TABLES OF WINS

A new feature and another very important quality of our book is the full table of possible wins for each of the systems presented. The tables give the distribution of wins over all possible draws and are excellent tools for determining which system to choose and what the expected win could be provided you hit some (usually at least three) of the numbers drawn. Let us take a look at the table of possible wins for System # 20. This table contains 19 lines, each representing one possible distribution of wins. However, a line might represent several non-esentially-different possible distributions (see below). The first column of the table shows how many of your numbers are actually drawn. The last column shows the probability of the corresponding distribution.

Guessed	6	5	4	3	%
6	1	-	12	4	2.38
	1	-	10	8	7.14
	-	3	8	7	28.57
	-	3	7	9	28.57
	-	2	9	8	28.57
	-	-	15	2	4.77
5	-	1	4	10	23.81
	-	1	3	11	23.81
	-	-	7	6	23.81
	-	-	5	11	23.81
	-	-	5	10	4.76
4	-	-	3	4	2.38
	-	-	3	2	4.76
	-	-	2	7	28.57
	-	-	1	9	28.57
	-	-	1	8	35.72
3	-	-	-	5	8.33
	-	-	-	4	16.67
	-	-	-	3	75.00

For example, if you play System # 20 and 4 of your 10 numbers are drawn, then the system guarantees you at least one 4-win. However, you will actually win more than the guaranteed one 4-win: There are five possibilities that are clearly seen from the table. You can either get one 4-win and either 8 or 9 3-wins with probabilities 35.72% or 28.57%, correspondingly, or you can get two 4-wins and seven 3-wins (probability 28.57%), or three 4-wins and either two or four 3-wins with probabilities 4.76% or 2.38% correspondingly. Similarly, if you correctly guess only three numbers, you get at least three 3-wins, or more precisely, three 3-wins with probability 75%, four 3-wins with probability 16.67%, or five 3-wins (probability 8.33%). For those of you who are not familiar with probabilities we include a brief explanation: Suppose you have played long enough with the same system and hit 3 of the numbers many times. Then, in approximately 75 out of 100 cases, you will have three 3-wins; in 17 (16.67, to be precise) out of 100 cases, you will have four 3-wins, and in 8 (8.33, to be precise) out of 100 cases, you will get five 3-wins.

Presenting individually every line in the full table is not always physically possible; in many cases, the full table would contain up to several thousands entries. In such cases, we present an abbreviated table. An abbreviated table still comprises all possible distributions of wins, but most of the lines in such a table actually represent several lines from the full table. We have chosen to keep distinction between the highest prizes. For example, had the table for System # 20 been much longer, we could have written the abbreviated 6-wins section as

Guessed	6	5	4	3	%
6	1	-	10-12	4-8	9.52
	-	3	7-8	7-9	57.14
	-	2	9	8	28.57
	-	-	15	2	4.77

instead of

Guessed	6	5	4	3	%
6	1	-	12	4	2.38
	1	-	10	8	7.14
	-	3	8	7	28.57
	-	3	7	9	28.57
	-	2	9	8	28.57
	-	-	15	2	4.77

We can justify such abbreviations by observing that what matters most is the highest-ranked prizes (those in the leftmost non-empty column of the corresponding part of the table). What you get in lower-ranked prizes is usually just a small percentage of the entire win.

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