Prize6 | Prize5 | Prize4 | Prize3 | Count | Probability |
---|---|---|---|---|---|

0 | 0 | 15 | 2 | 10 | 0.0476190 |

0 | 2 | 9 | 8 | 60 | 0.2857142 |

0 | 3 | 7 | 9 | 60 | 0.2857142 |

0 | 3 | 8 | 7 | 60 | 0.2857142 |

1 | 0 | 10 | 8 | 15 | 0.0714285 |

1 | 0 | 12 | 4 | 5 | 0.0238095 |

Prize6 | Prize5 | Prize4 | Prize3 | Count | Probability |
---|---|---|---|---|---|

0 | 0 | 0 | 0 | 12721488 | 0.9097293 |

0 | 0 | 0 | 3 | 822510 | 0.0588187 |

0 | 0 | 0 | 4 | 182780 | 0.0130708 |

0 | 0 | 0 | 5 | 91390 | 0.0065354 |

0 | 0 | 1 | 8 | 55575 | 0.0039742 |

0 | 0 | 1 | 9 | 44460 | 0.0031793 |

0 | 0 | 2 | 7 | 44460 | 0.0031793 |

0 | 0 | 3 | 2 | 7410 | 0.0005298 |

0 | 0 | 3 | 4 | 3705 | 0.0002649 |

0 | 0 | 5 | 10 | 468 | 0.0000334 |

0 | 0 | 5 | 11 | 2340 | 0.0001673 |

0 | 0 | 7 | 6 | 2340 | 0.0001673 |

0 | 0 | 15 | 2 | 10 | 0.0000007 |

0 | 1 | 3 | 11 | 2340 | 0.0001673 |

0 | 1 | 4 | 10 | 2340 | 0.0001673 |

0 | 2 | 9 | 8 | 60 | 0.0000042 |

0 | 3 | 7 | 9 | 60 | 0.0000042 |

0 | 3 | 8 | 7 | 60 | 0.0000042 |

1 | 0 | 10 | 8 | 15 | 0.0000010 |

1 | 0 | 12 | 4 | 5 | 0.0000003 |

]]>

OUTRAGEOUS LOTTO CLAIMS

In 1997 Dr Iliya Bluskov wrote his thesis titled "

http://www.collectionscanada.

TheCover Bluskov uses guarantees in a hypothetical and non-existent 6/14 Lotto game that unequivocally a match-4 will be obtained,not only when all the 3003 combinations of 6 from 14 areconsidered or the 2002 combinations of 5 from 14 but also whenthe 1001 combinations of 4 from 14 are considered.

What does this Cover, which can be described using the syntax C(14,6,4,4,1)=80 guarantee in a 6/49 Lotto game? The answer is a BIG FAT NOTHING! For the minimum guarantee in a 6/49 Lotto game a C(49,6,3,6)=163 is needed ie 163 lines - no ifs, no buts. The coverage for the C(14,6,4,4,1)=80 for any match in a 6/49 Lotto game is only 21.82% compared to 80 random selections using the full Pool of 49 of 78% + or - 1.

However, according to Dr Iliya Bluskov it "

The next paragraph introduces the reader to the Iliya Bluskov art of devious, deceitful semantics and just outright lies. The paragraph is reproduced below; let's examine it phrase by phrase.

playing for such a guaranteed win? If we compare

playing with 80 random tickets against 80 tickets

forming a (14,6,4) covering we see that the probability

of a 6-win ("hitting the jackpot") is the same for

each ticket; namely 14c6^-1. However, if any 4 of

the numbers drawn are among the 14 numbers chosen by

the syndicate, then the 80 tickets of a (14,6,4)

covering guarantee at least one 4-win while 80 random

tickets (on the same 14 numbers) guarantee nothing!

This property of the coverings is attractive to some

lottery players and there are many books (see, for

example, [32] or [46]) and computer software

available describing coverings. In this application,

the coverings are often referred to as wheels or

lottery systems."

The paragraph begs the question to any rational and mildly analytical reader, "Why random selections from only 14 numberswhen the example is for a 6/49 Lotto game?". Also, "Where woulda normal player go to get 80 random selection lines from a Poolof only 14?"

Now, knowing Iliya Bluskov and most of his tactics from the other article I started titled :-

Professor Iliya Bluskov promotes deceitful claims for Lotto Covers or Wheels

https://groups.google.com/

- the first accusation he will make is to accuse me of rigging the 80 random lines of 6 from 14. Well, at the bottom of this page I have embedded the reputable Randomizer.org RNG for your convenience with instructions.

Let's examine this very loud sentence,

14 numbers chosen by the syndicate, then the 80

tickets of a (14,6,4) covering guarantee at least one

4-win while 80 random tickets (on the same 14 numbers)

guarantee nothing!"

Far from being no guarantee after the draw as Iliya Bluskov states for 80 Random Selections of 6 numbers from 14, if three numbers or four are seen to be in the draw then there is a 4if6 guarantee as well as a 3if4 and consequently 3if5 and 3if6.

Range | Absent Integers | 3if3 Covered | 3if3 Uncovered | 3if4 Covered | 4if4 Covered | 4if4 Uncovered | 4if5 Covered | 4if5 Uncovered | 4if6 Covered | Repeats |

1 to 80 | 0 | 360 | 4 | TRUE | 692 | 309 | 1989 | 1 | TRUE | 2 |

81 to 160 | 0 | 358 | 6 | TRUE | 704 | 297 | 1996 | 6 | TRUE | 0 |

161 to 240 | 0 | 360 | 4 | TRUE | 711 | 290 | 1988 | 14 | TRUE | 1 |

241 to 320 | 0 | 359 | 5 | TRUE | 686 | 315 | 1989 | 13 | TRUE | 1 |

321 to 400 | 0 | 357 | 7 | TRUE | 673 | 328 | 1991 | 11 | TRUE | 2 |

401 to 480 | 0 | 362 | 2 | TRUE | 717 | 284 | 2000 | 2 | TRUE | 1 |

481 to 560 | 0 | 362 | 2 | TRUE | 721 | 280 | 1998 | 4 | TRUE | 1 |

561 to 640 | 0 | 364 | 0 | TRUE | 707 | 294 | 1993 | 9 | TRUE | 4 |

641 to 720 | 0 | 362 | 2 | TRUE | 702 | 299 | 1987 | 15 | TRUE | 1 |

721 to 800 | 0 | 363 | 1 | TRUE | 727 | 274 | 1999 | 3 | TRUE | 0 |

801 to 880 | 0 | 357 | 7 | TRUE | 690 | 311 | 1986 | 16 | TRUE | 2 |

881 to 960 | 0 | 352 | 12 | TRUE | 684 | 317 | 1976 | 26 | TRUE | 2 |

961 to 1040 | 0 | 361 | 3 | TRUE | 708 | 293 | 1989 | 13 | TRUE | 0 |

1041 to 1120 | 0 | 358 | 6 | TRUE | 702 | 299 | 1982 | 20 | TRUE | 2 |

1121 to 1200 | 0 | 356 | 8 | TRUE | 690 | 311 | 1982 | 20 | TRUE | 1 |

1201 to 1280 | 0 | 352 | 12 | TRUE | 694 | 307 | 1981 | 21 | TRUE | 1 |

1281 to 1360 | 0 | 358 | 6 | TRUE | 689 | 312 | 1995 | 7 | TRUE | 2 |

1361 to 1440 | 0 | 357 | 7 | TRUE | 703 | 298 | 1996 | 6 | TRUE | 2 |

1441 to 1520 | 0 | 362 | 2 | TRUE | 729 | 272 | 1997 | 5 | TRUE | 1 |

1521 to 1600 | 0 | 360 | 4 | TRUE | 707 | 294 | 1990 | 12 | TRUE | 2 |

Range | 6/49 3if6 Coverage | Absent Integers | Repeats | 3if6 Covered | 3if5 Covered | 3if4 Covered | 3if3 Covered | 3if3 Uncovered | 4if6 Covered | 4if5 Covered | 4if5 Uncovered | 4if4 Covered | 4if4 Uncovered |

1 to 20 | 8.96 | 0 | 1 | TRUE | TRUE | TRUE | 119 | 1 | TRUE | 252 | 0 | 166 | 44 |

21 to 40 | 8.77 | 0 | 2 | TRUE | TRUE | TRUE | 116 | 4 | TRUE | 251 | 1 | 156 | 54 |

41 to 60 | 8.44 | 0 | 0 | TRUE | TRUE | TRUE | 111 | 9 | TRUE | 251 | 1 | 149 | 61 |

61 to 80 | 8.90 | 0 | 0 | TRUE | TRUE | TRUE | 118 | 2 | TRUE | 251 | 1 | 164 | 46 |

81 to 100 | 8.96 | 0 | 0 | TRUE | TRUE | TRUE | 119 | 1 | TRUE | 252 | 0 | 164 | 46 |

101 to 120 | 8.83 | 0 | 2 | TRUE | TRUE | TRUE | 117 | 3 | TRUE | 252 | 0 | 162 | 48 |

121 to 140 | 8.96 | 0 | 0 | TRUE | TRUE | TRUE | 119 | 1 | TRUE | 251 | 1 | 170 | 40 |

141 to 160 | 8.77 | 0 | 1 | TRUE | TRUE | TRUE | 116 | 4 | TRUE | 250 | 2 | 161 | 49 |

161 to 180 | 9.03 | 0 | 2 | TRUE | TRUE | TRUE | 114 | 6 | TRUE | 249 | 3 | 153 | 57 |

181 to 200 | 8.96 | 0 | 0 | TRUE | TRUE | TRUE | 119 | 1 | TRUE | 252 | 0 | 172 | 38 |

201 to 220 | 8.96 | 0 | 0 | TRUE | TRUE | TRUE | 119 | 1 | TRUE | 252 | 0 | 172 | 38 |

221 to 240 | 8.37 | 0 | 0 | TRUE | TRUE | TRUE | 110 | 10 | TRUE | 248 | 4 | 143 | 67 |

241 to 260 | 9.03 | 0 | 1 | TRUE | TRUE | TRUE | 120 | 0 | TRUE | 252 | 0 | 169 | 41 |

261 to 280 | 8.96 | 0 | 1 | TRUE | TRUE | TRUE | 119 | 1 | TRUE | 252 | 0 | 173 | 37 |

281 to 300 | 8.77 | 0 | 1 | TRUE | TRUE | TRUE | 116 | 4 | TRUE | 251 | 1 | 162 | 48 |

301 to 320 | 8.63 | 0 | 0 | TRUE | TRUE | TRUE | 114 | 6 | TRUE | 252 | 0 | 160 | 50 |

321 to 340 | 8.70 | 0 | 0 | TRUE | TRUE | TRUE | 115 | 5 | TRUE | 251 | 1 | 153 | 57 |

341 to 360 | 8.57 | 0 | 1 | TRUE | TRUE | TRUE | 113 | 7 | TRUE | 247 | 5 | 153 | 57 |

361 to 380 | 8.90 | 0 | 1 | TRUE | TRUE | TRUE | 118 | 2 | TRUE | 252 | 0 | 169 | 41 |

381 to 400 | 9.03 | 0 | 0 | TRUE | TRUE | TRUE | 120 | 0 | TRUE | 252 | 0 | 173 | 37 |

1st row enter 80

2nd row enter 6

3rd row enter 1 to 14

4th row Yes

5th row Yes

After generating select copy to Excel.

In Excel highlight numbers and Copy

In Excel select your start cell and then Paste Special.

In the Paste Special dialogue check transpose.

Colin Fairbrother

]]>

Prize6 | Prize5 | Prize4 | Prize3 | Cnt | Probability | Likely 1000 Plays or 36 Draws |
---|---|---|---|---|---|---|

0 | 0 | 0 | 0 | 13327132 | 0.95 | 34 |

0 | 0 | 0 | 10 | 596960 | 0.04 | 2 |

0 | 0 | 6 | 16 | 57400 | 0.00 | 0 |

0 | 3 | 15 | 10 | 2296 | 0.00 | 0 |

1 | 12 | 15 | 0 | 28 | 0.00 | 0 |

Prize6 | Prize5 | Prize4 | Prize3 | Combs | Probability | Likely 1000 Plays or 36 Draws |
---|---|---|---|---|---|---|

0 | 0 | 0 | 0 | 7571012 | 0.54 | 19 |

0 | 0 | 0 | 1 | 5225888 | 0.37 | 14 |

0 | 0 | 0 | 2 | 759408 | 0.05 | 2 |

0 | 0 | 0 | 3 | 39728 | 0.00 | |

0 | 0 | 0 | 4 | 1268 | 0.00 | |

0 | 0 | 1 | 0 | 337260 | 0.02 | 1 |

0 | 0 | 1 | 1 | 42000 | 0.00 | |

0 | 1 | 0 | 0 | 7224 | 0.00 | |

1 | 0 | 0 | 0 | 28 | 0.00 |

For every draw playing the System 8 you have a 95% chance of getting nothing compared to 54% for the Partial Cover. If you like for the Cover/Wheel 1 in 20 will give you nothing compared to the Partial Cover with only 1 in 2 giving nothing.

Playing the System 8 you can expect to go 24 draws before a win compared to the Partial Cover with a win expected every 2nd draw.

A System 8 or Full Wheel 8 is highly volatile and can go playing the same numbers 175 draws or more without a win. Compare this to the Partial Cover that rarely goes more than 11 draws.

I strongly recommend that you randomize whatever set you are playing before every draw for the game you are playing. Don't fall into the trap of being a slave to Lotto, worrying about missing a draw because that might be the one when your numbers come up.

UK Costs and Payouts for 36 draws (1008 plays).

System 8 Prizes £25 x 20 = £500 Yield 24.8%

Partial Cover Prizes £25 x 14 + £50 x 4 + £100 x 1 = £550 Yield 27.28%

OR OPTIMUM STRUCTURED SETS

OR DISTORTED SETS

by Colin Fairbrother

Lotto players can refer to information printed or online from Lotto Operators which give the Odds for winning a prize for one line or ticket and in some cases for the minimum lines playable, which is simply the respective multiple of that applicable to one line.

In this article I will use the Classic Lotto game where 6 numbers or distinct balls are randomly picked from 49 and where a prize is obtained if in any line played there is a match of at least 3, 4, 5 or 6 integers. To simplify matters the bonus ball is ignored and the principles outlined here are applicable to any Pick 5 or Pick 6 Lotto game.

For any given Lotto game matrix the odds or probability, as I shall refer to it from hereon, can be calculated for any given match.

Consider first one line in our 6/49 game, say, 01 02 03 04 05 06, realizing the numbers used are just identifiers with no magnitude. This combination of 6 numbers or integers (CombSix) is just 1 combination to pit against the 1 combination first prize of which there are 13,983,816 distinct possibilities for the draw. Each line or draw also has 6 combinations of 5 integers, 15 combinations of 4 integers and 20 combinations of 3 integers for a possible match. One line is flawless and is no better than any other line.

Any combination of 3 integers will for an enumerated 13,983,816 CombSixes appear 15,180 times. Any combination of 4 integers will appear 990 times and any combination of 5 integers will appear 44 times. Due to overlaps the combinations when considered distinctly are 1,906,884 CombFives, 211,876 CombFours and 18,424 CombThrees.

= 1 / (13983816 / 246820)

= 1 / 56.6559273

= 0.0176504

Multiplying this probability for 1 draw gives 0.0176504 of a match-3.

Multiplying this probability for 29 draws gives 0.5118616 of a match-3.

Multiplying this probability for 57 draws gives 1.0060728 match-3's.

Multiplying this probability for 114 draws gives 2.0121456 match-3's

________________________________________________________

= 1 / (13983816 / 13545)

= 1 / 1032.3968

= 0.0009686

Multiplying this probability for 1 draw gives 0.0009686 of a match-4.

Multiplying this probability for 518 draws gives 0.5017348 of a match-4.

Multiplying this probability for 1033 draws gives 1.0005638 match-4's.

Multiplying this probability for 2065 draws gives 2.000159 match-4's.

________________________________________________________________

= 1 / 54200.837

= 0.0000184

Multiplying this probability for 1 draw gives 0.0000184 of a match-5.

Multiplying this probability for 27180 draws gives 0.500112 of a match-5.

Multiplying this probability for 54380 draws gives 1.000592 match-5's.

Multiplying this probability for 109000 draws gives 2.0056 match-5's.

________________________________________________________________

= 1 / (13983816 / 1)

= 1 / 13983816

= 0.0000001

While highly likely there is no guarantee you will get a 1st prize in 14,000,000 draws.

_________________________________________________________________

As the number of draws increases the likelihood of no prizes decreases.

_________________________________________________________________

By testing against all 13,983,816 possibilities a Prize Table can be produced for one line that gives exactly the same probability as the theoretical caculation. Multiplying the probabilty by the number of plays, which in this case is the same as the draws, is exactly the same as one would do to work out potential winnings using the theoretical calculation..

Combs Probability Likely Likely Likely Likely

6 5 4 3 1 29 518 27180

Draw Draws Draws Draws

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

0 0 0 0 13723192 0.9813625 1 28 508 26673

0 0 0 1 246820 0.0176540 0 1 9 480

0 0 1 0 13,545 0.0009686 0 0 1 26

0 1 0 0 258 0.0000184 0 0 0 1

1 0 0 0 1 0.0000001 0 0 0 0

_______________________________________________________

Note that for two or more CombSixes it is possible to build distortion into the set when compared to Random Selections where for say, a 6/49 Lotto game, it is extremely rare to get high repeat subsets. The System 8 or Full Wheel 8 will be used as an example of an abnormal set as enumerated below -

1 2 3 4 5 6

1 2 3 4 5 7

1 2 3 4 5 8

1 2 3 4 6 7

1 2 3 4 6 8

1 2 3 4 7 8

1 2 3 5 6 7

1 2 3 5 6 8

1 2 3 5 7 8

1 2 3 6 7 8

1 2 4 5 6 7

1 2 4 5 6 8

1 2 4 5 7 8

1 2 4 6 7 8

1 2 5 6 7 8

1 3 4 5 6 7

1 3 4 5 6 8

1 3 4 5 7 8

1 3 4 6 7 8

1 3 5 6 7 8

1 4 5 6 7 8

2 3 4 5 6 7

2 3 4 5 6 8

2 3 4 5 7 8

2 3 4 6 7 8

2 3 5 6 7 8

2 4 5 6 7 8

3 4 5 6 7 8

By testing against all 13,983,816 possibilities a Prize Table can be produced which gives the groupings and by dividing by 13983816 the probability for each group based on the structure of the set. If the same set is used for more simulated draws then simply multiplying the probabilty for each group by the number of simulated draws required will give proportionally the likely wins make-up.

Likely Wins From 28 Lines 6/49 Lotto with System 8 | |||||||||||||

6 | 5 | 4 | 3 | Combs | Probability | Likely 1 Draw | Likely 2 Draws | Likely 12 Draws | Likely 37 Draws | Likely 120 Draws | Likely 1936 Draws | Likely 2985 Draws | |

- | - | - | - | 13327132 | 0.9530397 | 1 | 2 | 11 | 35 | 114 | 1845 | 2845 | |

- | - | - | 10 | 596960 | 0.0426893 | 0 | 0 | 1 | 2 | 5 | 83 | 127 | |

- | - | 6 | 16 | 57400 | 0.0041047 | 0 | 0 | 0 | 0 | 1 | 8 | 12 | |

- | 3 | 15 | 10 | 2296 | 0.0001642 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | |

1 | 12 | 15 | 0 | 28 | 0.0000020 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |

13983816 | 1 | 2 | 12 | 37 | 120 | 1936 | 2985 | ||||||

These figures are a guide. For the more exotic like the 3 Fives with 15 Fours and 10 Threes ie each line of 28 line set has a hit then flexibility is required; 0.5 is only 2985 draws whereas closer to 1 is more like 6090 draws. Initially one can use the Ceiling function but if the total does not equal the draws a manual check may be required. The allocation between no prizes and prizes is the first priority and within prizes some can be consolidated to a lower prize but always guided by probability.

Building a Prize Table for the Twenty Eight

By testing against all 13,983,816 possibilities a Prize Table can be produced which gives the groupings and by dividing by 13983816 the probability for each group based on the structure of the set. If the same set is used for more simulated draws then simply multiplying the probabilty for each group by the number of simulated draws required will give proportionally the likely wins make-up.

Likely Wins 28 Lines Partial Cover, Unique Threes, Full Pool Optimized 6/49 Lotto | |||||||||

6 | 5 | 4 | 3 | Combs | Probability | Likely 1 Draw | Likely 2 Draws | Likely 37 Draws | Likely 1936 Draws |

- | - | - | - | 7571012 | 0.5414124 | 1 | 1 | 20 | 1048 |

- | - | - | 1 | 5225888 | 0.3737097 | 0 | 1 | 14 | 723 |

- | - | - | 2 | 759408 | 0.0543062 | 0 | 0 | 2 | 105 |

- | - | - | 3 | 39728 | 0.0028410 | 0 | 0 | 0 | 6 |

- | - | - | 4 | 1268 | 0.0000907 | 0 | 0 | 0 | 0 |

- | - | 1 | 0-1 | 379260 | 0.0271214 | 0 | 0 | 1 | 53 |

- | 1 | - | - | 7224 | 0.0005166 | 0 | 0 | 0 | 1 |

1 | - | - | - | 28 | 0.0000020 | 0 | 0 | 0 | 0 |

13983816 | 1 | 29 | 37 | 1936 | |||||

]]>

FOR SPECIFIED DRAWS AND

SET OF NUMBERS PLAYED

(includes summary of debate between Colin Fairbrother and

Professor Iliya Bluskov January 2014)

I pose the rhetorical question, " ... whether other than through sheer luck the odds can be bettered." in the header at my site LottoToWin. To any mathematician worth his salt the answer is no. That being so are their sets of numbers one can play in Lotto that get us pretty spot on with the odds? The answer is yes - I have shown the Steiner Cover C(22,6,3,3)=77 achieves that as much as is possible with a hypothetical Pick 6, Pool 22 Lotto game. (The syntex in order is Pool 22, Pick 6, Guarantee or Match 3, Hits and Minimum Lines 77.) The logical next question is, are there sets that reduce your chances of getting the maximum return in Lotto in the reasonable short term? - the answer is yes and I will demonstrate that below.

Prize tables are commonly given by Lotto Operators for a Lotto Design as in Australia for the System 7 and System 8 which are respectively all the Combinations of six integers for a Pool of 7 or 8 integers. eg see

Prize Divisions Tatts Lotto

The important point is that if playing a System 8 or Full Wheel 8 the Prize Table is not given for a hypothetical 6/8 Lotto game but for the actual Lotto game, say, 6/45. To do otherwise would be considered to be misinformation and grossly deceptive.

System Prize Tables can be produced mathematically but for other sets only through analysis of the Lotto design by testing it eg a 6/49 Lotto game against all the 13,983,816 possible combinations of six integers for prizes or matches and these can then be grouped. You can do it yourslf by getting the free CoverMaster program from John Rawson. For details see -

Constructing Best Lotto Covers or Wheels

In the Covermaster Detailed Report the probability for each group can be obtained by moving the decimal point to the left two places in the percentage column.

Despite trials backing up this method Bluskov maintains it is flawed and does not take into account the occasional big winner which would render the interpretation invalid. He maintains that despite the Lotto Design being already tested against the 13,983,816 possible CombSixes in a 6/49 Lotto game for prizes it should be done again for each prize group. The intention is obvious - to obfusticate and over complicate a simple task with a simple intention.

Bluskov laughs at the idea that lower prizes can be used to assess the merits of a Lotto playset despite it being proven time and again in trials. Of course a big win can occur but it can be set aside and reliance put on the more repetitive prize groups. All the Covers or Wheels tested at -

LOTTO WHEELS OR COVERS CON-ARTIST CLAIMS TOTALLY DEBUNKED IN TABLE by Colin Fairbrother

have been done in a consistent manner and not one has performed better in returns than Partial Covers with no repeat subsets, full Pool used and Coverage maximized. Some have given very poor returns.

In my popular free online article titled -

ANALYSIS OF 15 LOTTO NUMBER SETS - WORST TO BEST

the second worst is the System 8 or Full Wheel for Pool 8 when applied to a 6/49 Lotto game which is all 28 combinations of 6 integers from 8 integers. Here it is -

1 2 3 4 5 6

1 2 3 4 5 7

1 2 3 4 5 8

1 2 3 4 6 7

1 2 3 4 6 8

1 2 3 4 7 8

1 2 3 5 6 7

1 2 3 5 6 8

1 2 3 5 7 8

1 2 3 6 7 8

1 2 4 5 6 7

1 2 4 5 6 8

1 2 4 5 7 8

1 2 4 6 7 8

1 2 5 6 7 8

1 3 4 5 6 7

1 3 4 5 6 8

1 3 4 5 7 8

1 3 4 6 7 8

1 3 5 6 7 8

1 4 5 6 7 8

2 3 4 5 6 7

2 3 4 5 6 8

2 3 4 5 7 8

2 3 4 6 7 8

2 3 5 6 7 8

2 4 5 6 7 8

3 4 5 6 7 8

This Full Wheel has a lot of repetition of the subsets. Instead of 560 distinct CombThrees there are only 56 repeated 10 times. Instead of 420 distinct CombFours there are only 70 repeated 6 times. Instead of 168 CombFives there are only 56 repeated 3 times. Many Covers or Wheels have excessive repetition of the subsets.

Intuitively one would think, correctly, that it would be harder to get any of these prizes because of the repetition while realizing when they did occur there would be multiple prizes.

This Wheel has a guarantee for a hypothetical Pick 6 Pool 8 Lotto game but no such game exists. The guarantee is that after the draw if the 6 numbers drawn are in the 8 chosen then you win or share first prize. Of course this guarantee is totally irrelevant and useless when using this Wheel in a 6/49 Lotto game as only 28 of the 13,983,816 combinations are available just like any other jumbled up set of 28 lines. These deceptive lower Pool guarantees are not much different to saying if one of your lines has 6 integers that are the same as the winning 6 integers you win or share first prize.

Analysing this 28 line set by testing against the 13,983,816 possible combinations of six integers in a 6/49 Lotto game and then multiplying the probability by 36 for a good approximation of 1000 plays or 36 draws we get 36 most likely occurrences -

- - - - 13327132 0.9530397 34

- - - 10 596960 0.0426893 2

- - 6 16 57400 0.0041047 -

- 3 15 10 2296 0.0001642 -

1 12 15 0 28 0.0000020 -

In a trial over 36 draws we are expecting 2x10=20 match Threes.

The results below apply the 28 line Pool 8 Full Wheel over 36 draws using the UK Lotto results starting from draw 1 for 20 trials.

1 to 36 20 - - -

37 to 72 20 - - -

73 to 108 40 - - -

109 to 144 - - - -

145 to 180 20 - - -

181 to 216 10 - - -

217 to 252 50 - - -

253 to 288 30 - - -

289 to 324 10 - - -

325 to 360 - - - -

361 to 396 20 - - -

397 to 432 10 - - -

433 to 468 20 - - -

469 to 504 30 - - -

505 to 540 10 - - -

541 to 576 36 6 - -

577 to 612 20 - - -

613 to 648 - - - -

649 to 684 - - - -

685 to 720 10 - - -

There are 4 trials of 36 draws with no matches.

The trial average for match Threes is approx 18.

Total plays: 20160

Using standard UK costs and payouts of £2, £25 and £100

Cost Total: 28x36x2x20=£40320

Prize Total: £9500

Yield or Percentage Return: 23.56%

To nullify any accusations of rigging I use the record coverage

6/49 Partial Cover for 28 lines at -

John Rawson's site

exactly as provided by Adolf Muehl with no duplicate CombThrees.

(nb I do not endorse all these partiial Covers as after 73 lines they have duplicate CombThrees.)

Analysing this 28 line Partial Cover set by testing against the 13,983,816 possible combinations of six integers in a 6/49 Lotto game and then multiplying the probability by 36 for a good approximation of 1000 plays or 36 draws we get 36 most likely occurrences -

- - - - 7571012 0.5414124 20

- - - 1 5225888 0.3737097 13

- - - 2 759408 0.0543062 2

- - - 3 39728 0.0028410 -

- - - 4 1268 0.0000907 -

- - 1 0-1 379260 0.0271214 1

- 1 - - 7224 0.0051660 -

1 - - - 28 0.0000020 -

In a trial over 36 draws we are expecting 13x1=13 + 2x2=4 ie 17 match Threes and 1 match 4.

The results below apply the Partial Cover over 36 draws using the UK Lotto results starting from draw 1 for 20 trials.

1 to 36 17 1 - -

37 to 72 18 1 - -

73 to 108 17 2 - -

109 to 144 19 3 - -

145 to 180 18 3 - -

181 to 216 17 1 - -

217 to 252 19 1 - -

253 to 288 21 1 - -

289 to 324 20 2 - -

325 to 360 14 2 - -

361 to 396 15 - - -

397 to 432 13 - - -

433 to 468 17 2 1 -

469 to 504 15 1 - -

505 to 540 19 3 - -

541 to 576 15 1 - -

577 to 612 21 - - -

613 to 648 18 1 - -

649 to 684 5 1 1 -

685 to 720 23 1 - -

All trials of 36 draws have matches.

The trials average for match Threes is approx 17 as estimated.

The trials average for match Fours is approx 1 as estimated

Total plays: 20160

Using standard UK costs and payouts of £2, £25 and £100

Cost Total: 28x36x2x20=£40320

Prize Total: £13225

Yield or Percentage Return: 32.80%

Difference between Wheel and Partial Cover results: 9.24%

Note: If the two match Fives were treated as match Fours the

difference would still be 4.78% in favour of the Partial Cover.

Bluskov would have us believe that he and his cohorts promote lesser Pool Covers or Wheels with irrelevant guarantees so that users will have the sheer joy of using their favoured numbers in inferior sets for the actual Lotto game they are playing.

I never thought I'd read a Professor of Mathematics with a Doctorate casting doubt on the randomness of the draws because of ball imperfections. The truth is Bluskov is a fellow traveller and apologist for the fruit cake brigade in Lotto analysis as debunked by me in: -

Analysis of Lotto Draw History - the Final Word

Will their Lotto System work in the simplest case?

Six articles under heading of Lotto Filters Simply Do Not Work

As I have pointed out before the seed for deception can be traced back to Bluskov's thesis New Designs and Coverings where he trots out the line on Page 9 that a guarantee for a C(14,6,4,4)=80 in a hypothetical 6/14 Lotto game with only 3003 combinations of six integers somehow carries over beneficially to a 6/49 Lotto game with some 14 million. It doesn't - for the easiest to get prize 3if6 only 3,051,048 CombThrees are covered or 21.82% whereas the first 80 draws or Random Selections from the UK Lotto gives a 3if6 Coverage of 78%.

Here is the crunch- Bluskov disparages Random Selections as having no guarantee despite there being three and a half times more 3if 6 Coverage and that doesn't vary more than 1% for any other contiguous set of 80.

On the same page Bluskov insults the intelligence of the reader by stating with my capitals, "However, if any 4 of the numbers drawn are among the 14 numbers chosen by the syndicate, then the 80 tickets of a (14,6,4) covering guarantee at least one 4-win while 80 random tickets (ON THE SAME 14 NUMBERS) guarantee nothing!"

This is a thesis. HE IS REFERRING TO A 6/49 LOTTO GAME; SURELY 80 RANDOM TICKETS FROM A POOL OF 49 IS MORE RELEVANT! WHERE WOULD YOUR AVERAGE PLAYER GET 80 RANDOM TICKETS FROM 14 NUMBERS AND MORE TO THE POINT WHY WOULD THEY BOTHER?

---------------------------------------------------------------------------- ooo ----------------------------------------------------------------------------

By reading my last message above and then looking at previous messages in the thread a mockery is made of all the pretence, lies, innuendo and just plain stupidity of Dr Iliya Bluskov, Professor of Mathematics, University of Northern British Columbia.

A reasonable question is, "Having already the information in your last post why didn't you post it first?"

The short answer is I was playing with him - I wanted to draw him out and he obliged me beyond all of my expectations. Bluskov's intellectual arrogence and desperation to try and justify just plain nonsense got the better of him.

Some notable gaps in his knowledge base became evident:

**not recognising that theoretical calculations in Lotto accept**Bluskov makes the enormous error of assuming he

Random Selections as being a suitable reference base and

definitely rule out distorted sets with excessive repetition of

the subsets.

can do a formula calculation which is based on all the possibilities for

the Pool and Pick and all the subsets, which is simply not applicable

in the short or medium term. This is not the first time that learned

people have under-estimated Random Selections and withdrawn

papers or scurried to amend them.- any statistical calculation relies on having a suitable sampling and this

does not have to be the full population. - Random Selection Sets in Lotto have a remarkable consistency in

Coverage which over say 56 draws may not vary much beyond 1%. **Bluskov categorically states, ignoring all the evidence to the**

contrary, that no matter how distorted is a set of numbers

played in Lotto it will give the same return short or long term

as a non-distorted set.

Also reading the thread you will find Bluskov harping on Return on Investment (ROI) as if I knew nothing about it - this to a person who has actually been in business for nearly 40 years and is able to do accounts up to P/L and Balance Sheet etc. I never use "Investment" in relation to Lotto if only because your principle is lost from the time you buy tickets.

Making an exception and considering the UK Lotto the contribution of 1st Prize to the return is the same whatever the set as long as the lines are unique. Multiplying the 1st prize payout, say an average £4 million by the probability 0.0000000715112 gives £0.286. For 2nd Prize we have £50,000 x 0.0000004 giving £0.022 contribution. For all intents and purposes the overwhelming majority of Lotto players paying £2.00 per ticket will not see a penny of this 31p for

For the UK 6/49 Lotto there are to 1/2/2014 1890 draws since 1994 with

3,125,000

with each player buying an average of 4 lines or tickets ie average

12,500,000 plays per draw

The average number of 1st and 2nd prize winners per draw is

expected return to most players

to leave out 1st and 2nd tier prizes

as the overwhelming

99.99968% of players per draw

do not receive any benefit from them.

- In a separate thread I poured scorn on Iliya Bluskov for not ruling out a lower bound of first 54 then 87 for C(49,6,3,6) in a post at rec.gambling.lottery in January 1996. At the time the lowest bound was 174 which became 168 in June 1996 due to Uenal Mutlu lowering the C(27,6,3,4) to 91, which was subsequently lowered by D Stojiljkovic and Rade Belic to 86 in 1998 to give 163.

A rudimentary look at graph lines substituting values as known in January 1996 and illustrated at**CORRELATION BETWEEN LOTTO COVER OR WHEEL GUARANTEES FOR VARIOUS POOL SIZES**shows such unrealistic values to be simply impossible.

. - In the link above I pour scorn on the tenuous comparison made by Iliya Bluskov in trying to promote a C(14,6,4,4)=80 Cover with a guarantee for a hypothetical 6/14 Lotto game to play in a 6/49 one in his 1997 thesis titled
. Of course the guarantee does not apply to the 6/49 game but Bluskov still applauds his non applicable guarantee by stating that a Random Selection on the same 14 numbers does not have a guarantee.*New Designs and Coverings*

Begs two questions -

"**Why confine the Random Selections to a Pool of 14 in a 6/49 Lotto game?"****"What is the relevance of a 80 line non-applicable Cover guarantee for a Pool of 14 in a 6/49 Lotto game to a****Random Selection of 80 CombSixes****with a non-guarantee from the same 14 integers? Why not from 49 to give a partial Cover with undoubtedly a better Coverage?"**

. **You can view or download the thesis here: New Designs and Coverings.**

The pdf file is 98 pages - unless you're a mathematician the first 30 pages are all that is needed to confirm my quotes.

Sources:

THE ULTIMATE BOOK ON LOTTO SYSTEMS

Thread (click here) started November 15, 2012 in the unmoderated newsgroup Rec.Gambling.Lottery in which Iliya Bluskov debated with me until the final coup de gras message as at the top of this page but first posted here.

RGL 8/1/2014

RGL 9/1/2014

RGL 11/1/2014

"This system has 30 combinations; the title is an "if" statement, and putting such information there is not exactly "hiding it", is it?"

But is it a Lotto System or rather a Lotto Observation? Look at the top of this article

RGL 11/1/2014

DECEPTIVE LOTTO WHEEL CLAIMS BY PROF ILIYA BLUSKOV

Basically Iliya Bluskov is trying to pass off Lotto Systems with a valid guarantee for the Pool used as being beneficially applicable to Lotto games where the Pool is much greater, which it isn't and in other words pandering to the Lotto predictionists and occultists, without admitting it.

Consider one line, say 44 45 46 47 48 49 where the Pool is 49. If the winning draw is 01 02 03 47 48 49 then from the 260,624 combinations of six covered by this line we have a match with 47 48 49. But for a Cover or Wheel you don't need to know the draw result before it is applicable. The whole notion is absurd but makes sense once you take into account the occult side where some people think they can narrow down the Pool in the next draw - and that basically is what Iliya Bluskov is addressing while trying to pass it off as having some credibility in mathematics.

Now, consider the line 01 02 03 04 05 06. By itself we don't know what Pool it is being applied against and it therefor needs to be specified. It is a 1st Prize winner for a hypothetical Pool 6 Lotto game as it is the only Pick of 6 integers possible and in the syntax is

It is not a Cover for a Pool greater than 9. Notice you don't need to know the draw before it is valid; there are no "ifs".

RGL 11/1/2014

The monstrous gaps in Dr Iliya Bluskov's knowledge about the characteristics of this subject and his naive understanding defy the imagination. He simply surmises erroneously without doing the necessary work to check things out.

For 50 draws or 1,000 plays we need 50 results and by simply multiplying the probability for each category by 50 we calculate the 50 results that are most likely. For 3,200 draws or 64,000 plays we have 11 of the categories into play, including a match 5; no need to multiply by some 700,000 draws or 14,000,000 plays or 13,446 years if playing once per week.

LOTTO GAME

Prize6 | Prize5 | Prize4 | Prize3 | Combs | Probability | 50 Draws | 100 Draws | 200 Draws | 400 Draws | 800 Draws | 1600 Draws | 3200 Draws |
---|---|---|---|---|---|---|---|---|---|---|---|---|

0 | 0 | 0 | 0 | 12721488 | 0.9097294 | 46 | 91 | 182 | 364 | 728 | 1456 | 2911 |

0 | 0 | 0 | 3 | 822510 | 0.0588187 | 3 | 6 | 12 | 24 | 47 | 94 | 188 |

0 | 0 | 0 | 4 | 182780 | 0.0130708 | 1 | 1 | 3 | 5 | 11 | 21 | 42 |

0 | 0 | 0 | 5 | 91390 | 0.0065354 | 0 | 1 | 1 | 3 | 5 | 11 | 21 |

0 | 0 | 1 | 8 | 55575 | 0.0039742 | 0 | 1 | 1 | 2 | 3 | 6 | 13 |

0 | 0 | 1 | 9 | 44460 | 0.0031794 | 0 | 1 | 1 | 3 | 5 | 10 | |

0 | 0 | 2 | 7 | 44460 | 0.0031794 | 0 | 1 | 2 | 5 | 10 | ||

0 | 0 | 3 | 2 | 7410 | 0.0005299 | 0 | 1 | 1 | 2 | |||

0 | 0 | 3 | 4 | 3705 | 0.0002649 | 0 | 1 | |||||

0 | 0 | 5 | 10 | 468 | 0.0000335 | 0 | ||||||

0 | 0 | 5 | 11 | 2340 | 0.0001673 | 0 | 1 | 1 | ||||

0 | 0 | 7 | 6 | 2340 | 0.0001673 | 0 | ||||||

0 | 0 | 15 | 2 | 10 | 0.0000007 | 0 | ||||||

0 | 1 | 3 | 11 | 2340 | 0.0001673 | 0 | 1 | |||||

0 | 1 | 4 | 10 | 2340 | 0.0001673 | 0 | ||||||

0 | 2 | 9 | 8 | 60 | 0.0000043 | 0 | ||||||

0 | 3 | 7 | 9 | 60 | 0.0000043 | 0 | ||||||

0 | 3 | 8 | 7 | 60 | 0.0000043 | 0 | ||||||

1 | 0 | 10 | 8 | 15 | 0.0000011 | 0 | ||||||

1 | 0 | 12 | 4 | 5 | 0.0000004 | 0 | ||||||

13983816 | 1.00 | 50 | 100 | 200 | 400 | 800 | 1600 | 3200 |

3if6 COVERAGE OF 9,175,924 COMBS OR 34.38183%

Prize6 | Prize5 | Prize4 | Prize3 | Combs | Probability | 50 Draws | 100 Draws | 200 Draws | 400 Draws | 800 Draws | 1600 Draws | 3200 Draws |
---|---|---|---|---|---|---|---|---|---|---|---|---|

0 | 0 | 0 | 0 | 9175924 | 0.656182 | 33 | 66 | 131 | 263 | 525 | 1050 | 2100 |

0 | 0 | 0 | 1 | 4160976 | 0.297557 | 15 | 30 | 60 | 119 | 238 | 476 | 952 |

0 | 0 | 0 | 2 | 356044 | 0.025461 | 1 | 2 | 5 | 10 | 20 | 41 | 82 |

0 | 0 | 0 | 3 | 14432 | 0.001032 | 1 | 2 | 3 | ||||

0 | 0 | 0 | 4 | 360 | 0.000026 | |||||||

0 | 0 | 1 | 0 | 252300 | 0.018042 | 1 | 2 | 4 | 7 | 15 | 29 | 58 |

0 | 0 | 1 | 1 | 18600 | 0.001330 | 1 | 1 | 2 | 4 | |||

0 | 1 | 0 | 0 | 5160 | 0.000369 | 1 | ||||||

1 | 0 | 0 | 0 | 20 | 0.000001 | |||||||

13983816 | 1.00 | 50 | 100 | 200 | 400 | 800 | 1600 | 3200 |

Lotto Set | ESTIMATED YIELD OR PERCENTAGE RETURN FOR MOST LIKELY WINS | ||||||

USING UK LOTTO COST OF £2 PER LINE AND PAYOUTS OF £25 MATCH 3, £100 MATCH 4 AND £1000 MATCH 5 | |||||||

50 Draws | 100 Draws | 200 Draws | 400 Draws | 800 Draws | 1600 Draws | 3200 Draws | |

1000 Plays | 2000 Plays | 4000 Plays | 8000 Plays | 16000 Plays | 32000 Plays | 64000 Plays | |

Partial Cover 20 Lines | 26.25% | 26.25% | 26.88% | 26.88% | 27.03% | 26.95% | 27.68% |

C(10,6,4,4)=20 Cover | 16.25% | 19.38% | 20.31% | 20.47% | 25.70% | 25.94% | 27.56% |

Colin Fairbrother ]]>

The claims by Professor Iliya Bluskov that he has "the best lottery systems" in a booklet titled "The Ultimate Book On Lotto Systems" are proved wrong in this article and in a table that compares many Partial Pool Covers with my Full Pool Partial Covers for the Pick 6, Pool 49 Lotto game where the -

**Full Pool for the applicable Lotto game are used.****Paying Subsets are not repeated.****Coverage is maximized for both 3if3 and 3if6.**

A Lotto System (Cover or Wheel) is defined by the number (C) of Plays, Lines, Picks or Blocks) of a specified size that

eg 1 C(49,6,3,6,1)=163 means for a Pool of 49 and a Pick of 6 a minimum of 163 lines is needed to guarantee a Match of 3 integers at least 1 time for all the combinations of 6 integers (Hits) from the Pool.

If you prefer let's look at the definition by Iliya Bluskov, January 30, 1996 which can be confirmed here: -

Lottery System Definition by Iliya Bluskov

is called an (n,k,p,t) - lottery system (wheel) if for every p-subset

P of V one can find a k-subset (ticket) L of S such that L and P have at least t numbers in common."

THE GUARANTEE IS "... one can find ..."

THE "IF" IN THAT DEFINITION REFERS TO WHETHER IT QUALIFIES AS A COVER OR WHEEL BY HAVING A MATCH; BY HIS OWN DEFINITION IT CANNOT BE DESCRIBED AS A SYSTEM, WHEEL OR COVER WHEN THERE IS NO MATCH BETWEEN A TICKET OR LINE AND THE SUBSET SPECIFIED, WHICH IS THE CASE FOR PARTIAL POOL COVERS.

THERE IS NO CONDITION TO THAT GUARANTEE; THE PRIZE IS OBTAINED IRRESPECTIVE OF THE DRAW RESULT. LET ME EMPHASIZE THAT - THE GUARANTEE APPLIES NO MATTER WHAT THE DRAW RESULT.

THE "GUARANTEE" THAT BLUSKOV WRITES ABOUT IS NOT A GUARANTEE AT ALL FOR THE GAME YOU ARE PLAYING BECAUSE IT MAYBE APPLIES AFTER THE DRAW. IT'S A CON-ARTIST TRICK.

With only a few exceptions (where the Pool is one to three integers more, the Cover is a Steiner System and the prize guarantee is of a lesser value) the guarantee does not carry over to a Lotto game that has more integers iin the Pool than there are in

Iliya Bluskov compares his Covers or Wheels to those of Gail Howard and for the given Pool and real guarantee justifies them being better by a lesser number of lines thus saving money. That being said there is little doubt that the cost or monetary return is of prime importance as in Percentage Return or Yield and on this basis they fail miserably. The writings of Iliya Bluskov are full of contradictions and sneaky inferences most unbecoming of a Professor in Mathematics.

Consider the classic Pick 6, Pool 49 Lotto game and the best structure of 20 lines to play in that game. Dr Bluskov or his speil merchants claim you will do better by playing 20 lines that only use 10 of the 49 available integers and which has a guarantee of a 4 match

From January, 1997 serious Lotto Systems enthusiasts produced lists for the best Partial Covers including this one started by Uenal Mutlu. Partial Cover list for 6/49 Lotto game. A current list is maintained by John Rawson, the author of Covermaster and is available here. This list I am not entirely in agreement with as it has duplicate CombThrees from 74 Combinations on whereas my Cover C(49,6,3,6,1)=365 is both progressive and has no duplicate CombThrees and consequently a natural distribution. The Cover C(49,6,3,6,1)=163 has a very distorted distribution with the single match 3 win exceeding the 2 x match 3 and the 3 x match 3.

Partial Covers have a scientific basis and contrast strongly with the Partial Pool Covers or Wheels used by predictionists and occultists who having convinced themselves that they have narrowed down the Pool for the next draw justify their use. Having grown up with this in his native Bulgaria, Bluskov remains in a time warp pandering to such wierdos and using words such as "guess" when he really means "predict" and in the epitome of duplicity using

To have a

The coverage of the Lotto Wheel with a 4if4 guarantee in a 6/10 Lotto game for all Prize groups when applied to the 6/49 Lotto game is only 9%, whereas the first 20 Random Selections or draws in the UK Lotto has a Coverage of 31% (and for any other consecutive 20 lines within 1%) and my Partial Cover 34%.

MY PARTIAL COVER WITH ONLY 66%.

Here is a meaningful guarantee -

As I have repeatedly pointed out - Coverage alone does not determine the best PERCENTAGE RETURN or YIELD for a given Lotto play set or design. The repetition of paying subsets significantly effects the yield.

Each Pick 6 Line has

20 CombThrees,

15 CombFours

and 6 CombFives.

20 CombThrees,

15 CombFours

and 6 CombFives.

So, for 20 lines we should optimally have 400 CombThrees, 300 CombThrees and 120 CombFives. Looking at the repetition tables below we see for the Cover we have less than half the Combthrees distinct ie120 and less than three quarters of the CombFours distinct ie 210.

Fig 1

Fig 2

For a given Lotto game and a specific Cover or Wheel a table of wins can be calculated. In Australia the Lotto operator provides them for System entries or Full Wheels. The important point is that if playing a System 8 or Full Wheel 8 the Prize Table is not given for a hypothetical 6/8 Lotto game but for the actual Lotto game, say, 6/45. See Tatts Lotto Systems Prize Table in Australia To do otherwise would be considered to be misinformation and grossly deceptive.

If playing in a 6/49 Lotto game using the C(10,6,4,4)=20 Cover or Wheel why does Professor Iliya Bluskov consider a table of wins for a 6/10 Lotto game rather than a 6/49 Lotto game appropriate other than to ostensibly deceive?

I have my own Lotto Analyzer program, written by myself, which can give me the complete breakdown of prize groups but for the purpose of comparison and possible confirmation by yourself let's use John Rawson's free Covermaster. Below is the real prize table in a 6/49 Lotto game when considering all possible combinations of 6 integers from a Pool of 49.

Fig 3

Fig 4

Comparing the two tables we see in Table 4 that for the possible 210 combinations of 6 integers (10c6) there are 10 that give 15 match 4's with 2 match 3's (4.76%) and 60 that give 2 match 5's with 9 match 4's and 8 match 3's (28.57%). However, when examined in Table 3 where there are 13,983,816 combinations of 6 integers for the same prize groups we have respectively percentages of 0.00007% ie a lot greater improbability than that of winning 1st prize (0.00014) and 0.00043%.

Fig 5

Fig 6

Using Fig 3 we can apply proportionality and get a good indication of expected wins for 1000 plays or 50 draws. Move the decimal point to the right in the % column to get the probability and then multiply by the simulated draws required ie 1000/20=

No Wins 0.90973 x 50 45.48 45

3 Match x 3 0.05881 x 50 2.94 3

3 Match x 4 0.01307 x 50 0.65 1

3 Match x 5 0.00653 x 50 0.33

4 Match x 1 + 3 Match x 8 0.00397 x 50 0.20 1

4 Match x 1 + 3 Match x 9 0.00318 x 50 0.16

4 Match x 2 + 3 Match x 7 0.00318 x 50 0.16 _____

50

Using the current ticket cost of £2 per line and payouts of £25 for a match 3 and £100 for a match 4 we have a sum of 3x75 + 1x100 + 1x100 = 425 to give a Yield of 21.25%.

For a

No Wins 0.65618 32.80 33

3 Match x 1 0.28616 14.31 15

3 Match x 2 0.02795 1.40 1

3 Match x 3 0.00144 0.07

4 Match x 1 0.01937 0.97 1

__

50

Using the same costs and payouts the sum is 15x25 + 1x50 + 1x100 = 525 to give a Percentage Return or Yield of 26.25%

I have prepared a table that compares the yield obtained for a given number of lines in a 6/49 Lotto game which confirms what I am saying. This table has been prepared by calculating the coverage of a given set of numbers of the 13,983,816 possibilities and grouping the prize categories.

The table shows that the Full Pool partial covers I advocate using and which are available at LottoToWin are superior to partial Pool covers.

Below is a flyer received in my mailbox in November 2012 which prompted me to start a thread in the newsgroup rec.gambling.lottery where eventually Dr Bluskov responded in January 2014.

Unfortunately, Dr Bluskov didn't respond very well eventually resorting to using nazi terminology as he could not come up with any contra meaningful arguements. For example where I multiply the probability for the various prize groups by the number of draws required to arrive at a simplified prize list with total prize group wins equal to the number of draws he would not accept this even after it was pointed out to him that it correlated with trial runs against random selections or a Lotto draw history.

Dr Buskov proposed that the only meaningful data would be after multiplying the probability for each prize group by say close to 14,000,000 to achieve what?

This line was still maintained after I showed the Steiner C(22,6,3,3)=77 in a hypothetical 6/22 Lotto game gave exactly the same quantities of match 3's, match 4's and match 5's as per probability formula with that of the totals for each prize groups after mutiplying by 13.

Dr Buskov also accused me of trying to destroy his academic reputation. All I have done is made other academics aware of what he has been up to and even ordinary everyday people with common sense and some ability in critical thinking can see through the deceptions. Dr Bluskov destroyed whatever part of his academic reputation that has suffered by his own actions.

Please read also PRIZES IN LOTTO ILIYA BLUSKOV v COLIN FAIRBROTHER

Colin Fairbrother

]]>

Lotto 6/49 Comparison Trials of 56 Random Selections with Wheel Pool 9 Key 1 Lines 56 in UK Lotto | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Draw Range | Wheel Pool 9 Key 1 | Random Selections | |||||||||||

Nil | 3'sx10 | 3'sx20 | 4'sx4 & 3'sx24 | 4'sx10 & 3'sx30 | Old Prizes | Wheel Win | Nil | 3's | 4's | 5's | Old Prizes | Random Win | |

1 to 52 | 48 | 3 | 1 | £500 | 20 | 51 | 1 | £570 | 1 | ||||

53 to 104 | 47 | 4 | 1 | £600 | 16 | 60 | 3 | £780 | 1 | ||||

105 to 156 | 48 | 2 | 1 | 1 | £880 | 1 | 17 | 58 | 4 | £820 | |||

157 to 208 | 45 | 4 | 2 | 1 | £1700 | 1 | 19 | 46 | 3 | £640 | |||

209 to 260 | 49 | 1 | 2 | £500 | 17 | 51 | 3 | £690 | 1 | ||||

261 to 312 | 49 | 3 | £300 | 26 | 41 | 3 | £590 | 1 | |||||

313 to 364 | 48 | 3 | 1 | £500 | 19 | 45 | 4 | £690 | 1 | ||||

365 to 416 | 48 | 3 | 1 | £500 | 26 | 49 | 2 | £610 | 1 | ||||

417 to 468 | 49 | 2 | 1 | £1100 | 1 | 26 | 37 | £370 | |||||

469 to 520 | 50 | 2 | £200 | 22 | 44 | 3 | £620 | 1 | |||||

521 to 572 | 51 | 1 | £100 | 17 | 62 | 2 | £740 | 1 | |||||

573 to 624 | 47 | 1 | 3 | 1 | £1180 | 23 | 46 | 3 | 2 | £3640 | 1 | ||

625 to 676 | 51 | 1 | £100 | 25 | 42 | 2 | £540 | 1 | |||||

677 to 728 | 45 | 3 | 4 | £1100 | 23 | 39 | 2 | 1 | £2010 | 1 | |||

729 to 780 | 47 | 2 | 3 | £800 | 1 | 20 | 52 | 4 | £760 | ||||

781 to 832 | 47 | 2 | 2 | 1 | £1080 | 1 | 19 | 62 | 1 | £680 | |||

833 to 884 | 45 | 5 | 1 | 1 | £1180 | 1 | 21 | 44 | 6 | £800 | |||

885 to 936 | 47 | 4 | 1 | £600 | 15 | 48 | 3 | £660 | 1 | ||||

937 to 988 | 49 | 1 | 1 | 1 | £780 | 14 | 52 | 5 | £820 | 1 | |||

989 to 1040 | 49 | 2 | 1 | £400 | 25 | 38 | 2 | £500 | 1 | ||||

1041 to 1092 | 47 | 1 | 3 | 1 | £1600 | 21 | 46 | 3 | 1 | £2140 | 1 | ||

1093 to 1144 | 49 | 2 | 1 | £400 | 17 | 53 | 4 | £770 | 1 | ||||

1145 to 1196 | 49 | 2 | 1 | £400 | 15 | 47 | 2 | £590 | 1 | ||||

1197 to 1248 | 50 | 2 | £400 | 13 | 72 | 3 | £900 | 1 | |||||

1249 to 1300 | 50 | 2 | £400 | 19 | 50 | £500 | 1 | ||||||

1301 to 1352 | 48 | 2 | 1 | 1 | £880 | 20 | 43 | 4 | 2 | £3670 | 1 | ||

1353 to 1404 | 50 | 2 | £200 | 23 | 39 | 5 | £690 | 1 | |||||

1405 to 1456 | 50 | 2 | £200 | 20 | 48 | 3 | £660 | 1 | |||||

1457 to 1508 | 46 | 4 | 2 | £800 | 1 | 20 | 52 | 1 | £580 | ||||

1509 to 1560 | 51 | 1 | £200 | 20 | 61 | 1 | £670 | 1 | |||||

1561 to 1612 | 48 | 2 | 1 | 1 | £1580 | 1 | 19 | 54 | 2 | £540 | |||

1613 to 1664 | 49 | 2 | 1 | £400 | 25 | 40 | 1 | £460 | 1 | ||||

1665 to 1716 | 49 | 2 | 1 | £400 | 14 | 67 | 4 | £910 | 1 | ||||

1717 to 1768 | 50 | 1 | 1 | £1000 | 1 | 21 | 48 | 2 | £600 | ||||

1860 to 1911 | 50 | 1 | 1 | £1250 | 1 | 17 | 49 | 4 | £730 | ||||

Totals | 72 | 40 | 8 | 5 | £24210 | 10 | 1736 | 95 | 6 | £32060 | 25 | ||

Averages | 48 | £692 | 20 | £916 |

**For the 35 Trials each of 52 draws, Random Selections did better for 25 ie 71% compared to only 10 ie 29% for the Pool 9 Key 1 Wheel.**

**Average nil draw returns for the trials is 48 for the Wheel while the Random Selections is only 20.**

**Overall Percentage Return using old UK ticket costs and payouts is 31.46% for Random Selections with the Pool 9 Key 1 Wheel far behind at 23.75%**

**The Wheel uses transparent, non contrived integers of 1 to 9 over 35 segments of 52 lines in the UK Lotto history. The Random Selections were the previous 56 draws at the time in the UK Lotto.**

**On three occasions the return of the Wheel over 52 draws was only 10 match Three wins - in old ticket cost and payouts this is £100 back from £2912 wagered or 3.43% and in new - £250 back from £5824 or 4.29%. **

**The lowest for my nominated Random Selections was 37 match Threes giving returns of 12.7% old and 15.88% new.**

**The highest return for all the trials was £3670 from Random Selections and this was applicable for 2nd highest (£3640), 3rd highest (£2140) and 4th highest (£2010). The best the Wheel could manage was £1700.**

Colin Fairbrother

]]>

by Colin Fairbrother

The format for the Australian Powerball game changed from June 1, 2013 from Pick 5 from 45 and PB from 45 to **Pick 6 from 40 and PB from 20. **This prompted me to look at the merits of continuing to play Saturday Lotto with its Pick 6 from 45 or changing to the new Powerball format.

For many years I have always decided on which game to play regularly by which gives the best percentage return over a reasonable number of plays - say 1000 or at least 500. In my case I only spend $11.80 per week and for the big 1st prize payouts I double that for no good reason. I always play sets where the CombThrees are not repeated, all the integers are used and the coverage is maximized as from LottoToWin.

I'm quite happy with the frequency of wins per draws played getting recently in April/May 4 wins in 5 draws played and not so long ago 4 wins consecutively. Percentage return is spot on with expectation per the odds.

To make the comparison between say, the Australian Saturday Lotto game and the new Powerball game I look at the odds for the lower tier prizes, decide on an amount to spend over a year and then calculate the percentage return.

Spending $11.80 per week at $0.655 per line on the Saturday Lotto amounts to $613.60 over a year playing 18 lines per draw or 936 lines per annum. For Saturday Lotto the lowest odds prize at 1 in 144 plays is 1 main + the 2 bonus numbers paying around $14.00. Over 936 plays I can expect around 7 of these. Next up is at 1 in 306 odds 3 main + 1 bonus number which pays around $23.00 and I should expect 3 of these. Less likely is getting 4 main correct with odds of 1 in 738 paying around $34.00 and I should get 1 of these. So, adding up expected prizes gives $201.00 for an outlay of $613.55 and an expected return of some 33%.

The cost per line is higher for the Australian Powerball game at $0.925 per line so for $613.55 per year wagered this is some 13 lines per draw or 663 lines per annum. The easiest prize is 2 main + PB at odds of 1 in 110 so one could expect 6 of these paying around $13.00. Next up is 4 main at odds of 1 in 480; one can expect 1 of these paying around $27.00. Getting 3 main + PB at odds of 1 in 641 pays around $37.00 and one can expect one of these. For the year one can expect prizes of only $142.00 for an outlay of $613.55 giving a lowly 23% return.

This comparison clearly shows that one is better off playing the Australian Saturday Lotto rather than the new Powerball by some 10%. I invite you to compare the games on offer in your country or state and find out which gives the better return for a given amount wagered.

Colin Fairbrother

For many years I have always decided on which game to play regularly by which gives the best percentage return over a reasonable number of plays - say 1000 or at least 500. In my case I only spend $11.80 per week and for the big 1st prize payouts I double that for no good reason. I always play sets where the CombThrees are not repeated, all the integers are used and the coverage is maximized as from LottoToWin.

I'm quite happy with the frequency of wins per draws played getting recently in April/May 4 wins in 5 draws played and not so long ago 4 wins consecutively. Percentage return is spot on with expectation per the odds.

To make the comparison between say, the Australian Saturday Lotto game and the new Powerball game I look at the odds for the lower tier prizes, decide on an amount to spend over a year and then calculate the percentage return.

Spending $11.80 per week at $0.655 per line on the Saturday Lotto amounts to $613.60 over a year playing 18 lines per draw or 936 lines per annum. For Saturday Lotto the lowest odds prize at 1 in 144 plays is 1 main + the 2 bonus numbers paying around $14.00. Over 936 plays I can expect around 7 of these. Next up is at 1 in 306 odds 3 main + 1 bonus number which pays around $23.00 and I should expect 3 of these. Less likely is getting 4 main correct with odds of 1 in 738 paying around $34.00 and I should get 1 of these. So, adding up expected prizes gives $201.00 for an outlay of $613.55 and an expected return of some 33%.

The cost per line is higher for the Australian Powerball game at $0.925 per line so for $613.55 per year wagered this is some 13 lines per draw or 663 lines per annum. The easiest prize is 2 main + PB at odds of 1 in 110 so one could expect 6 of these paying around $13.00. Next up is 4 main at odds of 1 in 480; one can expect 1 of these paying around $27.00. Getting 3 main + PB at odds of 1 in 641 pays around $37.00 and one can expect one of these. For the year one can expect prizes of only $142.00 for an outlay of $613.55 giving a lowly 23% return.

This comparison clearly shows that one is better off playing the Australian Saturday Lotto rather than the new Powerball by some 10%. I invite you to compare the games on offer in your country or state and find out which gives the better return for a given amount wagered.

Colin Fairbrother

Overall chances of a win in the Australian 6/45 Lotto game with two extra bonus numbers from the same Pool of 45 are 1 in 84 plays. More specifically the lowest prize is 1 main plus the 2 Bonus numbers with a 1 in 144 chance. The next is 3 main with either one of the 2 Bonus numbers with a 1 in 297 chance and the next is 4 main with a 1 in 733 chance.

The cost for 1 line or play is $0.66 so, for 18 lines $11.80 and 36 $23.60. The cost for the five lines is $70.80 and the prize total is $63.80.

The screen shot below shows 4 wins in 5 consecutive draws or 4 wins in 98 plays or 1 in 25 or (63.8/70.89) x 100 = 90.11% return. Lucky!

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