# Wheels as Filters

#### Thorngren

##### Member
A wheel is NOT the greatest thing since nocturnal ball games for winning a lottery. It is nothing more than a filter and exhibits the reflexive property of a filter. The reflexive property of a filtered draw, simply stated from the Law of Multiplication for an outcome with more than one result, says that the probability the filter will be successful times the probability the filtered draw will win the lottery is the same as that for a random draw (long term random). Consider a 6/49 lottery without draw replacement and without a bonus ball and a 12 number wheel with 6 draws for a guaranteed 4 of 6 win. The probability that your twelve numbers will have the winning 6 numbers becomes 49!(49-6)(48-6)...(44-6)/(6!12!(49-12)!) = 1/15134. This is the probability the filter will succeed. The probability the wining ticket will be in the six tickets you play becomes 6 times the probability of a 6/12 lottery 12!/(6!6!) = 1/924. Hence the probability of winning on these six tickets becomes six times 1/(15134 x 924) = 1 /13983816 which, of course, is six times the probability of a single random draw. But then again, you might get lucky, you might see something no one else does, which is the fun in playing.

John T. Thorngren
Leveraging a Lottery
(c) 1996, 1999
ISBN 1-58500-715-3