Newsletter Signup
Stay informed with the
NEW Casino City Times newsletter!
Recent Articles
Best of Donald Catlin

Gaming Guru

author's picture
 

Selling Dreams

3 December 2005

By Donald Catlin

Former Yankee catcher Yogi Bera is reputed to have said, "I never make predictions, especially about the future." Well, I tend to agree with Yogi, however if a couple of years ago someone would have asked me if I thought my name would be appearing in Woman's World magazine, I would have told them that they were crazy. Well, not only did it appear last year in the October 19th, 2004 issue but it is going to appear again this January. Why? Because I'm famous? Hardly! No, it's because I wrote The Lottery Book, The Truth Behind the Numbers.

During the week of October 17th of this year, my email was buzzing and my phone was ringing off the hook. The reason was that the Grand Prize in the October 19th Powerball drawing was estimated to be $340 million. Every time the grand prize in either Powerball or Mega Millions reaches one of these huge totals, radio stations from around the country search the web for lottery info and my name pops up. Tuesday and Wednesday of the week of the 17th I did four live interviews on morning talk shows. I should add that the following week the Lotto game in the Canadian province of Saskatchewan reached 40 million, a big total for this game, and I spoke to a radio station in that province as well. These all sounded pretty much the same and I'll get back to that issue a bit later in this article. In addition, probably because of all the Powerball hoopla, the Woman's World magazine was apparently prompted to do an article about lotteries and they called me as well during this same period.

The Powerball game has changed a bit since I wrote my book, so it occurred to me that it would be a good idea to use this article to update the facts about Powerball. I should say, however, that when I wrote The Lottery Book I was well aware that lottery games frequently change, so I classified them by type as well as I could and explained to the reader how to do the calculations to analyze each type of game. So, if you want to know how I computed the numbers I will present below, my book is still timely in that regard and you can just turn to the pages on Powerball and replace 53 by 55 and follow the same calculations I presented there.

Here are the facts. August 28th of this year the Multistate Lottery Corporation (MUSL) raised the number of white balls in the Powerball game from 53 to 55; the number of red (powerballs) remained at 42. So currently a player selects five white balls from 1 to 55 and one red ball from 1 to 42. In the table below I show the frequency with which a player's choice will match the MUSL drawing and the corresponding payoff for such a match. Each play costs $1, although for an additional $1 the player can take a chance on a randomly picked multiplier that multiplies any non-jackpot by 2, 3, 4 or 5. I will not address this feature below. Note that the notation 4 + PB means that the player matched 4 of the white numbers as well as the powerball number.

Outcome

Frequency

Payoff

5 + PB

1

Grand Prize

5

41

$200,000

4 + PB

250

$10,000

4

10,250

$100

3 + PB

12,250

$100

3

502,250

$7

2 + PB

196,000

$7

2

8,036,000

0

1 + PB

1,151,500

$4

1

47,211,500

0

0 + PB

2,118,760

$3

0

86,896,160

0

Total -

146,107,962

--

Powerball Frequencies and Payoffs

 

Several things are immediately clear from this chart. First of all the chance of winning the grand prize is 1 in 146,107,962. The number of losers is the sum of the frequencies for 2, 1, or 0 white balls and no powerball and this figure is 142,116,660. Equivalently, subtracting this number from the total number of combinations, we see that there are 3,991,302 chances of winning something. This represents a 2.73% hit frequency. So if you play Powerball it is very likely (better than 97%) that you won't win anything.

What about the house edge in Powerball? An equivalent question is what percentage of the money played is returned to the players. As we'll see, this depends upon the size of the grand prize. Here are the facts. If we assume that 146,107,962 tickets are sold and each one corresponds to one of the possible outcomes, then everything will be paid according to the frequencies shown above. Thus we have to take the number of times each outcome occurs and multiply it be the amount of the prize paid for that outcome. This gives us the following table

Outcome

Frequency

5 + PB

GP

5

8,200,000

4 + PB

2,500,000

4

1,025,000

3 + PB

1,225,000

3

3,515,750

2 + PB

1,372,000

1 + PB

4,606,000

0 + PB

6,356,280

Total -

28,800,030 + GP

The percentage returned to the player would be the number 28,800,030 + GP divided by 146,107,962 and expressed as a percentage.

This brings up another issue. Players sometimes wonder how large the Grand Prize has to be for the game to return over 100% to the player. This is easy to figure. We simply set

28,800,030 + GP = 146,107,962

and solve for GP; the answer is 117,307,932. So it would seem like a grand prize of $340 million would certainly be well over 100%. Not so fast. The $340 million advertised by MUSL represents an annuity that is paid out over a 29-year period. If you want to take the money as a lump sum, which is what the prize is actually worth, you have to take a fraction of the $340 million. What size is the fraction? I explain that in my book. The lottery has to make some assumptions about inflation, potential earnings, and so on and decide how much they would have to invest today to fund the annuity for the next 29 years. This fraction changes with time but is currently 0.483558994. In other words, a lump sum payment here would be this fraction times $340 million; the figure is $164,410,058, which is indeed enough to make the game one that returns over 100% to the players. Whether or not this is a compelling reason to buy a lottery ticket is another matter and I address this in my book. The salient point is that this money is not evenly distributed to the players. Rather, most of it goes to a few players (the October 19th drawing had one Grand Prize winner) and, as we noted earlier, most players get nothing back at all. This is why I titled this article the way I did. The main things that the lottery is selling with these huge prizes are dreams.

What about those morning radio interviews I mentioned earlier? The weather today will be colder on Thursday to be followed by Friday. Keep listening to WPDQ for details on our pierced navel contest. Now say welcome to Dr. Don Catlin a noted lottery expert (yeah right, I'm even in Woman's World)) who will give us the skinny on playing the lottery… blah, blah, blah. The question I am always asked is if there is some advice I can give players to increase their chances of winning. The answer is always the same; I have no such advice. The lotteries go to great lengths to ensure that their drawings are totally random and independent from one another. They do this precisely because they don't want to be beaten -- and believe me, they are not beaten. There are charlatans around who will sell you books with winning lottery systems, but the only winners from these systems are the folks selling the books. Don't waste your money on such things. (Related to this, see my article entitled Lottery Nonsense that is in the archives on this site.)

What advice can I honestly give you? Well, although you can't increase your chances of winning you can slightly increase the chances that you don't have to share a winning prize with many other players. You can do this by avoiding so-called lucky numbers like 1, 7, 11, or 13 or avoiding numbers used in birthdays, such as 19. Notice I said "slightly." I think a better piece of advice is to let the lottery computer pick your numbers. Let me explain why. Humans have built in biases concerning what they think is likely and what is not. For example, I think that most people would think that a lucky number or their birthday is more likely to occur than, say, the numbers 1, 2, 3, 4, 5. A computer has no such bias; every number combination is (correctly) considered as equally likely. So I believe that the random drawing of the computer is more likely to give you a number combination not shared with another player than a number you pick yourself. Along these lines let me share an interesting bit of history with you. On October 1, 2005 the Fantasy Five game in Florida (a 5 from 36 rolldown game) had winning numbers of 1, 3, 5, 7, and 11 and there were 40 winners who had all five numbers correct. On October 3 this same game had winning numbers of 4, 5, 6, 7, and 32 and there were no winners having all five numbers correct. Interesting isn't it?

One other frequently asked question during these interviews is if I myself play the lottery. The answer is occasionally. I also don't expect to win, which is why it is only occasionally. When I do play I usually play scratch tickets since they are generally a better bet than the other games. Notice I said "better". They still aren't all that great. But as I document in my book, my family has some fun with them at Christmas time, so shortly after you read this I'll be over at Lenny's Liquor store laying out good money for bad bets. See you next month.

Donald Catlin
Don Catlin is a retired professor of mathematics and statistics from the University of Massachusetts. His original research area was in Stochastic Estimation applied to submarine navigation problems but has spent the last several years doing gaming analysis for gaming developers and writing about gaming. He is the author of The Lottery Book, The Truth Behind the Numbers published by Bonus books.

Books by Donald Catlin:

Lottery Book: The Truth Behind the Numbers