Graeme −> Odds and Ends −> CA Lottery

The California Lottery is really several different games.  The big one is Lotto, which is now called "Super Lotto Plus".  In this game, you pick five numbers from 1 to 47 and a MEGA number from 1 to 27.  Here are the ways you can win:

 Match Odds 1 in Approximate Prize Expected Value of 1 Ticket All 5 of 5 And Mega 41416353 \$33,000,000 \$0.80, if just one winner All 5 of 5 1592937 \$24,000 \$0.01 Any 4 of 5 and Mega 197221 \$1,500 \$0.01 Any 4 of 5 7585 \$100 \$0.01 Any 3 of 5 And Mega 4810 \$50 \$0.01 Any 3 of 5 185 \$10 \$0.05 Any 2 of 5 And Mega 361 \$10 \$0.03 Any 1 of 5 And Mega 74 \$2 \$0.03 None of 5 Only Mega 49 \$1 \$0.02 Overall odds of winning 23 Total:  \$0.97

This table shows the odds of winning.  The prize amount varies from week to week, so I show the approximate amount of the prizes usually paid.  The "Expected Value" of a ticket is the probability of winning multiplied by the expected amount you would get if you won.  The top prize varies quite a bit -- it starts at \$7,000,000 and then increases with each drawing where there is no top prize winner.  While the jackpot increases, the probability of there being just one winner decreases, so the expected top prize value per ticket probably tops out at about a dollar.   You might think this could make the total expected value of a ticket greater than a dollar, which would mean if you could buy up all the tickets, you could make a profit!  But, alas, the top prize is paid out over 26 years, making its present value about half its face value.

Still, you might be the lucky winner.  You never know.  To help you find out, I made an Excel spreadsheet you can use to enter the numbers from your ticket, and it will tell you whether you won.  It's useful if you can type faster than you can think (or know someone who does).  Here it is, if you want to use it.