Sanderson M. Smith
Home  About Sanderson Smith  Writings and Reflections  Algebra 2  AP Statistics  Statistics/Finance  Forum
SuperLOTTO Plus was introduced by the California Lottery on June 4, 2000. There are nine ways to win, and the jackpot starts at seven million dollars.
The rules for SuperLOTTO Plus are relatively simple. There are two number sets:
Set A: The integers from 1 to 47 inclusive.
Set B: The integers from 1 to 27 inclusive.
A player spends $1 for the privilege of selecting five numbers from Set A, and one number, called the MEGA number, from Set B. All prize payout amounts are parimutual. That is, the amount of money varies from week to week, depending upon the sales levels and the number of winners. The jackpot prize, obtained when one matches all five numbers and the MEGA number, has a stated minimum value of seven million dollars.
There are nine ways to win in SuperLOTTO Plus. Probabilities and odds associated with the game are displayed in the table below. Here are some notes and observations relating to the table:
It is often helpful to represent very small probabilities in the form 1/x using the algebraic identity
x = 1/(1/x), if x is not zero.
For instance, the probability of hitting the jackpot is 0.0000000241451 (see table). Using the algebraic identity, this can be written as
0.0000000241451 = 1/(1/0.0000000241451) = 1/41,416,353.
In other words, the odds of winning the jackpot are 1 in 41,416,353.
Here is a statistical analysis of SuperLOTTO Plus:
EVENT 
SYMBOLIC PROBABILITY 
NUMERICAL PROBABILITY 
ODDS: 1 in  
Match FIVE and MEGA 
(5C5)(42C0)(1/27)/47C5 
2.41451E08 
41,416,353 
Match FIVE and NO MEGA 
(5C5)(42C0)(26/27)/47C5 
6.27771E07 
1,592,937 
Match FOUR and MEGA 
(5C4)(42C1)(1/27)/47C5 
5.07046E06 
197,221 
Match FOUR and NO MEGA 
(5C4)(42C1)(26/27)/47C5 
0.000131832 
7,585 
Match THREE and MEGA 
(5C3)(42C2)(1/27)/47C5 
0.000207889 
4,810 
Match THREE and NO MEGA 
(5C3)(42C2)(26/27)/47C5 
0.005405111 
185 
Match TWO and MEGA 
(5C2)(42C3)(1/27)/47C5 
0.002771852 
361 
Match ONE and MEGA 
(5C1)(42C4)(1/27)/47C5 
0.013512778 
74 
Match NONE and MEGA 
(5C0)(42C5)(1/27)/47C5 
0.020539423 
49 
 

TOTAL PROBABILITY OF WINNING SOMETHING = 0.0425746088 
0.042574608 = 23

As the table indicates, the probability of hitting the jackpot is quite small. To use a time perspective, suppose you continually "invested" $1 per second in SuperLOTTO Plus. Mathematically speaking, you would have to play continuously for over 15 months to expect to hit the jackpot once. And, you could expect to invest over 41 million dollars to get a return that could be as small as 7 million dollars.
But then, while they may be few and far between, there are those who spend $1 and end up as big winners in games like SuperLOTTO Plus.
"Oh, many a shaft at random sent
Finds mark the archer little meant."
Sir Walter Scott: The Lord of the Isles
Home  About Sanderson Smith  Writings and Reflections  Algebra 2  AP Statistics  Statistics/Finance  Forum
Previous Page  Print This Page
Copyright © 20032009 Sanderson Smith