Consecutive Numbers (Pairs) 5/34 Lotto

[Sammy]

Hi All,

Hope you can help?:

I am interested in finding out the Probability of Consecutive Pairs, Triads, Quads, and Quints.

Using a 5/34 Lotto - can anyone advise how I calculate the Probability for any general Pairs, Triads, Quads, and Quints
as below:

1) One consecutive Pair/ Doublet (any 2 sequential numbers).

2) Two consecutive Pairs/ Doublets (any 2x2 sequential numbers; 11,12 & 18,19).

3) One consecutive Triad/ Triplet (any 3 sequential numbers).

4) One consecutive Quad/ Quadruplet (any 4 sequential numbers).

5) One consecutive Quint/ Quintuplet (any 5 sequential numbers).


And, is the method of calculation used for the above the same when specifying the Probability for named specific numbers, i.e. One consecutive Doublet/ Pair (11,12) as opposed to any consecutive Pair?

Also how does the method of calculation and Probability differ, if I say:

1) EXACTLY One consecutive Pair/ Doublet (any 2 sequential numbers) or ....

2) AT LEAST One consecutive Pair/ Doublet (any 2 sequential numbers).

Your help and assistance with detailed examples of how the calculations are performed is very much appreciated, together with any further information on the EXACTLY and AT LEAST methods of calcuation and their relevance.

ps. I have spreadsheet software.

Cheers
Sammy

 

[GillesD]

Lottery 5 / 34

I had some problems calculating the theorical values but when cycling through all 278,256 combinations, this is what I get:

- 142,506 combinations with no consecutive numbers (1-1-1-1-1);
- 109,620 combinations with 2 consecutivenumbers and the other numbers separate (2-1-1-1 or 1-2-1-1 or 1-1-2-1 or 1-1-1-2);
- 12,180 combinations with 2 sets of 2 consecutive numbers and the other one separate (2-2-1 or 2-1-2 or 1-2-2);
- 12,180 combinations with 3 consecutive numbers and the other numbers separate (3-1-1 or 1-3-1 or 1-1-3);
- 870 combinations with 3 consecutive numbers and 2 consecutive numbers (3-2 or 2-3);
- 870 combinations with 4 consecutive numbers and the other one separate(4-1 or 1-4);
- 30 combinations with 5 consecutive numbers (5).

When I have a little more time, I will try to get the formula to get those results (most likely with the COMBIN function in Excel).

 

[Sammy]

Re: Lottery 5 / 34

Hi GillesD,

Thank you very much for assistance.

GillesD, I found a Post in Tips & Strategies by Matrix on 10-25-2003 Binomial Theorem in Lotto.
http://www.lotto649.ws/showthread.php?s=&threadid=2643&highlight=binomial+theorem+in+lotto

I'm not sure if I'm comparing like with like, or even if your calculations in Matrix's Post is applicable to my original requests. It looks a bit similar to what I may be after - if you have the time could you possibly have a look at the above link for that Posting.

I would appreciate your opinion and assistance as I may be leading myself in the wrong direction!

Further help most appreciated.

ps. You've probably gathered mathematical skills and statistical knowlegde far from great!

Cheers
Sammy

I had some problems calculating the theorical values but when cycling through all 278,256 combinations, this is what I get:

- 142,506 combinations with no consecutive numbers (1-1-1-1-1);
- 109,620 combinations with 2 consecutivenumbers and the other numbers separate (2-1-1-1 or 1-2-1-1 or 1-1-2-1 or 1-1-1-2);
- 12,180 combinations with 2 sets of 2 consecutive numbers and the other one separate (2-2-1 or 2-1-2 or 1-2-2);
- 12,180 combinations with 3 consecutive numbers and the other numbers separate (3-1-1 or 1-3-1 or 1-1-3);
- 870 combinations with 3 consecutive numbers and 2 consecutive numbers (3-2 or 2-3);
- 870 combinations with 4 consecutive numbers and the other one separate(4-1 or 1-4);
- 30 combinations with 5 consecutive numbers (5).

When I have a little more time, I will try to get the formula to get those results (most likely with the COMBIN function in Excel).