Most probable range of Gap TotalsPrev TopicNext Topic

• KevinJoseph

  

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  Dec 17, 2021, 9:14 am

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  Folks I am wondering if it is possible to devise a method based on the Gap distribution (Chart L) in the Advantage Gold software.

  I am particularly interested in the Gap Totals covered in charts L.3 and L.4

  Would it be possible to formulate a strategy similar to Gail's 70% rule for the Sum range (Chart F) for example?

  With Gail 70% Sum rule she gives us the mid-point or most probable sum which is helpful as it shows us the Sum which has the most ways of happening.

  Is it possible to figure out which Gap Total has the most ways of happening?
• garyo1954

  

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  Dec 17, 2021, 10:46 am

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  Yes.....a 4/35 looks like this when you get the gap totals....70% would be between 16 and 30......
  
  

  GAPS	Hit
  1 =	0
  2 =	0
  3 =	32
  4 =	93
  5 =	180
  6 =	290
  7 =	420
  8 =	567
  9 =	728
  10 =	900
  11 =	1080
  12 =	1265
  13 =	1452
  14 =	1638
  15 =	1820
  16 =	1995
  17 =	2160
  18 =	2312
  19 =	2448
  20 =	2565
  21 =	2660
  22 =	2730
  23 =	2772
  24 =	2783
  25 =	2760
  26 =	2700
  27 =	2600
  28 =	2457
  29 =	2268
  30 =	2030
  31 =	1740
  32 =	1395
  33 =	992
  34 =	528
  35 =	0

   

  Notice the top where the totals are close together 2730,2772,2783,2760.....don't be surprised if these create a jagged peak.

  To take it to the next level determine the three number gap signature for every combination in your 4/28 and how many times it hits throughout the matrix.
  
  G

  I'm probably here unless I'm not.
  Dreaming would be a perfectly useless function if it's only purpose was to entertain.
• KevinJoseph

  

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  Dec 17, 2021, 11:29 am

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  In response to garyo1954

  Quote: Originally posted by garyo1954 on Dec 17, 2021

  Yes.....a 4/35 looks like this when you get the gap totals....70% would be between 16 and 30......
  
  

  GAPS	Hit
  1 =	0
  2 =	0
  3 =	32
  4 =	93
  5 =	180
  6 =	290
  7 =	420
  8 =	567
  9 =	728
  10 =	900
  11 =	1080
  12 =	1265
  13 =	1452
  14 =	1638
  15 =	1820
  16 =	1995
  17 =	2160
  18 =	2312
  19 =	2448
  20 =	2565
  21 =	2660
  22 =	2730
  23 =	2772
  24 =	2783
  25 =	2760
  26 =	2700
  27 =	2600
  28 =	2457
  29 =	2268
  30 =	2030
  31 =	1740
  32 =	1395
  33 =	992
  34 =	528
  35 =	0

   

  Notice the top where the totals are close together 2730,2772,2783,2760.....don't be surprised if these create a jagged peak.

  To take it to the next level determine the three number gap signature for every combination in your 4/28 and how many times it hits throughout the matrix.
  
  G

  Thanks for replying Gary, I know that in a 4/28 game the gap totals can range from a minimum of 0 to a maximum of 24.

  But I have no idea of how to work out the expected/probability of hits for each gap total.

  I'm also clueless as to how you worked out the 70% most probable gap total range of 16-30 for a 4/35 format.

  I was hoping someone who was good with Maths could assist me with how I could work this out for any lotto regardless of format.
• garyo1954

  

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  Dec 17, 2021, 11:56 am

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  In response to KevinJoseph

  Quote: Originally posted by KevinJoseph on Dec 17, 2021

  Thanks for replying Gary, I know that in a 4/28 game the gap totals can range from a minimum of 0 to a maximum of 24.

  But I have no idea of how to work out the expected/probability of hits for each gap total.

  I'm also clueless as to how you worked out the 70% most probable gap total range of 16-30 for a 4/35 format.

  I was hoping someone who was good with Maths could assist me with how I could work this out for any lotto regardless of format.

  Not sure how you're doing gaps. 
  
  Taking the difference between each number in set 1 2 3 4 gives a gap total of 3; gap signature is 1,1,1. (Same if you subtract the first number from the fourth)
  Highest number set with a 1 for the first number is 1 26 27 28.
  28 - 1 would give a gap total of 27.   
  
  So the gap totals possible are between 3 and 27. That means you'd have 2925 possible three number gap signatures from 1,1,1; to 25,1,1.
  
  Or we're not doing gaps in the same manner. 
  
  G

  I'm probably here unless I'm not.
  Dreaming would be a perfectly useless function if it's only purpose was to entertain.
• KevinJoseph

  

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  Dec 17, 2021, 12:24 pm

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  In response to garyo1954

  Quote: Originally posted by garyo1954 on Dec 17, 2021

  Not sure how you're doing gaps. 
  
  Taking the difference between each number in set 1 2 3 4 gives a gap total of 3; gap signature is 1,1,1. (Same if you subtract the first number from the fourth)
  Highest number set with a 1 for the first number is 1 26 27 28.
  28 - 1 would give a gap total of 27.   
  
  So the gap totals possible are between 3 and 27. That means you'd have 2925 possible three number gap signatures from 1,1,1; to 25,1,1.
  
  Or we're not doing gaps in the same manner. 
  
  G

  Gary perhaps I have gotten it wrong, but on page 84 in the Advantage Gold manual it states the following:

   

  "The easiest and most useful gap calculation is the gap total and it is simply the largest number less the smallest number less the number of gaps between them. In the PA640 game with the bonus excluded there are 6 numbers with 5 gaps. The largest gap would be 40 - 1 - 5 gaps = 34.

  Like most statistics in lottery, what happens most is what has the most ways of happening, and what happens least is what has the fewest ways of happening. In the PA 6/40 game, there are 3,838,380 combinations of 40 numbers taken 6 at a time (i.e. without the bonus number). The largest possible gap total is achieved when a combination contains both 01 and 40 and the possible ways that can happen comprise a full wheel with two power numbers which has a total of 73,815 combinations and is just 1.92% of the possible combinations. In the 621 games of the PA 6/40 game, Menu Option L3 shows it happened only 8 times -- certainly not something you would want to bet on. The only way to get a gap total of zero is to have a group of strictly consecutive numbers. In the PA 6/40 game, there are only 35 ways this can happen so it should be an extremely rare event and indeed never happened in the 621 games of the PA 6/40 lotto. Again you would not want to waste money on such combinations."

   

  If the maximum gap total in a 6/40 game is 40 - 1 - 5 gaps = 34 then I assumed a 4/28 would be calculated as 28 - 1 - 3 gaps = 24 but perhaps I've got that wrong?

  I've just checked chart L3 in the Advantage Gold software for my 4/28 game and it lists gap totals for 0-24 so I thought this confirmed my calculation but perhaps not? I also did the same test with a 4/30 game and got a maximum gap total of 26 (i.e 30-1-3=26) so perhaps Advantage Gold calculates differently than yourself Gary?
• garyo1954

  

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  Dec 17, 2021, 12:34 pm

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  In response to garyo1954

  Quote: Originally posted by garyo1954 on Dec 17, 2021

  Not sure how you're doing gaps. 
  
  Taking the difference between each number in set 1 2 3 4 gives a gap total of 3; gap signature is 1,1,1. (Same if you subtract the first number from the fourth)
  Highest number set with a 1 for the first number is 1 26 27 28.
  28 - 1 would give a gap total of 27.   
  
  So the gap totals possible are between 3 and 27. That means you'd have 2925 possible three number gap signatures from 1,1,1; to 25,1,1.
  
  Or we're not doing gaps in the same manner. 
  
  G

  4/28 gap totals......

  GAPS	Hit
  1 =	0
  2 =	0
  3 =	25
  4 =	72
  5 =	138
  6 =	220
  7 =	315
  8 =	420
  9 =	532
  10 =	648
  11 =	765
  12 =	880
  13 =	990
  14 =	1092
  15 =	1183
  16 =	1260
  17 =	1320
  18 =	1360
  19 =	1377
  20 =	1368
  21 =	1330
  22 =	1260
  23 =	1155
  24 =	1012
  25 =	828
  26 =	600
  27 =	325
  28 =	0
  29 =	0
  30 =	0
  31 =	0
  32 =	0
  33 =	0
  34 =	0
  35 =	0

   

  Your game has 20475 combinations. You need 14333 combinations to get 70%. 
  Gap totals between 13 and 24 add up to 14707 (about 72%).
  
  G
  
  

  I'm probably here unless I'm not.
  Dreaming would be a perfectly useless function if it's only purpose was to entertain.
• Speler

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  Dec 17, 2021, 12:50 pm

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  In response to KevinJoseph

  Quote: Originally posted by KevinJoseph on Dec 17, 2021

  Gary perhaps I have gotten it wrong, but on page 84 in the Advantage Gold manual it states the following:

   

  "The easiest and most useful gap calculation is the gap total and it is simply the largest number less the smallest number less the number of gaps between them. In the PA640 game with the bonus excluded there are 6 numbers with 5 gaps. The largest gap would be 40 - 1 - 5 gaps = 34.

  Like most statistics in lottery, what happens most is what has the most ways of happening, and what happens least is what has the fewest ways of happening. In the PA 6/40 game, there are 3,838,380 combinations of 40 numbers taken 6 at a time (i.e. without the bonus number). The largest possible gap total is achieved when a combination contains both 01 and 40 and the possible ways that can happen comprise a full wheel with two power numbers which has a total of 73,815 combinations and is just 1.92% of the possible combinations. In the 621 games of the PA 6/40 game, Menu Option L3 shows it happened only 8 times -- certainly not something you would want to bet on. The only way to get a gap total of zero is to have a group of strictly consecutive numbers. In the PA 6/40 game, there are only 35 ways this can happen so it should be an extremely rare event and indeed never happened in the 621 games of the PA 6/40 lotto. Again you would not want to waste money on such combinations."

   

  If the maximum gap total in a 6/40 game is 40 - 1 - 5 gaps = 34 then I assumed a 4/28 would be calculated as 28 - 1 - 3 gaps = 24 but perhaps I've got that wrong?

  I've just checked chart L3 in the Advantage Gold software for my 4/28 game and it lists gap totals for 0-24 so I thought this confirmed my calculation but perhaps not? I also did the same test with a 4/30 game and got a maximum gap total of 26 (i.e 30-1-3=26) so perhaps Advantage Gold calculates differently than yourself Gary?

  Like most statistics in lottery, what happens most is what has the most ways of happening, and what happens least is what has the fewest ways of happening.

  Ah, no. Let's say that your lotto has around 20000 combinations and the lotto lifetime is about 500 drawings. You eventually play 40 drawings in a row and give up. It is not because some pattern or combination type has a higher frequency that it will be drawn. 
  Let's say that you have a case of 80% probability and you play that. The outcome is from a 2% case and you made a giant loss playing the 80% probability.
  Try filtering and compare the results, or take an outcome that you have and filter the set to playable size.
• garyo1954

  

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  Dec 17, 2021, 12:55 pm

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  Where are you reading that? 
  It makes sense, but why is she subtracting the number of gaps? 
  
  She is doing it differently. 
  
  G

  I'm probably here unless I'm not.
  Dreaming would be a perfectly useless function if it's only purpose was to entertain.
• Speler

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  From their glossary.

  To show how this score is calculated, for the combination 07-16-24-39-49-53 the gaps would be:
  
  16-07 = 9
  24-07 = 17
  39-07 = 32
  49-07 = 42
  53-07 = 46
  24-16 = 8
  39-16 = 23
  49-16 = 33
  53-16 = 37
  ...

  The unique gaps are 4, 8, 9, 10, 13, 15, 17, 23, 25, 29, 32, 33, 37, 42, 46. This combination has 15 unique gaps (the most it can have for a pick-6) but we adjust it by 5 in the case of pick-6 lotteries (the number of gaps between the lowest and highest numbers in a combination) so that the actual score would be 15 - 5 = 10. If we didn't adjust this, the lowest score would be 5 for a pick-6. This adjustment makes zero the lowest score for any pick-size and makes it easier to compare. Obviously this is not a calculation that is convenient to compute by hand.

  ----

  They basically calculate |a_i-a_i+x| or delta or abs(delta).
  There are 6*5/2 deltas.
  N6-N1+1 is in fact the span.
  I read that they have unique gaps lowest and highest. Seems to be a lazy option.
• garyo1954

  

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  Dec 17, 2021, 1:04 pm

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  I agree but I don't. 
  
  If you take the overall anything you can think of and compare it to the totals of the game the percentages will be pretty close.
  So what happens the most will happen the most. It may not happen in short term series of draws, but it will catch up to the percentages over time. 
  

  If you play 40 days and give up, you probably weren't committed. Or maybe you need to be committed for wasting all that money!
  G

  I'm probably here unless I'm not.
  Dreaming would be a perfectly useless function if it's only purpose was to entertain.
• garyo1954

  

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  Dec 17, 2021, 1:08 pm

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  In response to Speler

  Quote: Originally posted by Speler on Dec 17, 2021

  From their glossary.

  To show how this score is calculated, for the combination 07-16-24-39-49-53 the gaps would be:
  
  16-07 = 9
  24-07 = 17
  39-07 = 32
  49-07 = 42
  53-07 = 46
  24-16 = 8
  39-16 = 23
  49-16 = 33
  53-16 = 37
  ...

  The unique gaps are 4, 8, 9, 10, 13, 15, 17, 23, 25, 29, 32, 33, 37, 42, 46. This combination has 15 unique gaps (the most it can have for a pick-6) but we adjust it by 5 in the case of pick-6 lotteries (the number of gaps between the lowest and highest numbers in a combination) so that the actual score would be 15 - 5 = 10. If we didn't adjust this, the lowest score would be 5 for a pick-6. This adjustment makes zero the lowest score for any pick-size and makes it easier to compare. Obviously this is not a calculation that is convenient to compute by hand.

  ----

  They basically calculate |a_i-a_i+x| or delta or abs(delta).
  There are 6*5/2 deltas.
  N6-N1+1 is in fact the span.
  I read that they have unique gaps lowest and highest. Seems to be a lazy option.

  Does it explain anywhere why she subtracts the number of gaps?
  I understand her doing it but why?
  
  Is it just condenses the totals into a shorter form or what?
  
  G

  I'm probably here unless I'm not.
  Dreaming would be a perfectly useless function if it's only purpose was to entertain.
• Speler

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  |N1-N2|: minimum:    maximum:    only: 
  |N1-N3|: minimum:    maximum:    only: 
  |N1-N4|: minimum:    maximum:    only: 
  |N1-N5|: minimum:    maximum:    only: 
  |N2-N3|: minimum:    maximum:    only: 
  |N2-N4|: minimum:    maximum:    only: 
  |N2-N5|: minimum:    maximum:    only: 
  |N3-N4|: minimum:    maximum:    only: 
  |N3-N5|: minimum:    maximum:    only: 
  |N4-N5|: minimum:    maximum:    only: 

  A fraction of my optional delta filter options. 
  I have to rework the code for PHP 8 this month. 
  I must review and test, next to applying changes due to the new version.
• Speler

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  In response to

  Quote: Originally posted by on May 16, 2024

  I need a hot shower, you need a cold one!
• Kennydundas

  

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  I need probable number for tonight Lott max jackpot + PLUS 11 MAXMILLIONS EST.
• Speler

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  In response to Kennydundas

  Quote: Originally posted by Kennydundas on Dec 17, 2021

  I need probable number for tonight Lott max jackpot + PLUS 11 MAXMILLIONS EST.

  I need a bucket full of gold coins. I asked the Irish dwarf but it wouldn't give them. ...