Sanderson M. Smith
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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 pari-mutual. 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 |
2.41451E-08 |
41,416,353 |
Match FIVE and NO MEGA |
(5C5)(42C0)(26/27)/47C5 |
6.27771E-07 |
1,592,937 |
Match FOUR and MEGA |
(5C4)(42C1)(1/27)/47C5 |
5.07046E-06 |
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
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