## Shining a light on the California Lottery

In the back of my mind, winning the lottery means becoming a millionaire (or better). Thus I find the following statements found in the website of the California Lottery very interesting.

Since 1985, the California Lottery has distributed more than \$27 Billion in winnings (including annuitized) with more than 2,842,467,062 winning tickets sold!

The amount of \$27 billion is a lot of money. This amount ought to be reassuring to anyone dreaming of winning big (think sitting in a beach chair holding a martini in a posh beach resort in the Caribbean). The number of winning tickets 2,842,467,062 is a huge number too. If I keep playing, could I be joining this huge legion of winners?

I noticed something else. Why is the total amount of winnings stated in a nice round number while the total number of winning tickets is not? Note that both figures are not meant to be exact amounts (more than \$27 billion and more than 2,842,467,062 winning tickets).

Why not express the number of winning tickets in a nice round number too? Could it be that this is intentional? Could it be that the display of the number 2,842,467,062 is designed to be fantasy inducing? I do not know for sure. But I have my suspicion. Understanding how to read large numbers will clear things up.

One million is 1,000,000 (one followed by 6 zeros). Note that one million is 1000 times of 1000. Putting it another way, if you receive \$1000 from each of 1000 people, you become a millionaire.

One billion is 1000 times of one million (1,000,000,000 or one followed by 9 zeros). If you have \$1 billion in wealth and you only spend \$1 million a year, it will take you 1000 years to deplete your wealth! Of course, in this scenario, we are not taking the time value of money into account (but that is another story).

So the number of winning tickets for the California Lottery since 1985 is 2,842,467,062 (about 2.8 billion tickets). Interestingly, this means that the average winning amount per ticket is slightly under \$10! This implies that most of the 2.8 billion tickets are for small prizes (way smaller than \$1 million).

So how many lottery prizes of \$1 million or more were won by players in the California Lottery in its 25-year existence? Fortunately, the data are available in the official website of the California Lottery, just that they are not conveniently summarized. I had to search for them county by county (there are 58 counties in California).

I searched the winning tickets by county and I found a total of 247 winning tickets, all in the amount of \$1 million or more. These 247 tickets amount to \$4,535,519,264 (or \$4.5 billion). So more than \$22.5 billion (=27-4.5) in winnings are for smaller prizes (e.g. a few hundreds to tens of thousands in dollars).

Out of 25 years of history in the California Lottery, there are only about 250 winning tickets with \$1 million or more in winning. On average, there are about 10 such winning tickets a year. So winning a small prize may have good odds (about 2.8 billion instances of small winning so far). But winning a huge jackpot in the California Lottery, one that you normally think of as setting you up for life, had only happened 250 times so far.

The California Lottery is in the business of selling dreams. It seems that fuzzy numbers help keep dreams alive. Interestingly, a large number such as 2,842,467,062 was transformed into a fuzzy number by not rounding it.

Even if I did not dig up numbers from the official website, I can still get a sense that there is only a small number of winning tickets worth \$1 million (or more). We can compare 2,842,467,062 with the sizes of the population in California, the United States and China.

The number 2,842,467,062 is almost 77 times the population of California (36.9 million in 2009), and is over 9 times the population of the United States (307 million in 2009). The population of China is 1.3 billion (in mid 2008). The number 2,842,467,062 is over twice the population of China.

Imagine that the number of millionaires created as a result of playing the California Lottery is twice the China population! If true, California would truly be a “Golden State”!

What can one get from buying a \$1 lottery ticket? Not sure what one can get other than a chance to fantasize (a form of cheap entertainment I suppose). The fact speaks for itself. Of the tens of billions of tickets bought in the 25-year history of the California Lottery, there were only 247 winning tickets that paid out \$1 million or more.