На русском: http://www.proza.ru/2010/11/01/558
Assuming we’re talking about a prize which is not the first, such as the 6 out of 6 (because here all the options are the same), then according to the range method, not all the combinations have the same chance of being drawn. For the most obvious example, let’s take the extreme case and calculate the options of drawing the first number (not the ball, since the lowest number becomes the first one, even if the ball was the last one to drop into the vessel) with the value of 1 out of 37. We have 6 balls and 37 possibilities, therefore each of the 37 numbers (including 1) can be in the opening 6 with the odds of 6 out of 37, and the one will always be the first one. This means we have the chance of 6 out of 37 or about 16 percent.
Now, let us imagine the odds of the first number being 32. This means that all the balls that are rolling in the vessel should be in the range between 32 and 37. This requires the final draw of the following numbers: 32, 33, 34, 35, 36, 37. Which means that the demand for one number becomes the demand for all the other numbers, which gives us a single option out of the possible 2,324,784. This comes to a chance of 0.000043%, far less than 16%.
And still, it won’t be right to focus on minimum and maximum alone, since according to the principle of systemaism, we should see the system as a whole. Therefore we assess all of the 6 balls together. The 1 can only come at the first ball, the two at the second or the first and so on. Therefore, only a number bigger than 5 or smaller than 33 can catch any of the balls and the lower the value of the number is, the higher are its chances to be at the beginning.
We shall select the base number for each of the balls and set the range. For example, a first ball with the base of 3 and a range of 2 covers the options of 1, 2, 3, 4, 5. The choice of the base number and the range can come from anything (mostly based on statistics, which are only partially true). Unfortunately, since I’ve signed a confidentiality and non disclosure agreement with my company, I can’t go further into the details of this method, despite the fact that the company progressed into a higher level and this method is outdated for it.
The author is the head of Programming and Statistics department of a lottery company in Israel.
Method "Grid": http://www.proza.ru/2010/11/25/896
Method "AI": http://www.proza.ru/2010/12/27/1080