Gap

[Ben]

Hi all,
Gap, Deltas Number, spacing....

Repeat and adjacent:

831 games had at least 1 repeat number
average 1.0 repeat nbrs per game

1786 games(91.3%) had at least 1 adjacent number
average 1.9 adjacent nbrs per game

Gap:
see the last 15 draws:
00=consecutive or adjacent

DRAW......LOTTO NUMBERS............GAPS
1944.. 03-04-08-12-24-28-31=> 00-03-03-11-03-02
1945.. 02-08-12-15-21-28-49=> 05-03-02-05-06-20
1946.. 06-16-23-24-31-34-39=> 09-06-00-06-02-04
1947.. 04-14-26-39-42-46-48=> 09-11-12-02-03-01
1948.. 03-11-19-29-34-35-36=> 07-07-09-04-00-00
1949.. 02-24-33-34-36-37-48=> 21-08-00-01-00-10
1950.. 01-05-16-17-31-38-45=> 03-10-00-13-06-06
1951.. 01-13-14-16-18-38-49=> 11-00-01-01-19-10
1952.. 01-12-13-16-20-24-26=> 10-00-02-03-03-01
1953.. 03-12-21-23-26-34-47=> 08-08-01-02-07-12
1954.. 06-18-23-24-28-38-46=> 11-04-00-03-09-07
1955.. 02-14-23-25-36-46-47=> 11-08-01-10-09-00
1956.. 10-14-20-28-32-33-40=> 03-05-07-03-00-06
1957.. 07-11-24-29-32-36-42=> 03-12-04-02-03-05
1958.. 05-06-14-29-33-43-47=> 00-07-14-03-09-03


Gap distribution for 1958 draws:

GAP....TIMES....%......CUMULATIVE
00....1670....14.2%....14.2%
01....1514....12.9%....27.1%
02....1267....10.8%....37.9%
03....1111......9.5%....47.3%
04......934......8.0%....55.3%
05......844......7.2%....62.5%
06......712......6.1%....68.5%
07......613......5.2%....73.8%
08......533......4.5%....78.3%
09......429......3.7%....81.9%
10......352......3.0%....84.9%
11......332......2.8%....87.8%
12......321......2.7%....90.5%
13......212......1.8%....92.3%
14......190......1.6%....93.9%
15......163......1.4%....95.3%
16......108......0.9%....96.2%
17........94......0.8%....97.0%
18........74......0.6%....97.7%
19........67......0.6%....98.2%
20........47......0.4%....98.6%
21........37......0.3%....98.9%
22........31......0.3%....99.2%
23........31......0.3%....99.5%
24........14......0.1%....99.6%
25........17......0.1%....99.7%
26..........7......0.1%....99.8%
27........11......0.1%....99.9%
28..........1......0.0%....99.9%
29..........5......0.0%....99.9%
30..........1......0.0%....99.9%
31..........3......0.0%..100.0%
32..........1......0.0%..100.0%
34..........1......0.0%..100.0%

 

[GillesD]

Ben's gap analysis

Interesting data very similar to the Delta theory but in this case, you included the Bonus number. But the real question is: "Is your data good?"

1 - Games with adjacent numbers:
You say 91.3% (1786 draws) had at least one adjacent number. Yet in the last 15 draws, the percentage is 73.3% (11 draws). Not meaningful draws or what. Using my database, I get 61.6% (1206 draws) with at least one adjacent number. Quite a difference.

2 - Gap distribution:
In many cases, I get the same data as you but for some numbers, it differs. For example:
#.......You..........Me
00....1670.......1668
01....1514.......1515
04......934.........936
05......844.........843
14......190.........189
20........47...........48
33..........0.............1

Also if you add all your frequencies (1670+1514+....), you get 11747. You should get 11748 or 1958 x 6.

3 - Repeat number:
Does "831 games had at least 1 repeat number" mean that at least one number is repeated from the previous draw for 831 draws (42.4%)?
If so, even without considering the Bonus number, I get 1113 draws (56.8%) with at least one repeat number. The theorical value for this is 56.4% and I think that when the Bonus number is included, the percentage for a repeat number increases to 62.5%

I may have one or two errors in my database (doubtful) but how about you?

 

[Ben]

Re: Ben's gap analysis

Interesting data very similar to the Delta theory but in this case, you included the Bonus number. But the real question is: "Is your data good?"

1 - Games with adjacent numbers:
You say 91.3% (1786 draws) had at least one adjacent number. Yet in the last 15 draws, the percentage is 73.3% (11 draws). Not meaningful draws or what. Using my database, I get 61.6% (1206 draws) with at least one adjacent number. Quite a difference.

2 - Gap distribution:
In many cases, I get the same data as you but for some numbers, it differs. For example:
#.......You..........Me
00....1670.......1668
01....1514.......1515
04......934.........936
05......844.........843
14......190.........189
20........47...........48
33..........0.............1

Also if you add all your frequencies (1670+1514+....), you get 11747. You should get 11748 or 1958 x 6.

3 - Repeat number:
Does "831 games had at least 1 repeat number" mean that at least one number is repeated from the previous draw for 831 draws (42.4%)?
If so, even without considering the Bonus number, I get 1113 draws (56.8%) with at least one repeat number. The theorical value for this is 56.4% and I think that when the Bonus number is included, the percentage for a repeat number increases to 62.5%

I may have one or two errors in my database (doubtful) but how about you?

Hi GillesD,
I have to make an audit for all my data. (1958 draws) i think, i have some errors entry, and i do it right now.
thankS GillesD.

 

[Snides]

Something's funny here.. I get the following results from my database.

draw count with one or more repeaters: 1234
draw count with no repeaters 725

draw count with one or more consecutives; 954
draw count with no consecutives: 1005

The above results are not including the bonus number

 

[Beaker]

Hi all,
Gap, Deltas Number, spacing....

Repeat and adjacent:

831 games had at least 1 repeat number
average 1.0 repeat nbrs per game

1786 games(91.3%) had at least 1 adjacent number
average 1.9 adjacent nbrs per game

9 out of 10 draws has a pair??? Not sure its that high check your data - its high but not that high.

 

[Snides]

it is way too high beaker, even counting the bonus number I can't get any higher than 1600 consecutive (adjacent) numbers in total by counting every consecutive and not how many draws have consecutives..

There is only 954 draws with consecutives but there are 1600 consecutives, so, certainly some draws have 2, some 3 etc..

and at 954 draws having consecutives, that's less than 50%, or in school terms, a fail.. so, do you use consecutives as a positive filter? or a negative one?

 

[Beaker]

it is way too high beaker, even counting the bonus number I can't get any higher than 1600 consecutive (adjacent) numbers in total by counting every consecutive and not how many draws have consecutives..

There is only 954 draws with consecutives but there are 1600 consecutives, so, certainly some draws have 2, some 3 etc..

and at 954 draws having consecutives, that's less than 50%, or in school terms, a fail.. so, do you use consecutives as a positive filter? or a negative one?

For 1959 total draws I get the following:

Without bonus 953 = 746 with only 1 consecutive, 207 with two or more pairs triples,quads etc.
With bonus 1207 = 815 with just 1 and 392 with two or more pairs triples/quads etc

So with bonus 61.6% have at least 1 consecutive which confirms GillesD's data above.

 

[Beaker]

<snip>
and at 954 draws having consecutives, that's less than 50%, or in school terms, a fail.. so, do you use consecutives as a positive filter? or a negative one?

Strictly speaking, you are right - slightly less that 1/2 of the regular numbers in a draw will have at least 1 pair. Flip a slightly weighted coin
I'm not sure what the expected value for the regular numbers would be.

 

[Snides]

But there's still the question of the repeaters from last draw..

Gilles says "even without considering the Bonus number, I get 1113 draws (56.8%) with at least one repeat number." BUt my count comes out to 1234 draws without the bonus.. how many do you get?

 

[Beaker]

But there's still the question of the repeaters from last draw..

Gilles says "even without considering the Bonus number, I get 1113 draws (56.8%) with at least one repeat number." BUt my count comes out to 1234 draws without the bonus.. how many do you get?

For 1959 total draws I get the following for repeaters:

Without bonus: 1115 draws = 800 with 1 repeater, 315 with 2 or more

With bonus: 1350 draws = 833 with just 1 repeater, 517 with 2 or more repeaters

So, with bonus 68.9% draws have at least 1 repeater.

 

[GillesD]

Repeat and pairs

For 1959 draws, I get for repeating numbers in the next draw:

- 845 wtih 0 repeater (43.2% vs 43.6%)
- 800 with 1 repeater (40.9% vs 41.3%)
- 279 with 2 repeaters (14.2% vs 13.2%)
- 34 with 3 repeaters (1.7% vs 1.8%)
- 1 with 4 repeaters (0.1% vs 0.1)

Also for pairs and other consecutive, I get:
- 1005 with no consecutive (51.3% vs 50.5%)
- 747 single pairs (38.1% vs 38.8%)
- 122 with 2 pairs (6.2% vs 5.8%)
- 1 with 3 pairs (0.1% vs 0.1%)
- 63 with 3 consecutive (3.2% vs 3.9%)
- 15 with 3 consecutive and 1 pair (0.8% vs 0.6%)
- 5 with 4 consecutive (0.3% vs 0.3%)
- 1 with 5 consecutive (0.1% vs 0.0%)

The first % mentionned is the actual value or the number of times / number of draws (1959). The second % is the theorical value or the real number of possibilities / all possivilities (13,983,816).

As it is, Lotto 6/49 is fairly near the expected value which would indicate good randomness.

 

[Ben]

Re: Repeat and pairs

For 1959 draws, I get for repeating numbers in the next draw:

- 845 wtih 0 repeater (43.2% vs 43.6%)
- 800 with 1 repeater (40.9% vs 41.3%)
- 279 with 2 repeaters (14.2% vs 13.2%)
- 34 with 3 repeaters (1.7% vs 1.8%)
- 1 with 4 repeaters (0.1% vs 0.1)

Also for pairs and other consecutive, I get:
- 1005 with no consecutive (51.3% vs 50.5%)
- 747 single pairs (38.1% vs 38.8%)
- 122 with 2 pairs (6.2% vs 5.8%)
- 1 with 3 pairs (0.1% vs 0.1%)
- 63 with 3 consecutive (3.2% vs 3.9%)
- 15 with 3 consecutive and 1 pair (0.8% vs 0.6%)
- 5 with 4 consecutive (0.3% vs 0.3%)
- 1 with 5 consecutive (0.1% vs 0.0%)

The first % mentionned is the actual value or the number of times / number of draws (1959). The second % is the theorical value or the real number of possibilities / all possivilities (13,983,816).

As it is, Lotto 6/49 is fairly near the expected value which would indicate good randomness.

Hi all

First, thanks for all and i'm impressioned for your skills and professionalism

Ok, GillesD, your data is without bonus number, i get same.

Now for Adjacent number,
Analyzing, the 2 last draws:

1958===05-06-14-29-33-47-(43)
adjacent to pics for next draw:
04-05-06-13-15-28-30-32-34-46-48-(42-44)

1959=== 05-06-13-22-29-46-(08)
we have 4 adjacent numbers: 05-06-13-46

For gap: 00.....IS Consecutive (remove adjacent).
05-06-13-22-29-46-(08)==00-06-09-07-17-(1)



Have a nice weekend and good luck in your games

 

[Beaker]

Ben, your observation about adjacent numbers is correct - they happen frequently. In fact, if you consider 1-off adjacent and 2-off adjacent, and you include the number that hit, you are considering max 21 numbers and 35 numbers respectively.
Consider this, in the draw before last, you had 5-6-14-29-33-47 B43

So 1-off adjacent gives you:

4-5-6-7-13-14-15-28-29-30-32-33-34-42-43-44-46-47-48

and 2-off adjacent gives:

3-4-5-6-7-8-12-13-14-15-16-27-28-29-30-31-32-33-34-35-41-42-43-44-45-46-47-48-49

The winners were: 5-6-13-22-29-46 B8 which gives 5 from 1-off and 6 from 2-off.

I often consider 1-off and 2-off from the last draw and the draw before - going 2 and 3 draws back. If you tie this in with other stats, LDs, decades and announcers, it can really narrow the odds.

Good strategy

Your term "Gap" is known better as "Delta" I can't remember the delta website but essentially play delta 1 - either the number 1 or a pair, remove any delta above 15 and have at least 1 repeating deltas

Here is the Delta website. LT if this is inappropriate just remove the link.

 

[GillesD]

Question to Ben

Ben, you quoted:

1958===05-06-14-29-33-47-(43)
adjacent to pics for next draw:
04-05-06-13-15-28-30-32-34-46-48-(42-44)

Any reason why 07 would not be in your list? If 06 came out in draw #1958, then 07 is quite adjacent to it.

 

[GillesD]

Data on Delta

In the Delta theory, the bonus number is not considered and the lowest number of the 6 numbers is part of the group of 6 Deltas (the other being the differences between two consecutive numbers when placed in in order).

Up to now, with 1959 draws, Deltas of 15 and lower represent 90.2% of the 11,754 Deltas. The maximum Delta obtained is 38.

Draws with repeating Deltas represent 67.2%.

But if you combine the two conditions, at least one repeating Delta and no Delta over 15, only 37.8% of the draws pass.

 

[Beaker]

Re: Data on Delta

In the Delta theory, the bonus number is not considered and the lowest number of the 6 numbers is part of the group of 6 Deltas (the other being the differences between two consecutive numbers when placed in in order).

Up to now, with 1959 draws, Deltas of 15 and lower represent 90.2% of the 11,754 Deltas. The maximum Delta obtained is 38.

Draws with repeating Deltas represent 67.2%.

But if you combine the two conditions, at least one repeating Delta and no Delta over 15, only 37.8% of the draws pass.

Thanks for that data GillesD - great stuff

But if you combine the two conditions, at least one repeating Delta and no Delta over 15, only 37.8% of the draws pass

This is not very high at all

What is the % of Delta < 15, 2 or more deltas the same, and delta 1?

 

[Snides]

If we're looking for adjacents from one draw to the next I don't think they happen that often..

For 1958 draws I get a total of

427 off by - 4 from previous draw
455 off by - 3
502 off by - 2
543 off by - 1
581 off by 0
568 off by 1
489 off by 2
426 off by 3
456 off by 4

Up to off by 4's there's 4447 out of 11754 numbers drawn (no bonus).. which gives us 37.8%

Oh, actually, I should mention that this is position sensitive, so it's saying that the number in position 1 changed by -4 to +4, the number in position 2 changed by -4 to +4, etc..

 

[Ben]

Re: Question to Ben

Ben, you quoted:

1958===05-06-14-29-33-47-(43)
adjacent to pics for next draw:
04-05-06-13-15-28-30-32-34-46-48-(42-44)

Any reason why 07 would not be in your list? If 06 came out in draw #1958, then 07 is quite adjacent to it.

Hi GillesD,
07 is forgotten, involuntarily..sorry.
and thanks for information about deltas

Hi Beaker.
good idea
and thanks for the link.....i have to learn more from this site

Hi Snides,
i know, you too, you have great skills, like Beaker, Gilles, Dennis, brad...and LT with lotto tutor web site, we have to
help him (LT) to keep this site the best one .
Très bonne équipe, continuez..(great stuff, continue)