Double Blind

It’s a pretty sad statement on the stock market that my list of investment candidates is so dry that I have to keep writing about the lottery. I did an expected value analysis on June 3rd.

On June 11th, the Lotto MAX draw came up blank for the main $50 million prize three times in a row. Subsequently the jackpot has grown extraordinarily large – there will be a $50 million prize plus 45 estimated 1 million dollar draws on June 18th.

Analyzing the June 11th results, nobody won the main prize, but out of the 27 $1 million prizes:
12/27 were not won;
9/27 prizes were won by a single individual;
3/27 prizes were won by two individuals;
2/27 prizes were won by three individuals;
1/27 prizes were won by four individuals.

By looking at all the results, you can do some statistical reverse engineering and infer that approximately 18.2 million lottery tickets were purchased for this lottery. At $5 a piece, this is $91 million dollars, or another way of thinking about this is that about 53% of every man, woman and child in Canada bought a lottery ticket.

18.2 million lottery tickets, assuming a random distribution of numbers, coincidentally means that there was a 53.0% chance that the main prize would not be won, slightly better than a coin toss. If we pretended that every Canadian in the country (34 million) bought a lottery ticket (with their numbers drawn being randomly chosen), this would still leave a 30.5% chance of the main prize not being won.

So we move onto the June 18, 2010 Lotto Max and putting this into terms of probabilities, $5 buys you:

- a chance to win $50 million (1 in 28,633,528, with potential for splits). Expected value: $1.75
- 45 chances to win $1 million (1 in 28,633,528, with potential for splits). Expected value: $1.57
- A 1 in 4,090,504 chance to win roughly $580,000. Expected value: $0.142
- A 1 in 99,768 chance to win roughly $5,400. Expected value: $0.0541
- A 1 in 1,584 chance to win roughly $120. Expected value: $0.0758
- A 1 in 71.3 chance to win $20. Expected value: $0.281
- A 1 in 76.7 chance to win $20. Expected value: $0.261
- A 1 in 8.1 chance to win $5. Expected value: $0.617

Add all of this up, and you have a nearly expected-value lottery ticket (about $4.75 in expected value). This still doesn’t account for potential splits (which will happen and thus will make this expected value calculation much lower, especially with a split on the main prize) and still makes the lottery a losing proposition, but the lottery does offer what I consider to be a very good chance of winning a million dollars – again, assuming no splits, a $5 ticket will buy you a 1 in 622,468 chance of winning a million bucks or more. This is an order of magnitude better than the usual 1 in 5.6 million for the Lotto 6/49 (assuming you played $5 worth of Lotto 6/49 tickets, which costs $2 per play).

Coincidentally, 1 in 622,468 is within the bounds of your odds of getting struck by lightening in a single year, while normally your chances of winning a million dollar lottery prize are considerably worse than that.

However, these odds are considerably worse than your 1 in 257,340 chance of winning a million dollars, starting from $5 on a single-zero roulette wheel.

This entry was posted on Saturday, June 12th, 2010 and is filed under Commentary. You can follow any responses to this entry through the RSS 2.0 feed. You can skip to the end and leave a response. Pinging is currently not allowed.