February 12, 2010 GC posted a **NON-PROGRESSIVE** 358 line Cover in RGL which he passed off to his eternal shame as progressive. A simple check at 68 lines revealed only 11,298,393 combs covered or 80.79621% when 11,716,391 or 83.78536% is easily achieved in for example CoverMaster

Colin Fairbrother

]]>On January 30, 2010 Jaera punlished a

Ion Saliu posted a

Colin Fairbrother

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I have deliberately not got involved in producing the antithesis of Normal Distribution Lotto Covers which I will refer to as Abnormal Covers as I regard them as an abomination of what a logical and best paying Lotto Playset should be.

Since the 1980's with an increase in computing power made available to the general public a section of the mathematical community involved in combinatorics which can be traced back to Sophia in Bulgaria have foisted these nonsense Abnormal Covers or Wheels on the Lotto playing community that like to construct a set of numbers to play. **The hallmark of these misapplied Abnormal Covers is that with an objective of guaranteeing any prize for every draw in the lowest count of combinations played the likelihood of getting the lowest prize is increased way beyond its normal range.** In other words certainty of a pittance at whatever price to pitch a lower count of combinations played.

However, they have a fatal flaw as revealed by myself. When an equivalent number of combinations from a Normal Distribution Cover such as my C(45,6,3,6)=275 is compared with the Abnormal Distribution Cover such as C(45,6,3,6)=131 the lower yield of the latter is apparent. The absurdity is further revealed by my chart comparison where for a set of 131 combinations played the highest expectation should be 3 Threes which my chart line shows and the Abnormal shows pretty well the inverse.

For those of you who think I get some enjoyment out of showing up Abnormal Covers for what they are - well you're right. I'll keep at it increasing the pressure until some mathematician somewhere is prepared to come out and condemn this nonsense as it relates to Lotto or the perpetrators simply admit they got it wrong. Let's rub some salt in (I'm laughing as I type this) - taking the sum of the count of the coverage for each Threes Group and using the multiple as a factor (count of 2 3's x 2) for the C(45,6,3,6)=131 we get 18,853,948 and for the 131 combs of my C(45,6,3,6)=275 we get 21,166,977 - a 12.27% improvement.

The Pick 6 from Pool 45 Lotto games are played in Australia and Singapore where the former pays with two bonus integers and the latter with one. You can obtain a set of numbers to play using this structured template from a random order of the 45 integers from LottoToWin for only a $5.00 annual subscription.

The odds for getting a **Three win with a Bonus** integer can be calculated from

1 in 45c6 / 6c3 x (39c3 - 37c3)

which is 1 in 8145060 / (20 x 1369)

or 1 in 297.

which is 1 in 8145060 / (20 x 1369)

or 1 in 297.

The second table below shows the 3 prizes which you need to get before getting the paying prize which must have the bonus ball. **The odds for getting a Three only which is not paid on is roughly 1 in 45.** **A rule of thumb is that 15% or 0.15 of your expected Threes should convert to Three plus a Bonus.** To put that in perspective a good set of 22 structured numbers should average out to giving you a Three for every second draw played and the same set should give you a 3 + Bonus about every 14 draws and any prize in 13 draws (see table below). If you're not getting this then the explanation is that you are using stupid System plays such as System 8 which instead of using the 45 integers only uses 8 and is the second worse way to play! See my Comparison of 15 Lotto Structured Number Sets.

Table showing the relationship between the frequency of wins and the number of lines played from my Unique 3's™ in a 6/45 with two bonus integers Lotto game

Essentially this is a partial 3if3 Cover which from 1 to 380 combs is as good as any other, as long as each each comb is contributing a coverage of 20 distinct Threes from the 14,190 possible Threes. A 275 line 3if3 set with any distinct Threes is going to give 99.94% 3if6 coverage ie 4958 Sixes Uncovered. **However, if the Threes are chosen on the basis of maximizing progressively the coverage of the Sixes a proportionality is maintained especially up to around the 88% mark or 60 combs from where they taper off to about the 132 mark or 99.5% and from thereon it is practically a straight line.** By contrast a 3if3 without maximization of the Sixes at 60 Combs may only give about a 68.5% coverage a difference of around 21.5% or more.

For the distorted, abnormal distribution 131 line 3if6 Cover with repeat Threes the methodology in construction is to force low yielding combinations into the set at the expense of higher yielding ones. For 131 Combs played one should expect per probability calculation close to 3 prize Three wins per draw. The grouping of the possible winning combinations for the set played should reflect this by not having the group which delivers 1 Three win as dominant as is the case with the distorted Cover but the group that delivers 3 wins, as is the case with my set.

Even after sorting the 131 combs of the abnormal cover set by highest dependency the top 45 combs only give a coverage of 49% compared to my set with 77% and similarly only 37% for the top 22 compared to mine at 46%. In fact for the groups delivering greater than 1 win my set is ahead at every stage. Obviously, the obsession with guaranteeing a Three win every draw is pure folly and to advocate it as delivering better on average than Random Selections or my Unique 3's set with optimized coverage is no less than fraudulent.

The World Record 275 Lines Cover 6/45 Lotto Unique 3's™ Prize Report and Chart follows: -

Regards

Colin Fairbrother

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with either distinct combinations of two or three integers.

- The Pool must be used by an actual jackpot type Lotto Game eg West Virginia Pick 6/Pool 25.

. - The Prize Distribution must be normal so that the 3's x 1 is not greater than the 3's by 2. The dominant group for the 3's prizes should have the the groups above and below in gradual decay as in a Bell Curve. The first effect of this is to exclude artificial maximum packing using the C(22,6,3,3,1)=77 or C(26,3,3,1)=130 Steiner systems. eg the merging of these two systems gives a C(48,6,3,5)=207 which is also a cover for C(49,6,3,5)=207. For further information on this subject read the somewhat dated but very informative article by
**Uenal Mutlu**which was the original source article to the author.**"Theorem 3.1 includes also the well known two cases ... :**

C(v1,6,3,3,1,=b1) + C(v2,6,3,3,1,=b2) = C(v1+v2,6,3,5,1,=b1+b2

C(v1,6,3,3,1,=b1) + C(v2,6,3,4,1,=b2) = C(v1+v2,6,3,6,1,=b1+b2"

The second effect is that the Covers will be much longer albeit with an almost insignificant number of combinations in the non prize group. The author holds the view which is at odds with the general view on Covers that the prize return in playing Lotto should be the main consideration and not distortion just to guarantee what well may be an insignificant prize in relation to the amount outlayed.**eg If playing 300 lines and 300 combinations are uncovered then the chances of the winning number being a non prize is the same as winning first prize.**. - The Lotto game for the prizes considered pays in any order drawn.

. - The Covers must be substantial so unless the Pool is very high in Pick 6 games we start with distinct Threes.

. - You do not have to post the enumerated Cover; a summary is sufficient.

. - Presumably, you want credit for your claim so you need to supply your real name.

. - Spurious or doubtful claims will be sidelined to a temporary storage pending verification.

. - Only one record per Lotto game configuration can exist on an on-going basis in this thread; superseded records will be moved to another thread but moved back if the new record claim is not substantiated.

The methodology I have been espousing for some time is:

**Use the full pool of integers for the game. eg 45 or 49**

.**Produce a set of numbers that does not have repeat combinations of the integers if they are paid on in the game. eg Unique 3's ™**

.**Maximize the coverage (ie next best play without unnecessary optimization techniques) of the main winning combinations for combinations of 2 of the integers if they are paid on eg Powerball or 3 of the integers for the Pick 6 type games.**

**I deliberately chose to produce a progressively increasing coverage set where previous lines remain the same. While a marginal increase can be made in coverage through optimization techniques for a given number of combinations this does not necessarily increase the yield.**

**An example template follows for the Pool 25, Pick 6 West Virginia Cash 25 Lotto game.** The odds are 1:177,100 for 1st prize which pays $25,000, 1:1554 for 2nd prize which pays $250, 1:69 for 3rd prize which pays $10 and 1:9 for 4th prize which pays $1.00. Cost of entry is $1 per line so playing the first 8 lines of the cover randomized per game draw you should average out to a win of some sort per draw albeit as low as 10% of what you have outlaid. It is important that you retain the order of the blocks for what you play - with the integers randomized of course.

Prize Group Combinations % Chance Cum %Chance

1 Four & 0 to 9 Threes 73188 41.33 41.33

5 Threes 26928 15.20 56.53

4 Threes 23224 13.11 69.64

6 Threes 17445 9.85 79.49

3 Threes 10640 6.01 85.50

2 Fours & 0 to 7 Threes 10629 6.01 91.50

7 Threes 6533 3.69 65.19

1 Five & 0 to 6 Threes 4218 2.38 97.57

2 Threes 2324 1.31 98.89

8 Threes 1378 0.78 99.67

1 Three 227 0.13 99.79

9 Threes 160 0.09 99.88

3 Fours & 0 To 3 Threes 153 0.09 99.97

1 Six 37 0.02 99.99

10 Threes 16 0.01 100.00

As you can see you have a better chance of getting a Five and overall a 99.87% chance of getting something other than a solitary Three win. Interestingly, instead of 1st prize being the lowest chances of success group with 37 possible winning combinations for the draw that will give this there is a group that pays 10 Threes with only 16.

Line Block Coverage Cum Coverage % Cum Coverage

1 01 02 03 04 05 06 22060 22060 12.45623

2 07 08 09 10 11 12 21660 43720 24.68661

3 13 14 15 16 17 18 21260 64980 36.69113

4 19 20 21 22 23 24 20860 85840 48.46979

5 01 02 07 13 19 25 13420 99260 56.04743

6 03 04 08 14 20 25 12277 111537 62.97967

7 05 06 09 15 21 25 11134 122671 69.26651

8 10 11 16 17 22 23 10176 132847 75.01242

9 01 03 10 12 18 24 8510 141357 79.81761

10 02 05 11 12 14 24 6131 147488 83.27950

11 04 06 07 08 18 22 5904 153392 86.61321

12 09 12 16 17 19 20 4836 158228 89.34387

13 03 08 13 15 21 23 4106 162334 91.66233

14 04 10 11 13 15 20 2802 165136 93.24449

15 01 07 09 14 21 23 2590 167726 94.70694

16 02 06 08 16 17 24 2083 169809 95.88311

17 05 11 18 19 23 25 1799 171608 96.89892

18 03 05 07 15 16 22 1276 172884 97.61942

19 02 04 10 17 18 21 1023 173907 98.19706

20 06 09 12 13 14 22 952 174859 98.73461

21 01 04 15 17 24 25 563 175422 99.05251

22 01 05 08 10 19 20 444 175866 99.30320

23 03 06 07 11 19 20 349 176215 99.50028

24 02 09 15 18 22 23 266 176481 99.65047

25 11 12 13 16 21 25 230 176711 99.78035

26 04 05 07 09 13 24 142 176853 99.86053

27 06 10 14 16 19 25 100 176853 99.91699

28 02 06 12 20 23 25 50 177003 99.94522

29 01 03 08 09 17 22 36 177039 99.96555

30 04 12 14 15 19 23 25 177064 99.97967

31 01 06 16 18 20 21 15 177079 99.98814

32 03 05 10 13 17 25 8 177087 99.99265

33 08 10 14 15 22 24 6 177093 99.99604

34 03 11 14 18 21 22 4 177097 99.99830

35 01 06 11 13 23 24 1 177098 99.99887

36 02 07 14 17 20 22 1 177099 99.99943

37 03 09 16 23 24 25 1 177100 100.00000

Regards

Colin Fairbrother

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Perhaps you have wondered like me as to the minimum number of lines or blocks it would take to get 100% Coverage of the Sixes for a Three win but without repeating any Threes and progressively maximizing the Coverage of the Sixes. This is no trivial task and one that some thought lay outside the bounds of reasonable calculation on a modern fast computer. It probably can be done in RAM memory **alone** using arrays and storing just the results but I chose to progressively write to a database and once you do that things slow down significantly.

Putting it in perspective you can easily generate in about a minute a 3 if 3 for the maximum 496 lines without repeating a Three which is a Cover for the Sixes in a 6/49 game in lexicographic order. Previously, I did the cover in 450 Combs using last number order or progressively increasing the Pool with no repeat Threes but this Cover made no attempt to maximize the coverage of the sixes in the least number of lines. An improvement to 397 lines without repeat Threes was obtained using lexicographic order and with progressive best coverage of the Sixes and this was further improved using some tricks of the trade to 365 as given to the date of this post.

I am advocating that you will get better results in Lotto by using a design with no repeat combinations of 3 integers (Threes), using all the integers and maximizing the coverage of the Sixes because for each combination added : _

- 20 more unique Threes, 15 more unique Fours, 6 more unique Fives and 1 more unique Six go to increasing your chances of winning.

. - progressively the set is optimized for best coverage to minimize the number of combinations used in accordance with Cover convention.

. - no gimmicks or distortions are used unlike the majority of Covers or Wheels with Guarantees where anything goes as long as it reduces the number of combinations used with no regard for the decreased yield ie multiple and higher wins are sacrificed to give a lower number of combinations to guarantee a lower prize.

When this Lotto Play Set or 365 Line Cover is analyzed using my own Lotto Number Set Analyzer for all 13,983,816 possibilities more detail is obtained than shown below. eg 63 groups for when a Four is obtained with a varying number of Threes. This is simplified to 21 groups with a range given for the 3's.

The correct interpretation is important; it is not a history but rather a categorization of the possibilities for 1 draw. If the biggest category or grouping is no result then on the day that is your most likely result; it is an effective way of measuring the spread and magnitude of the prize groupings. This is the method the traditional "Coverists" use to test their wares so they can't knock it!

An incorrect interpretation (ie treating it as eqivalent to a history of draws) is easily shown to be distorted. Testing the playset against all and only the possible 13,983,816 combinations and treating them as draws gives at 52 draws per year something like 268,919 years. There is no guarantee that all the possible combinations would be draws in that time frame. In other words over 13983816 draws there will be lots of repeat sixes and if you divided the possibilities into two arbitrary groups of 6,991,908 then for each draw a six is just as likely to be in one group as in the other!

Further, when you do this type of analysis and proportionately decrease the groupings any set gives about what probability suggests which is unrealistic. The table below shows groupings for 1 draw and which group the single relevant number falls in is random but more likely to be in the larger groupings. **This correlates with the results borne out by realistic tests against actual Lotto histories that show the more you concentrate your numbers or repeat the subsets and the more you restrict the available integers then the more you reduce your chances of winning in the short term which is the way we all play Lotto!**

From the analysis of my C(49,6,3,6)=365 Lotto Cover with Unique Threes™ you see everything is in accordance with the odds. **Your chances of getting a Three in a 6/49 Lotto game are 1 in 56.655927 so for 365 combinations played one would expect an average of 6.44 wins per draw. Looking at the report from my analyzer below we see the dominant grouping at 2,096,805 possible draws or some 15% is that for 7 wins and that is as it should be.** The single Three win accounts, as it should do, for only 2346 possible draws or 0.01678% and you can see you are more likely to get 13 right at 7955 draws or .05689%. The results are easily seen as a classic normal or Bell Curve.

The question arises when pursuing the usual purported objective of a Cover ie to eliminate a no win for any draw result in the least number of lines, that in Lotto isn't the overall yield better improved by allowing a few no win results to exist? After all the prize for a Three win is just a token of some $2.00. Wouldn't one prefer an increase in the multiple win groupings rather than satisfy what is really a stupid objective in a game of chance of making a pittance prize certain by distorting the Normal Distribution in increasing the lowest single prize group?

Regards

Colin Fairbrother

Colin Fairbrother

ps 1 This is a first attempt and if you are so inclined easy to beat by a line or two. Don't post the enumeration for the plagiarists to pounce on - let me know by PM or email, I can easily verify by a few data specific questions.

by Colin Fairbrother

The details on this game are given mainly to illustrate that **the price of certainty in Lotto Designs can be very high. A much wiser course to follow is to tighten or tweak ones entitlement according to the odds without compromising the integrity of the design as far as achieving the higher prizes and forgo a certain prize for each draw.** In other words maximum percentage return with a normal distribution of the prize groupings for the winning possibilities. Playing just 230 lines from my My 275 lines with *Unique 3's*™ will give you an average win of 1 per draw which may be either a 3 + Bonus, Four or even a Five!

The Australian Pick 6 Lotto Games pay only on 4 or more hits in the main 6 integers or 3 in the main with either of the two bonus integers which are drawn without replacement. (2 in the main with the two bonus integers is not paid on.) My 275 lines with *Unique 3's*™ gives also the same number of lines with *Unique 4's*™. **As I have previously pointed out and to the best of my knowledge the first to do so in the other than formal mathematical literature on Lotto designs,** **uniqueness of subsets propagates upwards.**

To understand the analysis on this game it is opportune to refresh or acquaint you with the terminology. Understanding the scholarly articles on Lotto Designs can be hard going but part of the appeal of combinatorics, which is not for the faint hearted, is in the challenges to fully understanding what is going on. So much mis-information is given out as it pertains to Lotto by know alls who are really numerologists, occultists or just plain dim wits that think they understand, but in reality just waffle away without having a clue. You can take it from me, given that I program the calculations, which can be complex, that my definitions are correct.

**Pool or v**The integers from which you pick to fill in the squares on your entry form.

.**Pick or k**The count of the integers that form one line or block.

.**Match or Prize or Guarantee or t**Size of the combination that is guaranteed or paid on at least once if the Cover is complete for any of the winning number possibilities.

.**Nominated Combination from the Pool to Cover or Hits**The size of this combination can be larger than the main line as when an extra or bonus integer is picked in a Pick 6 game to pay on this with a Three from the main - this would be equivalent to a Match 4 in a combination of 7. So, even though you can only specify 6 integers per line the set may be constructed to ensure the possible combinations of 4 from 7 integers drawn are covered. It follows if this is done that 3 integers from the main winning number plus the bonus integer ie 4 hits in the Seven will give a Match or Prize and if not then a higher prize will apply.

Combinations of 6 integers (Six) Pool 45: 45c6 = 8,145,060

Combinations of 1 integer (One) Pool 45: 45c1 = 45

Ones in a Six line: 6c1 = 6

Appearance each One in all Sixes: 45c6/(45c1/6c1) = 8145060/7.5 =1,086,008

Occurrence each One in draws: 1 in 7.5

Chances of getting a One for each draw: 45c6/(6c1*39c5)=2.36 ie 1 in 2.36

Combinations of 2 integers (Two) Pool 45: 45c2 = 990

Twos in a Six line: 6c2 = 15

Appearance each Two in all Sixes: 45c6/(45c2/6c2) = 123,410

Chances of getting a Two: 45c6/(6c2x39c4) ie 1 in 7

Combinations of 3 integers (Three) Pool 45: 45c3 = 14,190

Threes in a Six line: 6c3 = 20

Appearance each Three in all Sixes: 45c6/(45c3/6c3) = 11,480

Chances of getting a non-payable Three: 45c6/(6c3x39c3) ie 1 in 45

Chances of getting a Three + Bonus: 45c6/(6c3x(39c3-37c3)) ie 1 in 297

Combinations of 4 integers (Four) Pool 45: 45c4 = 148,995

Fours in a Six line: 6c4 = 15

Appearance each Four in all Sixes: 45c6/(45c4/6c4) = 820

Chances of getting a Four: 45c6/(6c4x39c2) ie 1 in 733

Combinations of 5 integers (Five) Pool 45: 45c5 = 1,221,759

Fives in a Six line: 6c5 = 6

Appearance each Five in all Sixes: 45c6/(45c5/6c5) = 40

Chances of getting a Five: 45c6/(6c5x37c1) ie 1 in 36,690

Chances of getting a Five + Bonus: 45c6/(6c5x(39c1-37c1)) ie 1 in 678,755

(Interesting calculation for the Five as two of the integers push the prize level up to a Five + Bonus)

Combinations of 7 integers (Seven) Pool 45: 45c7 = 45,379,620

Fours in a Seven line: 7c4 = 35

Appearance each Four in all Sevens: 45c7/(45c4/7c4) = 10,660

(Where 8 integers are drawn (ie 2 bonus integers) it is still combinations of 7 as the two bonus integers together do not form a prize - it is one or the other.)

When constructing a set of numbers by choosing progressively the best coverage of the Fours in the Sixes or the Sevens, making sure not to repeat a Four, there is not much difference in the first 250 lines. After that it makes a considerable difference. The usual distorted, abnormal distribution Cover favouring a single 3+Bonus prize can be done in 1274 lines with many duplicate Fours. (For 1274 lines costing some $790 you have a 3.46% chance of getting a Five at $1600 paying about 53 times as much as a Three+B at $30.00 - a more rational way of looking at your partial chances of success ie losing money 94 times out of a 100.)

For a Gaussian, Normal Distribution or Bell Curve we are looking at around 1,900 lines and the 3+Bonus group with the most likelihood being, as expected, given the odds of 1 in 297, a multiple of 6. But at around 961 lines there is 99% coverage of any prize - it borders on insanity to pursue 100% coverage at more than double the cost. At 62˘ per line you are saving around $596.00 per draw. **A similar analogy can be made for playing only 230 lines per draw from my ****My 275 lines with ***Unique 3's*™** cover if you particularly want an average win per draw ie spending only $143 per draw and giving a consistent around 29% return compared to $790 for certainty which can deliver as little as 1 Four or around $51.00 or a lousy 6%. **

One can easily produce a set of 5923 lines in lexicographic order with *Unique 4's*™. A bit better reduction in lines is obtained by using Last Number Order or progressively increasing the pool of integers and calculating for *Unique 4's*™ , allowing the necessary duplication of the Threes we go from 275 to 5,823 lines. Each of the 87,345 fours from a possible 148,995 are unique in the set of 5,823 lines or blocks. **I have done a set with ***Unique 4's*™ and best coverage in around 3300 lines just for the record and just to see how many lines it would take. However, I have yet to be convinced it is anything other than pure folly to spend huge amounts on Lotto per draw. Spend like I do around $11.00 per week sometimes doubling that amount for a big Jackpot game. Be happy to get back what the odds say you should be getting for the lower prizes and maybe a bit more with a chance at the big one simply by having participated.

For the 5,823 set constructed by Last Number Order there was no progressive coverage calculation so, I was not expecting much and the testing I have done shows no dramatic improvement over random selections in either the short or long run. However the set is not distorted and has a normal distribution. Roughly, a bit over 15% of the Threes shown in the table would convert to a paying win of a Three + 1 Bonus integer. So, if you forked out some $3,610 you would get back each draw **a minimum** of about $500 which is roughly 14% and because this lowest payout grouping is 100th of 1% you can consider yourself very unlucky. In other words you would normally get much more than this. **Interestingly, the most dominant group is the Fives at 16.72894% which would return about 60% of the sum wagered $2166.00.** **To be in front then you would need to get a Five plus one of the bonus integers and that is a very tall order because roughly that translates to less than 1%.** **These kind of figures, which you won't find elsewhere, perhaps give you an understanding of why I view the con-artists in this field of interest with utter contempt.** A distorted cover with abnormal distribution favoring the lowest prize group ie 1 Four win with about 2 Three + Bonus (33%) followed by the second lowest ie 2 x Four wins with about 2 Three + Bonus (18%) can be done in 2668 lines.

For those that are thinking of replicating the calculations then a reasonable knowledge of working with arrays and expertise in coding to calculate coverage in the shortest possible time using methods that bypass a lot of the low rating possibilities is essential to keep computer time within reasonable bounds. You will need to build in methods for pausing, stopping and resuming (so you can use your computer for other tasks). It makes you very much aware of how that extra integer from 44 to 45 adds an extra 1,086,008 possibilities as does 48 to 49 add another 1,712,304.

6 Win 5 Win 4 Win 3 Win Comb 6's Comb 6's % Cum %

-----------------------------------------------------------------------------

- - 1 100-158 877 0.01077 0.01077

- - 2 92-165 9566 0.11745 0.12821

- - 3 83-167 50205 0.61639 0.74460

- - 4 73-172 172492 2.11775 2.86235

- - 5 67-177 421257 5.17193 8.03428

- - 6 58-179 759226 9.32131 17.35559

- - 7 57-178 1060037 13.01448 30.37006

- - 8 61-179 1175360 14.43034 44.80041

- - 9 59-179 1078551 13.24178 58.04219

- - 10 52-178 850310 10.43958 68.48177

- - 11 59-176 587541 7.21346 75.69523

- - 12 59-178 350948 4.30872 80.00395

- - 13 62-173 174179 2.13846 82.14242

- - 14 82-173 68332 0.83894 82.98135

- - 15 91-170 17774 0.21822 83.19957

- 1 0-10 60-186 1362582 16.72894 99.92851

1 0 0 100-203__ 5823__ 0.07149 100.00000

8,145,060

-----------------------------------------------------------------------------

- - 1 100-158 877 0.01077 0.01077

- - 2 92-165 9566 0.11745 0.12821

- - 3 83-167 50205 0.61639 0.74460

- - 4 73-172 172492 2.11775 2.86235

- - 5 67-177 421257 5.17193 8.03428

- - 6 58-179 759226 9.32131 17.35559

- - 7 57-178 1060037 13.01448 30.37006

- - 8 61-179 1175360 14.43034 44.80041

- - 9 59-179 1078551 13.24178 58.04219

- - 10 52-178 850310 10.43958 68.48177

- - 11 59-176 587541 7.21346 75.69523

- - 12 59-178 350948 4.30872 80.00395

- - 13 62-173 174179 2.13846 82.14242

- - 14 82-173 68332 0.83894 82.98135

- - 15 91-170 17774 0.21822 83.19957

- 1 0-10 60-186 1362582 16.72894 99.92851

1 0 0 100-203

8,145,060

Regards

Colin Fairbrother

Colin Fairbrother

ps If you are wondering about the 2nd last line in the table - note that there are 5,823 lines in the set - only 1 can be a winning six line but with 100 - 203 three wins, which would convert to about 15 to 20 3+ Bonus prizes, thrown in as well.

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