-4-5 and note there are 4 pairs, 12, 23, 34, 45.
Now look at 1-2-30-58-59. This set has two pairs and four consecutives.
Would the frequency of 2 pairs be the same as 4 consecutive numbers?

Bertil

 

[PAB]

Hi Bertil,

There is an alternative way of looking at 'consecutive' numbers., viz. as pairs. Look at 1-2-3-4-5 and note there are 4 pairs, 12, 23, 34, 45.
Now look at 1-2-30-58-59. This set has two pairs and four consecutives.
Would the frequency of 2 pairs be the same as 4 consecutive numbers?

Where do you get the four consecutives from?

You need to start a new thread to continue this discussion because it is off topic from what this thread is intended for as started by maureen1038.

Regards,
PAB


-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-
12:45, restate my assumptions.
(1) Mathematics is the language of nature.
(2) Everything around us can be represented and understood through numbers.
(3) If you graph the numbers of any system, patterns emerge. Therefore, there are patterns, everywhere in nature.

 

[Bertil]

5/50

PAB,
Your calculation looks like what I wanted.
My calculation for variance should have been 100x0.33x0.67=4.7% .

In the case of the PowerBall game it should have been 26x0.288x0.712=5.33
or a std.dev. =2.31 from an expected 7.49 in 26 draws.

Feel free to disagree with my calculation.

Bertil

I just tested 4 new sets of 26 draws and found 5.5.4 and 5 'pairs.
Together with the original set the mean is 5 with a std.dev. of only 0.7 for
sets of 26 draws. This looks very low compared with 7.49 and 2.31.
It makes me wander if there is an error someplace.

I count 4 consecutive numbers in 1-2-30-58-59 from two in the 1st pair and two in the last pair.
Bertil

 

[PAB]

Hi Bertil,

I count 4 consecutive numbers in 1-2-30-58-59 from two in the 1st pair and two in the last pair.

I see now, you mean the Consecutive Last Digits, it wasn't clear before.

You need to start a new thread to continue this discussion because it is off topic from what this thread is intended for as started by maureen1038.

Regards,
PAB


-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-
12:45, restate my assumptions.
(1) Mathematics is the language of nature.
(2) Everything around us can be represented and understood through numbers.
(3) If you graph the numbers of any system, patterns emerge. Therefore, there are patterns, everywhere in nature.