Assessing value in playing lotto
July 15, 2014 3:00 AM
by Elliot Frome
This past week, a friend sent me an e-mail along with a link to an article about a woman who has been seemingly making a habit of winning large prizes in scratch off lotteries.
I tend to be very skeptical of these types of articles. The Internet isn’t always the best place to find credible information. Some of you might recall a column I wrote several months ago about how one writer noted that a disproportionate number of winning multi-state lottery tickets were being sold in one state.
This “analysis” didn’t take into account the total number of tickets sold. It shouldn’t be much of a surprise if more winning tickets are sold in Pennsylvania vs. Rhode Island given that many more tickets are presumably sold in Pennsylvania.
As I read through this article, I find it far more insightful than I was expecting. To be clear, I am not advocating using any methods in the article. The piece makes a variety of assumptions that are not shown to be fact, but seem to make some sense. Let me try to summarize the basic concept of what is going on.
A state authorizes a scratch off lottery in which 3.6 million tickets will be sold at $50 a ticket. This generates $180 million. It will pay out a total of $140 million, which will include three $10 million dollar tickets. Just from this basic information we can derive a whole lot of information.
First, the odds of winning a $10 million prize is 1 in 1.2 million. At first glance, this might seem nice, but let’s remember each ticket is $50. So, the real prize is $200,000 for each $1 wagered. The remaining pot is $110 million.
If we take this $110 million and divide by the total revenue of $180 million, we find that without the three jackpot tickets, the payback is only 61.11%. The three jackpot tickets will add 16.67% for a total payback of just under 78%. Put simply, if I were to buy ALL 3.6 million tickets for $180 million, I’d win $140 million back for a net loss of $40 million. So, how does one make money doing this?
The answer comes down to that which allows all gamblers a better chance – information. Lotteries need to sell all of the tickets in order to make money. As a result, two things happen.
Per this article (and apparently confirmed with the company that makes most of the scratch off tickets in the U.S.) the top prizes are purposefully “randomly” distributed over the time period the tickets will be sold. So, in other words, they are not truly randomly distributed, but rather, there is a purposeful attempt to make sure the top three tickets cannot come up in the first 15% of the tickets sold.
If word got out that all three $10 million prizes were gone, sales would plummet. At the same time, if you know 1.8 million tickets have been sold and only one of the top prizes awarded, the odds change rather dramatically. The odds of winning a top prize drops to 1 in 900,000 and the payback presumably begins to climb. But how can a player know this is what happened?
Well, in order to keep up the excitement, the lottery gives us some of this information. In this particular case, our prolific winner used a website (which for the moment we have to assume had accurate information) that stated there were only 1.6 million tickets left and still two top prizes.
Assuming the smaller prizes are evenly distributed and remain at 61.11% payback, we can recalculate the impact of the top prize and find it now contributes 25% to the overall payback. But this still leaves us an overall payback of over 86%. Better than most lotteries, but still a losing proposition.
But, now the two concepts are combined. If the top prizes are distributed so each one will show up in its appropriate third of the tickets, then a top prize is likely to show in the next 400,000 tickets. If you can somehow buy (relatively quickly) 400,000 tickets, you would stand a very good chance of getting a $10 million ticket.
If we recalculate the payback at 1 in 400,000, we find that the payback now stands at about 111%. We are no longer talking about a typical sucker’s bet from the lottery but a significant player advantage opportunity. Of course, this still requires an investment of $20 million.
As the article shows, there are ways to greatly reduce this by buying tickets and taking the small winnings to buy more tickets. In this way, it would take “only” a few million to be able to buy all $20 million in tickets.
As stated earlier, many of the notions presented in the article are assumptions about what actually happened and rely on some guesswork as to exactly how scratch lotteries operate. I found the article most interesting because it was just a few months ago I was wondering about how these types of lotteries work while my family was collecting pieces in a supermarket promotion.
In these types of promotions (where you have to collect multiple pieces of a puzzle to claim a prize – a lot like how McDonald’s runs it “Monopoly” game), it seems if you collect a lot of pieces in a short period of time, you will quickly get duplicates. But a month later if you get some pieces, you’ll have almost none.
The stores don’t want the top prize to be won too early in the promotion or people may lose interest. They also have incentive to keep you coming back every once in a while during the life of the promotion. Thus, every piece may not be entirely random.
I don’t expect every piece to be as likely as every other piece, but I don’t expect the piece that is the unique piece to winning the top prize will be given out in the last month of a 5-month log promotion. I have often wondered if this type of manipulation renders the game not truly random and potentially runs afoul of some laws. But, I’ve yet to see someone make this guess.
I probably won’t start playing scratch off lottery tickets, but I found the article rather refreshing in that it used real math to make its case. This concept goes well beyond lotteries and applies to most every game in the casino. Luck is good in the short run, but knowledge is what works in the long run.
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Elliot Frome is a second generation gaming analyst and author. His math credits include Ultimate Texas Hold’em, Mississippi Stud, House Money and many other games. His website is www.gambatria.com. Contact Elliot at ElliotFrome@GamingToday.com.