Looking at this very quickly, and perhaps not seeing the entire picture, this is what I see now.
First, if the Lotto consists of balls numbered from 1 to 50, then the difference between the
high ball drawn and the low ball drawn varies from 5 to 49. 1 - 2 - 3 - 4 - 5 - 6 = 6 - 1 = 5 and
1 - x - x - x - x - 50 = 50 - 1 = 49. So, the differences for a Lotto consisting of 6 balls are:
5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,
37,38,39,40,41,42,43,44,45,46,47,48, and 49. Counting each difference yields 45 differences.
Finally, the PROBABILITY of a Lottery using balls 1 to 50 with a DIFFERENCE LESS THAN 21 IS:
P = (5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20) OR 16 DIFFERENCES / ALL 45 DIFFERENCES
= 16/45
= 35.5%
It appears to me that nearly thirty-six percent of the time you will see a difference of less than
21.
Scanning yesterdays results shows the following had drawings where the difference was less
than 21:
Wed Oct 15, 2008:
Illinois Little Lotto: 18 35 17
Illinois Lotto: 24 40 16
Kentucky Win For Life: 12 27 15 (Don't know anything about the "Win For Life" games.)
Multi-State Win For Life: 12 27 15
New Mexico Road Runner Cash: 23 32 9 (Don't know about this game either.)
Virginia Win For Life: 12 27 15