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!

 

 

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