Tuesday, November 20, 2007

How much should I pay for a chance at $20 Million?

Millions of Canadians purchase lottery tickets each week hoping to strike it rich. Why do Canadians buy lottery tickets even though the chances of picking the winning numbers are very very slim? Is this irrational? How much should I pay for a shot at a huge chunk of tax-free cash?

Economists tend to value prizes by multiplying the probability of winning and the prize value. Using this approach, I want to estimate the value a Super 7 ticket for Friday's $20 million draw.

To do this, I looked at the Super 7 website for the odds of winning the big prize. Assuming only one person can win the jackpot (for the moment), the probability of winning the $20 million Super 7 is 1 in 20,963,833. The value of my only shot at retiring early (by matching all 7 numbers) is valued at $0.95 (1/20963830 times $20M). However, there are other cash prizes. You can make a profit by matching 4 numbers (or 3 plus the bonus) or better - the odds of winning any cash prize are 1 in 30.72. Adding this, the value of a ticket rises to about $1.35 (given a host of assumptions about the number of winners and ticket sales). Lastly, 1 in 5.887 (about 17%) are the odds of winning a free ticket (which I value at near zero since it is really hard to sell on the street).

So there you have it: Each $2 play is worth about $1.35 (which I call the ticket's ‘investment value’) for this week's draw. Is it irrational to purchase a ticket? Well, at first glance, the answer is yes. However, we know that people don’t just buy it for the investment value, they buy it for fun! Moreover, taking the investment value and the fun factor together, it is easy to see that as the jackpot rises, both the investment value and day dreaming also rise, which leads to more and more people purchasing tickets.

Maybe buying a ticket is not so irrational after all. It is just that, at some jackpot level, people get more utility from buying a ticket than any other $2 investment or marginal consumption (such as a chocolate bar or an 8oz draft of Keith's at the Midtown Bar and Grill).

You may be asking when will the investment value be worth the $2 cost? Answer: When the jackpot reaches $33 million, assuming only one person can win the big prize.

Any other questions?
Appendix
This article makes an interesting comparison between buying a loto ticket and investing in the DotCom stocks in the late 1990s. Irrational or buying hope?

8 comments:

Francis Wooby said...

What's irrational is banking on winning the lottery as your retirement plan.

Canadian Economist said...

FW: ha ha ha. O'wait: Do you know someone doing this or are you suggesting that playing the stock market is like buying a lottery ticket?

Spudman said...

I've put my faith in my pension plan. As long as it doesn't pay out in lottery tickets, I'll do fine.

Canadian Economist said...

I am a big fan of pension plans - defined benefit plans, as opposed to defined contribution, are king but pensions are great. Like paying a mortgage, pensions are forced savings. Pensions almost always feature mandatory contributions by employees (and employers). Because life is front-end loaded (car, house, kids), it is extremely hard (and even frustrating) to make your contributions when you are 40 years from retirement, so it is good that someone makes you. As hard as it seems, it is well worth. Specially if you plan to live to 100 .

CresceNet said...
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barb michelen said...
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Francis Wooby said...

My, my, is that SPAM I smell in this comment section?

Canadian Economist said...

Spam removed. sick.