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Message Icon Topic: COMBINATORIAL SYSTEM, COVER OR WHEEL GUARANTEES Post Reply Post New Topic
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Colin F
Lotto Systems Tester Creator & Analyst
Lotto Systems Tester Creator & Analyst
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Quote Colin F Replybullet Topic: COMBINATORIAL SYSTEM, COVER OR WHEEL GUARANTEES
    Posted: May 07 2012 at 11:10pm
LOTTO WHEELS OR COVERS CON-ARTIST CLAIMS
TOTALLY DEBUNKED IN TABLE
by Colin Fairbrother

Lesser Pool Covers or Wheels are shown in the following table to overwhelmingly reduce your chances of winning a prize. Using the classic Pick 6, Pool 49 Lotto game (the principle is applicable to any Lotto game) the reduction can be as much as 65% in the reasonably short term, say, 1,000 plays.

Basically the extent of repetition of paying sub-set combinations in the set played such as CombThrees, CombFours and even CombFives along with how much of the Pool is used and good coverage will determine how well a play set structure will perform.

Meaning of Guarantee

The guarantee of the prize when playing a set of Lotto numbers which is a Cover or Wheel with guarantee is only applicable to the Pool of numbers used in that particular Cover or Wheel for the lowest set of lines. For the 6/49 Lotto game the record minimum set of lines with no ifs or buts is 163 for a CombThree prize. Prefixing a guarantee for a lesser Pool Cover or Wheel with a highly improbable 'if' does not make it more likely! If you play a 7 line Full Wheel or all the possible combinations of 6 from a Pool of 7 in a 6/49 Lotto game then, sure, if the 6 main integers drawn are in the 7 integers you have used in your Pool of 7 then you win or share first prize - but the likelihood of this happening is the same as playing any other 7 lines. The principle applies to the sub-prizes and because generally a Cover or Wheel for the minimum set of lines is distorted compared to random selections which are in accord with the odds your chances of success are diminished as the table below makes abundantly clear.

A 3if6 guarantee for a 6/49 Lotto game means that for all the 13,983,816 combinations of six integers at least one CombThree in each combination is in the 163 line set played. While it is possible to have 163 x 20 = 3260 CombThrees the 163 line set actually has only 3007 distinct CombThrees with 142 repeated twice, 11 three times, 18 four times, 5 five times and 3 six times.

Little mathematical ability is needed to work out that if a pool of 12 is used then the possible number of CombThrees is 220 (ie 12c3) but after 4 lines repeats are unavoidable and a minimum number of 15 lines is needed to get them all in. When this 15 line set is applied to a 6/49 Lotto game the coverage of the CombThrees is only 14.8% as shown in the table below. Using the first 15 lines from my 365 line set which uses the full Pool of 49 integers, no repeat CombThrees and coverage progressively calculated to next best play, a coverage some 50% more of 23.5% is obtained.

Generally, the choice between using the Full Pool or a Lesser Pool for a given Lotto game boils down to wanting overall a better percentage return or yield which is the universal method of measuring ones chances of success in a game of chance. Would you prefer 17 CombThree and 1 CombFour wins over 2 years playing 10 lines once a week in a 6/49 Lotto game or 12 CombThrees and 1 CombFour wins as is the case for a reduced Pool of 10 which has a GUARANTEE OF A COMBTHREE PRIZE FOR THE POOL OF 10 BUT NOT FOR THE POOL OF 49. I prefer the better percentage return or yield of 22.6% compared to 20.6% with more wins more often.

It is easily seen that using the full Pool for a 6/49 game gives better results than the Covers or Wheels where the Pool used is less than 49. While the guarantee does apply to the lesser Pool IT DOES NOT APPLY to the full Pool of 49 and usually because of the repetition of CombThrees, CombFours and even CombFives gives significantly less coverage and consequent yield.

Worth noting is the fact that since the full pool calculations have been done with no duplicate CombThrees then they are all optimized for 3if3 ie each added line covers the maximum 20 CombThrees in a line for the 18,424 possible CombThrees.

Comparing the 3if6 calculations for a given number of lines then the higher the 3if6 figure is the higher the likelihod of more wins more often and the higher the Yield figure the more likely you are to get the expected return over a reasonable number of draw participations. Most constructions will return the expected yield over a thousand or so draws but why wait 20 years when you can get that same return in 2 years?

One can also see that to win 1st prize in a 6/49 Lotto game ie 6if6 then whatever the method used to construct the set no difference is made to the likelihood of winning the jackpot as the only requirement is not to repeat a line.

As the increase in the Yield or Percentage Return is only around the 2 to 4 Percent compared to Random Selections it is only the finicky few, like myself, that bother to deliberately maximize the chances of a better return with the lower prizes and under no dellusions about the chances of winning first prize.

Comment is kept deliberately to a minimim to keep this an accurate reference table. Articles exposing the con-artists that promote these lesser pool Covers or Wheels will refer back to the following table.

Comparison Coverage and Yield for Lesser Pool Covers or Wheels applied to 6/49 Lotto Game

Copyright © Colin Fairbrother 2012
Lines Played Guarantee Pool used
for Guarantee
Coverage 6/49 Game
for Partial Cover (Nil) using max Pool for lines
and Partial Pool Covers
Expected Yield
for Draws required
to approximate
1000 Plays
3 if 6 4 if 6 5 if 6 6if6
13 if 66260624
1.86375%
13804
0.09871%
259
0.00185%
1
0.00000007%
23.6%
1000 draws
4 if 66
5 if 66
6 if 66
3 if 67
4 if 67
5 if 67
3 if 68
Fairbrother
Partial Cover
49
23 if 59481704
3.44472%
27203
0.19453%
518
0.0037%
2
0.00000014%
22.6%
500 draws
3 if 510504532
3.60797%
27572
0.19717%
3 if 511517148
3.69819%
27608
0.19743%
3 if 512520848
3.72465%
23.6%
500 draws
3 if 613520848
3.72465%
Fairbrother
Partial Cover
49520848
3.72465%
27608
0.19743%
23.6%
500 draws
33 if 48518104
3.70503%
33443
0.23916%
722
0.00516%
3
0.00000021%
20.6%
Say 333 draws
4 if 58571404
4.08618%
36764
0.2629%
765
0.00547%
15.0%
Say 333 draws
4 if 69575304
4.11407%
35564
0.25432%
728
0.00521%
23.6%
Say 333 draws
3 if 49636924
4.55472%
38964
0.27864%
773
0.00553%
19.6%
Say 333 draws
Fairbrother
Partial Cover
49780672
5.58268%
41412
0.29614%
777
0.00556%
23.6%
Say 333 draws
43 if 37432824
3.09518%
30163
0.2157%
763
0.00546%
4
0.00000029%
15.0%
250 draws
3 if 38656684
4.69603%
46604
0.33327%
1012
0.00724%
21.6%
250 draws
5 if 68656684
4.69603%
46604
0.33327%
1012
0.00724%
23.6%
250 draws
3 if 614924448
6.61084%
53476
0.38241%
1032
0.00738%
21.6%
250 draws
3 if 615896468
6.41075%
52768
0.37725%
22.6%
250 draws
Fairbrother
Partial Cover
491040096
7.46786%
55216
0.39486%
1036
0.00741%
23.6%
250 draws
54 if 47432824
3.09518%
31626
1.65852%
847
0.00606%
5
0.00000036%
18.6%
200 draws
4 if 611931215
6.65923%
59932
0.42858%
1238
0.00885%
23.6%
200 draws
Fairbrother
Partial Cover
491299120
9.29017%
69020
0.49357%
1295
0.00926%
65 if 57432824
3.09518%
31024
0.22186%
889
0.00636%
6
0.00000043%
17.0%
Say 167 draws
3 if 4121199058
8.57461%
77450
0.55385%
1542
0.01103%
21.6%
Say 167 draws
4 if 6121200168
8.58255%
78846
0.56384%
1554
0.01111%
Fairbrother
Partial Cover
491557744
11.13962%
82824
0.59228%
23.6%
Say 167 draws
76 if 6
System 7
7432824
3.09518%
31024
0.22186%
889
0.00636%
7
0.00000050%
16.0%
Say 143 draws
5 if 69874044
6.2504%
68304
0.48845%
1604
0.01147%
17.6%
Say 143 draws
3 if 39933324
6.67432%
71424
0.51076%
1640
0.01173%
20.6%
Say 143 draws
4 if 5101042992
7.45856%
76728
0.54869%
1699
0.01215%
19.6%
Say 143 draws
3 if 5151549064
11.07755%
95996
0.68648%
1813
0.01296%
22.6%
Say 143 draws
3 if 6181457522
10.42292%
91254
0.65257%
1801
0.01288%
20.6%
Say 143 draws
Fairbrother
Partial Cover
491815968
12.98621%
96628
0.691%
1813
0.01296%
23.6%
Say 143 draws
83 if 5161676136
11.98626%
105032
0.7511%
2060
0.01473%
8
0.00000057%
21.6%
125 draws
Fairbrother
Partial Cover
492073792
14.82994%
110432
0.78971%
2072
0.01482%
23.6%
125 draws
93 if 4131583778
11.32579%
112322
0.80323%
2308
0.0165%
9
0.00000064%
22.6%
Say 111 draws
3 if 6191652512
11.81732%
110773
0.79215%
2299
0.01644%
20.6%
Say 111 draws
Fairbrother
Partial Cover
492312716
16.53852%
124236
0.88843%
2331
0.01667%
22.6%
Say 111 draws
103 if 3101262328
9.02706%
108435
0.77543%
2510
0.01795%
10
0.00000072%
18.6%
100 draws
4 if 5111431048
10.2336%
112220
0.8025%
2471
0.01767%
4 if 6131615698
11.55406%
117330
0.83904%
2478
0.01772%
21.6%
100 draws
3 if 6201849694
13.22739%
124054
0.88713%
2554
0.01826%
20.6%
100 draws
Fairbrother
Partial Cover
492547860
18.22006%
138040
0.98714%
2590
0.01852%
22.6%
100 draws
113 if 3111641948
11.74177%
133595
0.95535%
2849
0.02037%
11
0.00000079%
21.6%
Say 91 draws
3 if 4141912218
13.67451%
139436
0.99712%
2833
0.02026%
20.6%
Say 91 draws
3 if 5172198856
15.72429%
147453
1.05445%
2845
0.02034%
21.6%
Say 91 draws
Fairbrother
Partial Cover
492782284
19.89646%
151844
1.08586%
2849
0.02037%
22.6%
Say 91 draws
125 if 58610148
4.97207%
56868
0.46341%
2268
0.01848%
12
0.00000086%
18.0%
Say 83 draws
4 if 49933324
6.67432%
103404
0.73945%
2964
0.0212%
14.0%
Say 83 draws
3 if 5182384112
17.04908%
163776
1.17118%
3108
0.02223%
21.6%
Say 83 draws
Fairbrother
Partial Cover
493016308
21.56999%
165648
1.18457%
23.6%
Say 83 draws
133 if 6212146942
15.35305%
150314
1.07491%
3216
0.023%
13
0.00000093%
21.6%
Say 77 draws
Fairbrother
Partial Cover
493249932
23.24067%
179452
1.28328%
3367
0.02408%
23.6%
Say 77 draws
145 if 6101262328
9.02706%
131562
0.94082%
3408
0.02437%
14
0.00000100%
17.6%
Say 71 draws
4 if 5121944978
13.90878%
168090
1.20203%
3614
0.02584%
20.6%
Say 71 draws
3 if 4152315016
16.55497%
175807
1.25722%
3602
0.02576%
Fairbrother
Partial Cover
493483156
24.90848%
193256
1.382%
3626
0.02593%
23.6%
Say 71 draws
153 if 3122069298
14.79781%
174528
1.24807%
3857
0.02758%
15
0.00000107%
20.6%
Say 67 draws
3 if 5192849672
20.37836%
199060
1.4235%
3877
0.02772%
22.6%
Say 67 draws
3 if 6222467416
17.6448%
179910
1.28656%
3817
0.0273%
21.6%
Say 67 draws
Fairbrother
Partial Cover
493705456
26.49817%
207060
1.48071%
3885
0.02778%
23.6%
Say 67 draws
163 if 4162826296
20.21119%
214915
1.53688%
4144
0.02963%
16
0.00000114%
22.6%
Say 63 draws
Fairbrother
Partial Cover
493927356
28.08501%
220864
1.57943%
23.6%
Say 63 draws
173 if 6232823186
20.18895%
211045
1.50921%
4391
0.0314%
17
0.00000122%
19.6%
Say 59 draws
Fairbrother
Partial Cover
494145602
29.64571%
234668
1.67814%
4403
0.03149%
23.6%
Say 59 draws
183 if 5202561412
18.31697%
204239
1.46054%
4493
0.03213%
18
0.00000129%
17.6%
Say 56 draws
Fairbrother
Partial Cover
494363448
31.20356%
248472
1.77685%
4662
0.03334%
22.6%
Say 56 draws
194 if 6152863861
20.47982%
240047
1.71661%
4917
0.03516%
19
0.00000136%
20.6%
Say 53 draws
Fairbrother
Partial Cover
494580702
32.75717%
262276
1.87557%
4921
0.03519%
22.6%
Say 53 draws
204 if 4101262328
9.02706%
165648
1.18457%
4880
0.0349%
20
0.00000143%
20.6%
Say 50 draws
3 if 4173280632
23.46021%
263367
1.88337%
5176
0.03701%
3 if 6243112646
22.25892%
235019
1.68065%
5002
0.03577%
Fairbrother
Partial Cover
494797556
34.30792%
276080
1.97428%
5180
0.03704%
22.6%
Say 50 draws
214 if 5132511978
17.96347%
242718
1.73571%
5415
0.03872%
21
0.00000150%
20.6%
Say 48 draws
3 if 3132540538
18.1677%
237678
1.69966%
5362
0.03834%
16.6%
Say 48 draws
3 if 5212884476
20.62725%
242030
1.73079%
5359
0.03832%
21.6%
Say 48 draws
Fairbrother
Partial Cover
495007243
35.80741%
289884
2.073%
5439
0.03889%
22.6%
Say 48 draws
225 if 6111641948
11.74177%
211343
1.51134%
5478
0.03917%
22
0.00000157%
18.6%
Say 45 draws
3x2 if 3122069298
14.79781%
250008
1.78784%
5698
0.04075%
17.6%
Say 45 draws
3 if 5223256671
23.28886%
267190
1.91071%
5698
0.04075%
19.6%
Say 45 draws
3 if 6253446256
24.6446%
267972
1.9163%
5658
0.04046%
21.6%
Say 45 draws
Fairbrother
Partial Cover
495216530
37.30405%
303688
2.17171%
5698
0.04075%
23.6%
Say 45 draws
23Fairbrother
Partial Cover
495422099
38.7741%
317492
2.27042%
5957
0.04260%
23
0.00000164%
23.6%
Say 43 draws
24Fairbrother
Partial Cover
495627268
40.24129%
331296
2.36914%
6216
0.04445%
24
0.00000172%
23.6%
Say 42 draws
253 if 3143051048
21.81842%
276668
1.97849%
6339
0.04533%
25
0.00000179%
21.6%
40 draws
4 if 6163468520
24.80382%
310618
2.22127%
6467
0.04625%
19.6%
40 draws
3 if 4183761287
26.89743%
322836
2.30864%
6467
0.04625%
20.6%
40 draws
3 if 6263934656
28.13721%
311107
2.22476%
6463
0.04622%
18.6%
40 draws
Fairbrother
Partial Cover
495825525
41.65905%
345100
2.46785%
6475
0.04630%
23.6%
40 draws
263 if 5233733446
26.69833%
310091
2.2175%
6710
0.04798%
26
0.00000186%
18.6%
Say 38 draws
Fairbrother
Partial Cover
496020368
43.0524%
358904
2.56657%
6734
0.04816%
23.6%
Say 38 draws
273 if 6274416434
31.58247%
348510
2.49224%
6993
0.05001%
27
0.00000193%
21.6%
Say 40 draws
Fairbrother
Partial Cover
496208606
44.39851%
372708
2.66528%
22.6%
Say 40 draws
286 if 6
System 8
8656684
4.69603%
59724
0.42709%
2324
0.01662%
28
0.00000200%
0 to 20.0%
Say 36 draws
Fairbrother
Partial Cover
496396444
45.74176%
386512
2.764%
7252
0.05186%
22.6%
Say 36 draws
294 if 5142893968
20.69512%
302148
2.1607%
7319
0.05234%
29
0.00000207%
15.6%
Say 34 draws
Fairbrother
Partial Cover
496583265
47.07774%
400316
2.86271%
7511
0.05371%
22.6%
Say 34 draws
305 if 59933324
6.67432%
103404
0.73945%
5124
0.03664%
30
0.00000215%
14.0%
Say 33 draws
3 if 4194250372
30.39494%
383203
2.74033%
7758
0.05548%
18.6%
Say 33 draws
3 if 5244090196
29.2495%
349056
2.49614%
7714
0.05516%
Fairbrother
Partial Cover
496769686
48.41086%
414120
2.96142%
7770
0.05556%
22.6%
Say 33 draws
313 if 3153595592
25.71252%
348099
2.4893%
7977
0.05704%
31
0.00000222%
19.6%
Say 32 draws
3 if 6284859715
34.75242%
396962
2.83872%
8025
0.05739%
21.6%
Say 32 draws
Fairbrother
Partial Cover
496955463
49.73938%
427924
3.06014%
8029
0.05742%
22.6%
Say 32 draws
324 if 4111641948
11.74177%
250008
1.78784%
7526
0.05382%
32
0.00000229%
11.0%
Say 31 draws
Fairbrother
Partial Cover
497140840
51.06503%
441728
3.15885%
8288
0.05927%
22.6%
Say 31 draws
334 if 6174077208
29.15662%
401256
2.86943%
8515
0.06089%
33
0.00000236%
19.6%
Say 30 draws
Fairbrother
Partial Cover
497314012
52.30341%
455532
3.25757%
8547
0.06112%
23.6%
Say 30 draws
343 if 5254758516
34.02874%
405240
2.89792%
8733
0.06245%
34
0.00000243%
20.6%
Say 29 draws
Fairbrother
Partial Cover
497486784
53.53892%
469336
3.35628%
8806
0.06297%
23.6%
Say 29 draws
353 if 4204530918
32.40116%
421917
3.01718%
8985
0.06425%
35
0.00000250%
21.6%
Say 29 draws
3 if 6295266110
37.6586%
437895
3.13144%
9033
0.0646%
22.6%
Say 29 draws
Fairbrother
Partial Cover
497653657
54.73225%
483140
3.45499%
9065
0.06482%
23.6%
Say 29 draws
36Fairbrother
Partial Cover
497820130
55.92272%
496944
3.55371%
9324
0.06668%
36
0.00000257%
23.6%
Say 28 draws
37Fairbrother
Partial Cover
497982492
57.08379%
510748
3.65242%
9583
0.06853%
37
0.00000265%
23.6%
Say 27 draws
385 if 6122069298
14.79781%
308616
2.20395%
8916
0.06376%
38
0.00000272%
15.6%
Say 26 draws
3 if 3164168472
29.80926%
438126
3.13309%
9818
0.07021%
18.6%
Say 26 draws
Fairbrother
Partial Cover
498144454
58.242%
524552
3.75114%
9842
0.07038%
22.6%
Say 26 draws
393 if 5265253798
37.57056%
459680
3.28723%
10045
0.07183%
39
0.00000279%
17.6%
Say 26 draws
3 if 6305906954
42.24136%
498278
3.56325%
10089
0.07215%
22.6%
Say 26 draws
Fairbrother
Partial Cover
498305963
59.39697%
538356
3.84985%
10101
0.07223%
404 if 5153595592
25.71252%
412852
2.95236%
9991
0.07145%
40
0.00000286%
14.6%
25 draws
3 if 4215107494
36.52432%
485810
3.47409%
10288
0.07357%
17.6%
25 draws
Fairbrother
Partial Cover
498467072
60.54908%
552160
3.94856%
10360
0.07409%
22.6%
25 draws
414 if 4122069298
14.79781%
359898
2.57368%
10025
0.07169%
41
0.00000293%
11.0%
Say 24 draws
Fairbrother
Partial Cover
498624873
61.67753%
565964
4.04728%
10619
0.07594%
22.6%
Say 24 draws
424 if 6185132262
36.70144%
514347
3.67816%
10878
0.07779%
42
0.00000300%
18.6%
Say 24 draws
Fairbrother
Partial Cover
498779624
62.78418%
579768
4.14599%
10878
0.07779%
22.6%
Say 24 draws
43Fairbrother
Partial Cover
498925529
63.82756%
593572
4.24471%
11137
0.07964%
43
0.00000307%
22.6%
Say 23 draws
443 if 3174763672
34.06561%
503112
3.59782%
11336
0.08107%
44
0.00000315%
20.6%
Say 23 draws
Fairbrother
Partial Cover
499071034
64.86809%
607376
4.34342%
11396
0.08149%
22.6%
Say 23 draws
453 if 5275770688
41.2669%
527466
3.77197%
11611
0.08303%
45
0.00000322%
17.6%
Say 22 draws
3 if 6316192996
44.28688%
544795
3.8959%
11547
0.08257%
18.6%
Say 22 draws
Fairbrother
Partial Cover
499215858
65.90374%
621180
4.44214%
11655
0.08335%
22.6%
Say 22 draws
463 if 4225602521
40.06432%
557053
3.98355%
11803
0.0844%
46
0.00000329%
20.6%
Say 22 draws
Fairbrother
Partial Cover
499360282
66.93654%
634984
4.54085%
11914
0.0852%
23.6%
Say 22 draws
47Fairbrother
Partial Cover
499501569
67.9469%
648788
4.63956%
12173
0.08705%
47
0.00000336%
21.6%
Say 21 draws
483 if 3185374992
38.43723%
561498
4.01534%
12364
0.08842%
48
0.00000343%
18.6%
Say 21 draws
Fairbrother
Partial Cover
499642456
68.9544%
662592
14.73828%
12432
0.0889%
23.6%
Say 21 draws
493 if 5286037010
43.17141%
556776
3.98157%
12579
0.08995%
49
0.00000350%
21.6%
Say 20 draws
3 if 6326688504
47.83032%
604804
4.32503%
12643
0.09041%
19.6%
Say 20 draws
Fairbrother
Partial Cover
499772284
69.88281%
676360
4.83673%
12691
0.09075%
22.6%
Say 20 draws
505 if 5101262328
9.02706%
165648
1.18457%
10038
0.07178%
50
0.00000358%
16.0%
20 draws
Fairbrother
Partial Cover
499901791
70.80893%
690128
4.93519%
12950
0.09261%
22.6%
20 draws
773 if 3217243446
51.79878%
932420
6.66785%
19943
0.14261%
77
0.00000551%
19.6%
Say 13 draws
3 if 3
Steiner
227857696
56.19136%
988988
7.07238%
19943
0.14261%
17.6%
Say 13 draws
Fairbrother
Partial Cover
4912293995
87.91588%
1059200
7.57447%
19943
0.14261%
21.6%
Say 13 draws
846 if 6
System 9
9933124
6.67432%
103404
0.73945%
5124
0.03664%
84
0.00000600%
20.0%
Say 12 draws
Fairbrother
Partial Cover
4912649151
90.45565%
1153921
8.25183%
21756
0.15558%
21.6%
Say 12 draws
85Fairbrother
Partial Cover
4912691622
90.75936%
1167401
8.34823%
22015
0.15743%
85
0.00000608%
23.6%
Say 12 draws
863 if 4278385300
59.96432%
1027937
7.3509%
22214
0.15886%
86
0.00000615%
17.6%
Say 12 draws
Fairbrother
Partial Cover
4912732005
91.04814%
1180845
8.44437%
22274
0.15928%
23.6%
Say 12 draws
1303 if 3
Steiner
2610130120
72.44174%
1633320
11.68007%
33670
0.24078%
130
0.0000092%
16.6%
Say 8 draws
Fairbrother
Partial Cover
4913679520
97.82394%
1766101
12.62961%
33670
0.24078%
22.6%
Say 8 draws
1633 if 64913983816
100.00000%
2016925
14.42328%
42157
0.30147%
163
0.0000116%
16.6%
Say 6 draws
Fairbrother
Partial Cover
4913890084
99.32971%
2197458
15.71429%
42217
0.30190%
22.6%
Say 6 draws
2106 if 6
System 10 *
101262328
9.02700%
165648
1.18457%
10038
0.07178%
210
0.0000150%
0 to 21%
Say 5 draws
Fairbrother
Partial Cover
4913966433
99.87569%
2797386
20.00445%
54390
0.38895%
22.6%
Say 5 draws
* 1000 plays at 210 plays per draw could easily give nothing over 5 draws and even 10 draws; minimum payout if prize is obtained is 35 CombThrees ie £350.00. If you want regular wins then a System at this number of lines is the worst way to play.

Colin Fairbrother

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