With the recent change in its matrix, Powerball reclaimed the infamous position of being the most outrageously exploitive lottery game in the United States, a position previously held by another despicable game known as the Mega Millions.
In the new Powerball matrix, which is denoted by 5/59 + 1/39 for brevity, the player selects 5 numbers 1 to 59, plus, a Powerball number 1 to 39. With such a format, the chances of winning the jackpot have jumped to nearly one in 200 million - to be exact they are 1 in 195,249,054. Similarly, Mega Millions with a matrix of 5/56 + 1/46, has jackpot odds of 1 in 175,711,536. When mentioned like this, they are nothing more than just numbers, but the real questions is what the physical significance of these numbers is.
A visitor to our web site once asked to buy the printout of all the possible Powerball combinations. At first thought, it would appear to be a simple and lucrative business idea since a few lines of computer program with a very powerful machine can generate the numbers. So far so good. Then, we tried to figure out what would be the size of the book that would hold all the numbers. We picked up the biggest and most common book around and it happened to be the Merriam-Webster's Collegiate dictionary, which has 1,600 pages of fine print and with 100 lines a page laid out in two columns. We determined that we can fit four columns of Powerball numbers on a page each with 100 lines, which means that we can print 400 combinations on a single page. Well, some of us were quite surprised to find out that the dictionary can hold only 640,000 combinations, and for all the 195,249,054 Powerball numbers we will require 305 dictionary-sized books. A similar calculation would result in 275 books for Mega Millions. You can now imagine what it means to pick the right Powerball or Mega Millions number combination in order to hit the jackpot.
As if picking the right book out of 305 or 275 is not hard enough, one has to flip through 1,600 pages of that right book to pick the right page, and then the right number out of the 400 numbers on a page. In fact, a player would be very lucky if he/she can pick the right book at the outset much less proceeding to the next two steps. It certainly is true to say that you have a better chance of being hit by lightning than to hit a jackpot. However, note that this cliche would be a fallacy if the last word, jackpot, as many people say it, is replaced by lottery, since thousands of people win 0,000 or more every year in the lottery while less than a 100 get killed by lightning. Moreover, if it serves as a consolation, you have a better chance of hitting either a Powerball or a Mega Millions jackpot than being elected as the President of the United States.
One may argue that Powerball and Mega Millions are not only about the jackpots, there are also lower prizes as well. Nevertheless, the odds of the second prizes are not comforting either. They are 1 in 5,138,133 for Powerball and 1 in 3,904,701 for Mega Millions to get a 5-of-5 without the Ball. These are equivalent to picking a number from 8 and 6 dictionary-sized books, respectively.
Although millions of people play these games, there is usually no jackpot winner week after week simply because the ticket sales are not large enough to cover all the possible combinations, therefore many numbers are left out. As a result, consecutive no-winner draws will drive the big prize up to several hundreds of millions of dollars. In fact, the people at Powerball and Mega Millions will be rejoicing every time there is no jackpot winner since it means more ticket sales; so will the players, since it means another shot at the big money on its next draw. Some people have even established the notion that these games are rigged to draw unsold numbers in order to elevate the jackpot. Why on earth would anybody bother to rig these games and get in trouble while the beautiful science of probability takes care of it.
Certainly, as the jackpot amount grows, more and more people start playing the game and more and more numbers get covered. Even the most ardent critics of the big lottery games will start spending a buck or two. Who will not be lured by the fact that a dollar can buy such an exorbitant amount. After all, it is, as the saying goes, nothing ventured nothing gained; or no guts no glory. And somewhere, sometime, however long it takes, somebody wins, and it might as well be you. But don't count on it, since it is like finding a number from 305 books each with 1600 pages and each page with 400 numbers.
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