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":

Avoid multiples of 7.
Avoid single-digit numbers 1-9.
Avoid numbers that form vertical, horizontal or diagonal patters on the bet slip.
Avoid 1-2-3-4-5-6 [and similar sequences].
Avoid having all numbers 1-31, because people often choose birthdates and other day numbers for their picks.
Include numbers ending in 1, 2, 8, 9, and 0 (most commonly picked numbers end in 3-7).

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.