How many 'pairs' in a 5/N lotto?

[Bertil]

Consider the PowerBall draw 1-2-30-58-59. It has two 'pairs', viz. 1-2 and 58-59. Here I call two consecutive numbers as a 'pair'. Please don't count
DD like 11, 22, 33 ... as a 'pair' in this context. Maybe there is a better
word than 'pair' to use in my problem.

My question is what would be the frequency of 'pairs' in any 5/N lotto?
I would be happy to learn about the PowerBall 5/59 lotto, unless there is
a general formula that applies to any 5/N lotto, such as Megamillion 5/56.

Would 1-2-3-4-5 have 4 pairs, 12, 23 , 34 and 45?

Bertil

 

[PAB]

Hi Bertil,

Consider the PowerBall draw 1-2-30-58-59. It has two 'pairs', viz. 1-2 and 58-59. Here I call two consecutive numbers as a 'pair'. Please don't count DD like 11, 22, 33 ... as a 'pair' in this context. Maybe there is a better word than 'pair' to use in my problem.

My question is what would be the frequency of 'pairs' in any 5/N lotto?
I would be happy to learn about the PowerBall 5/59 lotto, unless there is a general formula that applies to any 5/N lotto, such as Megamillion 5/56.

Would 1-2-3-4-5 have 4 pairs, 12, 23 , 34 and 45?

I would call them Consecutive Pair.........Consecutive Sextuple.

Now the thing here is that you need to clarify what EXACTLY you are after.
From your description I assume that you are actually only interested in Consecutive Last Digits, where numbers 1...9 are classified as Last Digits in their own right. Is this what you are asking because it is FUNDAMENTAL in calculating what it is that is required.
As an example, what calculations would you come up with for the combination???

1,2,3,41,42,53

Now if you are intending on using TWO different parameters to calculate the Consecutives then this will obscure the results and will probably end up with them being meaningless and useless.

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]

How many pairs...?

In your example 1-2-3-41-42-53 there are 6 drawn numbers. Let's
eliminate 53. I'm not interested in 6/N type games.

One could count 1-2, 2-3, and 41-42 as 'pairs'. Do not count 3-4.
But I would limit the count to 42-43 and thus try to determine
the frequency of 'isolated pairs', such as in 1-2-30-58-59. which
would count as 2 'consecutive pairs', 1-2 and 58-59.

Bertil

 

[PAB]

Sorry, updated statistics to follow!

 

[PAB]

Hi Bertil,

One could count 1-2, 2-3, and 41-42 as 'pairs'. Do not count 3-4.

By this I assume that you don't want to count 3-4 because in reality this is a Triple.???

But I would limit the count to 42-43 and thus try to determine the frequency of 'isolated pairs', such as in 1-2-30-58-59. which
would count as 2 'consecutive pairs', 1-2 and 58-59.

I think you meant to say 41-42 and NOT 42-43???

Here are the statistics for Consecutive Pairs for a C(59, 5) Lotto...

1 Consecutive Pair = 1,364,220
2 Consecutive Pairs = 78,705
1 Consecutive Pair With A Triple = 2,970
Total = 1,445,895

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]

How many pirs...

PAB,
That's excellent work. I just noticed that your previous total of 1.445.925
is 2970 larger than your new total 1.442.925 and equals the triples plus
a con.-pair.
Thanks for your fine work.

Bertil

 

[PAB]

Hi Bertil,

That's excellent work. I just noticed that your previous total of 1,445,925 is 2,970 larger than your new total 1,442,925 and equals the triples plus a consecutive pair.
Thanks for your fine work.

You are very welcome Bertil.

Yes, I realised that when I was adjusting the coding for the new set of figures for this thread. I should have pointed that out, sorry!

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.