Colin Fairbrother

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The preposterous BIG IF'S of Lotto Covers or Guarantee Wheels
 
From the very time that I became aware of Covers or Wheels with guarantees I asked myself is this really for real for the simple reason that those that espoused these absurdities referred to the condition to meet to get the guarantee in a way as if it was some trifle easily overcome! Nothing could be further from the truth as is apparent when referring to the table below! There are no Jackpot Lotteries for pretty much a Pool less than 25. Getting 3 right in say a Pool of 20 is way different to getting 3 right from the full Pool of numbers used in the Lotto game whether it be 25, 45 or 49.
 
For a Cover or Wheel with Guarantee that uses the full Pool of integers for that Lotto game as in C(49,6,3,6,1)=163 there is no IF - you are going to get a win every draw and damn the exorbitant cost for a pittance return! The syntax for this expression is - Cover(Max Integer, Pick, Prize Guarantee, Hits, Wins Guarantee)=Lowest Number of Combs. However, where the Pool is less than the maximum applicable to the game in this case 49 - then some pretty big IFs come into play.
 
Realize that the more constrictive the pool is the harder it is to get all the integers in that pool. For a 6/49 Lotto game where 6 integers are drawn the hardest is to get them in a Pool of 6 which is first prize followed by 7, 8 etc. This is why you need more combinations to get the guarantee as you increase the Pool size.
 
What's the point? Well, just like those lottery advertisements that say all you have to do to win is pick 6 numbers from say, 49 and then jump up and down for joy when the draw comes round so in Covers the big IF is often glossed over as if it is naturally going to happen. The reality is that those big IFs follow the odds and just don't happen that often.
 
Refer to the table below to get a reality check on just where the lower Pool sizes figure with the actual Lotto games' maximum Pool size. In particular note that in a 6/49 game the combinations from Pool 44 are about 50% of the maximum so if you are dealing with say Pool 22 this represents about ½ of 1% NOT 45%. Easy on the caffeine and give up the sugar!
 
In the table below pc6 (read as p choose 6) means all the combinations of 6 integers from the pool p. So, if p is 7 it is 7 combinations, if it is 8 then 28 combinations etc.
 
Pool
(p)
pc6 -
((p-1)c6) Combs
pc6
Combs
pc6 -
((p-1)c6)
Combs %
of Pool 49
Combs % of Pool 49
7
6
7
0.00004
0.00005
8
21
28
0.00015
0.00020
9
56
84
0.00040
0.00060
10
126
210
0.00090
0.00150
11
252
462
0.00180
0.00330
12
462
924
0.00330
0.00661
13
792
1,716
0.00566
0.01227
14
1,287
3,003
0.00920
0.02147
15
2,002
5,005
0.01432
0.03579
16
3,003
8,008
0.02147
0.05727
17
4,368
12,376
0.03124
0.08850
18
6,188
18,564
0.04425
0.13275
19
8,568
27,132
0.06127
0.19402
20
11,628
38,760
0.08315
0.27718
21
15,504
54,264
0.11087
0.38805
22
20,349
74,613
0.14552
0.53357
23
26,334
100,947
0.18832
0.72188
24
33,649
134,596
0.24063
0.96251
25
42,504
177,100
0.30395
1.26646
26
53,130
230,230
0.37994
1.64640
27
65,780
296,010
0.47040
2.11680
28
80,730
376,740
0.57731
2.69411
29
98,280
475,020
0.70281
3.39693
30
118,755
593,775
0.84923
4.24616
31
142,506
736,281
1.01908
5.26524
32
169,911
906,192
1.21505
6.48029
33
201,376
1,107,568
1.44006
7.92036
34
237,336
1,344,904
1.69722
9.61758
35
278,256
1,623,160
1.98984
11.60742
36
324,632
1,947,792
2.32148
13.92890
37
376,992
2,324,784
2.69592
16.62482
38
435,897
2,760,681
3.11715
19.74197
39
501,942
3,262,623
3.58945
23.33142
40
575,757
3,838,380
4.11731
27.44873
41
658,008
4,496,388
4.70550
32.15423
42
749,398
5,245,786
5.35904
37.51327
43
850,668
6,096,454
6.08323
43.59650
44
962,598
7,059,052
6.88366
50.48016
45
1,086,008
8,145,060
7.76618
58.24633
46
1,221,759
9,366,819
8.73695
66.98328
47
1,370,754
10,737,573
9.80243
76.78571
48
1,533,939
12,271,512
10.96939
87.75510
49
1,712,304
13,983,816
12.24490
100.00000
 
Regards
Colin Fairbrother  


This article first published on the web 19/11/2007 and has been viewed 10583 times.
The author may be contacted at fairbros@bigpond.com. To generate sets of Lotto numbers to play for most Lotto games around the world go to LottoToWin ® where for a US$5.00 annual subscription you can store the numbers as well, to check later for wins. The numbers produced have no duplicate subset combinations of two integers (if applicable) or three integers, use all the integers for the particular Lotto game and maximize the coverage of the potential winning main number. The articles on this site have been selected from the many at the forum LottoPoster
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