Figuring the Odds
Scratch Games, Raffle, and Progressive Print-N-Play
These games feature a predetermined number of tickets and a predetermined number of winners. The odds are simply determined by calculating the ratio of winning tickets to total tickets. If, for example, there are five top prizes out of 1,000,000 tickets, the odds of winning one of these prizes is 5 divided by 1,000,000, or 1 in 200,000. Overall odds of winning something on a Minnesota Lottery scratch ticket are 1:3.97.
Lotto Games Odds
For most lotto games, the calculation of odds and probability uses a mathematical function called the hypergeometric distribution. The exceptions are Daily 3 (see below) and games such as the Minnesota Millionaire Raffle and Progressive Print-N-Play that feature a fixed, predetermined number of tickets.
The hypergeometric distribution applies to cases where a set of object is divided into two sets. If we randomly draw r objects from this set, we want to know the probability that our draw will include exactly k objects of one of the two sets. A math textbook (such as "Feller, An Introduction to Probability Theory and its Application") or your local library can probably supply you with information about probability theory. In the descriptions below, these theories are applied to Minnesota State Lottery games. Remember that odds are the inverse of probability so if a formula has calculated the probability, you divide 1 by that number to get the odds.