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lexicographic clustering

Topic closed. 43 replies. Last post 9 years ago by time*treat.

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United States
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 Posted: January 29, 2008, 11:08 am - IP Logged

I'm not sure how someone would graph a list of 5-point groups without consolidating them into some single value like a sum or a lex value. A quick glance at my own numbers leads me to believe that a graph of either of those sets will look much like the ones in LottoVantage's blog

... that's if the combos are graphed as draw history. If they are graphed in a natural generated order, and consolidated, the sums create a bell curve.

In neo-conned Amerika, bank robs you.
Alcohol, Tobacco, and Firearms should be the name of a convenience store, not a govnoment agency.

London
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 Posted: February 20, 2008, 2:53 pm - IP Logged

I have no idea what you are all talking about! Sounds interesting though.

What about a 'lex' for 6/49?

Thank you

United States
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 Posted: February 20, 2008, 3:30 pm - IP Logged

We were looking to see if the number combinations were bunching up anywhere. Such a trend might be more noticeable if the combinations were expressed as a decimal representation, rather than a group of 5 numbers. That decimal representation is the 'lex number' and will depend on how many total numbers are in the draw range.

Now for 6/49 there are 13,983,816 combinations, so that's how many lex values there are.

The combination 01,02,03,04,05,06::49 would have a lex value of 1
The combination 01,02,03,04,05,07::49 would have a lex value of 2
The combination 01,02,03,04,05,08::49 would have a lex value of 3

The combination 43,44,46,47,48,49::49 would have a lex value of 13,983,814
The combination 43,45,46,47,48,49::49 would have a lex value of 13,983,815
The combination 44,45,46,47,48,49::49 would have a lex value of 13,983,816

Every other combination of 6 numbers chosen from a pool of 49 will have a lex value falling between 1 and 13,983,816.

The "::number" is important to because it sets the endpoints for the values.
The same 5 (or 6) number combination will usually have a different lex value if this "::number" changes.
(Except for 01,02,03,04,05::NN (or 01,02,03,04,05,06::NN.). It's lex is always 1)

In neo-conned Amerika, bank robs you.
Alcohol, Tobacco, and Firearms should be the name of a convenience store, not a govnoment agency.

San Angelo, Texas
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 Posted: February 23, 2008, 11:44 am - IP Logged

I wonder what these numbers would look like if you reduced the field using Alphanumeric Substitution.
I know for a fact that the total number of combinations would be drastically reduced.

In AS, the numbers are converted to letters using a fixed code. I.E. All single digits become As,
the teens (10-19) become Bs, the 20 (20-29) become Cs and (for a Pick 5 with less than 40 numbers) the 30s would become Ds.

Once converted, the letter combination AAAAA  would represent 'x' number of numerical combinations.

I use to have the total number of 5 letter combinations, the total number of triples, etc, but that data got lost in PC change few years ago.

In use, one would arrange the letter combinations in order of occurrence, pick which ones to play and assign appropriate numbers from whatever data streams are being used.

I've found that letter combinations beginning with AAB,  ABC, ABB, come up far more often then other
17 possibilities. The most frequent last 3 triples ending with CDD BCD are far more frequent than the other 18 possibilities.

Be interesting to see what you math experts can do with these arrangements.

NASHVILLE, TENN
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 Posted: February 24, 2008, 1:29 pm - IP Logged

I have taken a look at Tennessee's P5 game and found the lex number for 49 drawings.

The first column gives you the date of the drawing; the second column gives you the lex number for that data; and the third column has the lex numbers organized in ascending order.

I think this is what you are looking for.

 02.20.08 568,818 02.18.08 173,955 4,298 02.15.08 546,811 56,370 02.13.08 323,733 64,555 02.11.08 516,370 74,561 02.08.08 472,524 102,448 02.06.08 495,912 129,948 02.04.08 218,594 173,955 02.01.08 358,749 179,973 01.30.08 129,948 187,451 01.28.08 318,345 204,419 01.25.08 465,755 207,053 01.23.08 571,768 213,490 01.21.08 341,270 218,594 01.18.08 4,298 223,394 01.16.08 393,743 242,658 01.14.08 383,644 246,101 01.11.08 344,579 266,220 01.09.08 242,658 279,049 01.07.08 547,452 289,270 01.04.08 383,727 318,345 01.02.08 422,118 323,733 12.31.07 399,389 341,270 12.28.07 179,973 344,579 12.26.07 289,270 345,402 12.24.07 484,973 358,749 12.21.07 496,620 364,050 12.19.07 459,536 383,644 12.17.07 102,448 383,727 12.14.07 74,561 393,743 12.12.07 460,112 399,389 12.10.07 501,987 416,460 12.07.07 416,460 422,118 12.05.07 213,490 422,933 12.03.07 64,555 443,968 11.29.07 443,968 446,081 11.28.07 246,101 459,536 11.26.07 422,933 460,112 11.23.07 279,049 465,755 11.21.07 558,965 472,524 11.19.07 345,402 484,973 11.16.07 364,050 495,912 11.14.07 56,370 496,620 11.12.07 187,451 501,987 11.09.07 223,394 516,370 11.07.07 266,220 546,811 11.05.07 204,419 547,452 11.02.07 446,081 558,965 10.31.07 207,053 568,818 571,768

United States
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 Posted: February 24, 2008, 3:59 pm - IP Logged

Yep, that's what we were checking, GASMETERGUY. I've noticed that some things are common among pick-5 games even if they have different pool sizes (e.g. 39 vs. 36).

In neo-conned Amerika, bank robs you.
Alcohol, Tobacco, and Firearms should be the name of a convenience store, not a govnoment agency.

NASHVILLE, TENN
United States
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 Posted: February 24, 2008, 8:23 pm - IP Logged

Yep, that's what we were checking, GASMETERGUY. I've noticed that some things are common among pick-5 games even if they have different pool sizes (e.g. 39 vs. 36).

So what conclusion might one draw from the information I have posted above?

Where would you "draw the line" assuming there is a line to draw?

United States
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 Posted: February 25, 2008, 11:24 am - IP Logged

What I'm referring to is the clustering of the lex values, not groups of 2 or 3 numbers.

Example: In a 5/39 game, there are 575,757 total combos. These can be represented as combo 1 through combo 575,757. These can be divided into 9 groups of 57,575 combos and 1 group of 57,582 combos.

 group lex vals start combo end combo 1 1 ~ 57,575 01,02,03,04,05:39 01,13,19,22,25:39 2 57576 ~ 115150 01,13,19,22,26:39 02,10,21,22,32:39 ... ... ... ... 10 518176 ~ 575,757 14,20,23,33,39:39 35,36,37,38,39:39

What I'm trying to find out is if, in the draw history, any of those groups contain significantly more or less than 10% of the drawn numbers. It doesn't have to be a 5/39, I'm just using that as an example.

GASMETERGUY,

For a 5/39 game, this is how I divided it (10 groups) of ~57,600. You could use 20 groups of half the size.

As you can see from the earlier replies, we each used a sample size of over 1000 drawings. I think 50 is way too small a sample size for pick-5 type games. As for my own game, even with a sample size over 1000, I didn't find much variation (<5%). RJOh's lottery is also 5/39 like yours, and since he was the only one who understood & tested what I was talking about, his replies are also useful.

My conclusion was 'old' data and theories need not be tossed after a matrix change.

Folks may want to dig up their pre-matrix change stuff for PB & MM.
Not what I set out to prove, but useful.

Overall, I think we found, instead of a new method, a way of seeing if the drawings are drifting off "normal". If you see numbers falling in one group more than the others, you'll know someone messed up the software again and to play accordingly.

In neo-conned Amerika, bank robs you.
Alcohol, Tobacco, and Firearms should be the name of a convenience store, not a govnoment agency.

NASHVILLE, TENN
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 Posted: February 25, 2008, 4:02 pm - IP Logged

I agree that 50 is way too small of a sample size.  1000 draws would be much better.  Tennessee's P5 game is seven months old and there have been approxiately 84 drawings to date.  I have to work with what I have.

And I agree that adding a number or two should not change anyone's method.  What has been developed for 35 numbers should ( I repeat, should) work with 39, 40, or 44 numbers.  It should also work whether the game is P5 or P6.  But I play patterns.   I do not use mathemetics except to determine which pattern to play.

After posting my first reponse to your thread, I began thinking about lex numbers.  The only use I can find at this time is to divide the total number of sets in half.  My pattern would then be:  Did the winning number set fall in the upper half or lower half of the total available?  How many upper half were there?  How many lower half were there?  Is there a preponderance of one over the other?

Might there be another pattern?  I think there is but my feeble mind can not grasp the concept.

United States
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 Posted: February 25, 2008, 4:52 pm - IP Logged

TN may have changed their method of drawings seven months ago, but their pick-5 game goes all the way back to Sept 1, 2004. Maybe you are using a different source?

I just checked their site. It's all there, over 500 drawings for pick-5.

In neo-conned Amerika, bank robs you.
Alcohol, Tobacco, and Firearms should be the name of a convenience store, not a govnoment agency.

NASHVILLE, TENN
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 Posted: February 25, 2008, 8:36 pm - IP Logged

I begin with the RNG numbers.  I feel there is a vast difference between RNG and ball drawn numbers.

The only "proof" I have is the fact that with ball drawn numbers, there were many times when a number went more than 40 draws before coming out.   With RNG numbers, that is not the case.  All the numbers will be drawn within 35 draws.  This makes me feel there is a vast difference between the two systems.

Some of my other patterns have also been skewed because of RNG numbers.

NASHVILLE, TENN
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 Posted: February 26, 2008, 8:21 pm - IP Logged

In case there is someone who cares, the mid-point for a Pick 5 out of 39 game is:

5 - 16 - 22 - 26 - 29 (lex # 287,878)

or

5 - 16 - 22 - 26 - 28 (lex # 287,877)

depending on where you wish to draw the line between Upper Half and Lower Half.

NASHVILLE, TENN
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 Posted: February 26, 2008, 9:13 pm - IP Logged

After checking the last 90 draws for the Tennessee P5 game, there are 45 draws in the Lower Half and 45 draws in the Upper Half.

This means something but I don't have a clue as to what it may signify.

Any thoughts?

Any one?

United States
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 Posted: February 26, 2008, 11:51 pm - IP Logged

45 numbers have plenty of room to spread out in a space of ~288K nums. A space that large with a data set so small won't tell you much unless there is a software glitch that sends everything to one side or the other.

There are probably better filters to work with such small data sets. 90 points in a field of 575,757 is not enough to tell you much, unless you devise a filter that makes them clump near each other (like a number or pair that shows up relatively often).

In neo-conned Amerika, bank robs you.
Alcohol, Tobacco, and Firearms should be the name of a convenience store, not a govnoment agency.

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