MEGA Millions Lottery

The chance of winning the MEGA Millions lottery jackpot is 1 in 303 million (more precisely, 1 in 302,575,350.)  To put this in perspective:

If you buy 50 tickets per week you will win the jackpot once every 116,000 years.

If every time you drive a mile you buy a MEGA Millions ticket, you will make an average of 633 round trips to the moon before you win the jackpot.

Suppose you have one friend in Canada.  Suppose you put the names of everyone in Canada in a hat and draw a name at random.  Suppose you then buy a MEGA Millions ticket. You are 9 times more likely to draw your friend’s name than you are to win the jackpot.

Since the chance is so low of winning the Mega Millions jackpot, why are there winners?   It’s because of the “Law of Very Large Numbers”:  Given enough opportunity, any weird thing will happen just due to chance.   In other words, as long as there is opportunity for weird things to happen, chance alone explains strange coincidences, mystical occurrences, and other bizarre events.  In the case of the MEGA Millions lottery, there are jackpot winners because so many people buy tickets.  The chance may be almost zero that you or I will win the jackpot, but if more than 300 million tickets are sold, there is a good chance that someone will win.

Luck is a group phenomenon.  In the case of the Mega Millions jackpot, for every lucky winner, there is, on average, an unlucky group of 303 million losers.

When you buy a Mega Millions ticket, you pick Pick 5 numbers from 1 to 70 and 1 MEGA number from 1 to 25.   There are about 303 million ticket combinations.  Since the winning ticket is chosen at random, that’s why the chance of winning the MEGA Millions jackpot is about 1 in 303 million.

If you were to buy every possible ticket combination, it would cost you about $303 million.  When nobody wins for awhile, since prize money carries over to the next drawing when there is no winner, sometimes, the jackpot might  exceed $303 million.  Suppose the jackpot reaches $500 million.  Then if you invest $303 million in buying every possible ticket combination, you are guaranteed to win the jackpot, giving you an apparent profit of $500 million minus $303 million, or $197 million.  Unfortunately, if you fill out 3 tickets per minute, 24 hours per day, it will take 192 years to fill out all possible ticket combinations.  And even though you would be assured of winning the jackpot, if some other lucky player also wins, you would need to split the pot with them.  Also, you need to pay taxes on net gambling winnings.  So making a large bet like this is probably not a good idea, even if you figure out a way to do it.