Cigarettes and the Lottery

A simple thought experiment - if you go to you local convenience store every day, and buy a pack of cigarettes and a lottery ticket, which is more likely: That the cigarettes will kill you or that you will win the lottery? I beleive that the cigarettes will kill you long before you win the lottery. But most people act in the exact opposite way, otherwise they would buy neither cigarettes nor the lottery ticket. Let's find out below.

First, of course, we'll have to figure out all sorts of details. How old are you? Are you a regular smoker already? How long do you do this for? Let's make up some numbers so we can begin calculations - we can always ajust them later if we change our mind about the details.

Age 20
Gender Male
Cigarettes
Bought Per Day
2 packs ($10/day)
Lottery Tickets
Bought Per Day
10 tickets ($10/day)
State where we
play Lottery
California
Previous Smoker? No
Experiment
Duration
50 years

Lottery Chances

Alright, since we've decided that we're playing the lottery 10 times a day for 50 years, and we're playing in California, we now have all the data we need to figure out our odds of winning the jackpot.

50 years x 365 days/year * 10 ticket/day = 182500 tickets

Odds of Winning the California Lotto Jackpot (Match all six numbers): 1 in 41,416,353

182500 / 41,416,353 = 1 / 226.93892 ... or approx 1 in 227

Wow... 1 in 227 is pretty good odds, isn't it? Maybe I was wrong about my guess. Of course, our test subject also spent $182,500 on Lotto tickets, which is gone forever regardless if he wins or (more likely) loses. (Dumped into a savings account at 5% interest, it compounds to over $800k after 50 years, so that would seem to be a safer way to become a millionaire).

Smoking Chances

Now it gets harder. Cigarettes have been shown to have all kinds of bad effects, and many of them are notoriously hard to measure. Here are a few:

There's a lot of ways we could try to figure this out, but let's cheat: I've discovered a pro-tobacco website that discusses the issue. Their figure is 1 in 12. The figure that they state for a rival government claim is 1 in 3. These seem like good upper and lower bounds for the odds, so let's use them, though of course when I have more time I'd like to come back to this and look deeper.

Don't forget - the figure for investing the money is the same as for the lottery: $182,500 in outlays, if invested at 5%, comes out to over $800k. Those yearly trips to Maui sure would help fight those nicotene cravings.

Wrapping Up - Figure the Odds

Now all that's left is figure the reletive odds.

Odds of winning Lotto after 50 years of 10 tickets a day play: 1 in 227
Odds of dying from smoking every day for fifty years: between 1 in 3 and 1 in 12
Smoking is more likely to kill you: between 76 and 19 times more likely. Yow.

I expected there to be a difference, but not one so... stark.

So, to recap: If you buy 2 packs of cigarettes, and 10 lottery tickets, you're at least 20 times more likely to die than win the lottery... and you're probably 50 times more likely to die than win the lottery.

Sources referenced:
CDC Website on health effects of cigarette smoking.
The Heartland Institute (what looks like a pro-smoking lobby - check it out yourself) has a writeup of the possible odds of death by smoking. They give it 1 in 12, though their number seems a bit streched. The gov't number they cite, 1 in 3, also seems stretched as well, so I feel good about naming those upper and lower bounds.