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Improve Your Lottery Expected Value

Fun with statistics

The January 1, 1998, Denver Post newspaper included an article with information of interest to lottery enthusiasts. The article is incorrectly titled "Boosts your odds to win." While the tips do not change the odds of winning, they will decrease the probability of having to share prizes with other winners. The techniques are attributed to Alan Reiss of U.S. Mathematical Labs in Wayland, Massachusetts.

"The key is choosing unpopular numbers":

If your are so fortunate as to win, please be sure to let me know. I would be delighted to be able to say that one of my clients or course participants "won it big."


In Colorado, we pick numbers from 6 of 42 balls (numbered 1-42). The probability that the first ball selected is one of ours is 6/42. If the first ball has one of our numbers, the probability that the next ball is also one of our numbers is then 5/41. And so forth. Thus, the probability of winning first prize is (6*5*4*3*2*1)/(42*41*40*39*38*37) = 6!36!/42! = 1/5,245,786.


—John Schuyler, January 1998.

Copyright 1998 by John R. Schuyler. All rights reserved. Permission to copy with reproduction of this notice.