Texas lotto, statistics, and the principle of double effect
I've been thinking about the lottery a little bit today because one of our nurses received a lottery ticket from a friend and was asking us how to find out if she won. So given an important clinical question (a question asked in clinic is a clinical question, right?) I did a little research on the Texas lottery website. Per their site the odds of winning the jackpot are 1:25,827,165. However the numbers go from 1 to 54, so I calculate 54*53*52*51*50*49 = 1:18,595,558,800 almost 1000 fold worse odds. Mathematicians/lotto fans can you tell me what I'm doing wrong? Do I have some fundamental misunderstanding of how the lottery works? If their odds are correct, it seems like rational economics would tell you that you should buy a ticket anytime the pot is > $25 million. But that can't be right because a syndicate would form and buy the pot if it were that easy. What's going on here?
On another note, growing up I was taught that gambling was immoral. However, this has not prevented me from making some charitable contributions to a few select Indian tribes who just so happen to run gaming establishments. Which brings me to the principle of double effect. In medical ethics this most often comes up in the context of pain control and end of life care. It is considered morally permissible to give large doses of morphine with the intention of treating pain, even though there is the foreseeable double effect of hastening death through respiratory failure. Can a similar principle of double effect make gambling morally permissible? ie if I view playing the lottery as a voluntary tax to support Texas education but with the double effect of a small but non-zero chance of hitting the jackpot? Similarly, is gambling in an Indian casino morally superior to gambling in a commercial casino in Vegas because you expect to be benefiting a historically repressed minority? On the flip side, if you gamble with the expectation/intention of winning, is it better to do it in Vegas because you'd be taking money from a less vulnerable entity?
Mathematicians and ethicists, send me your thoughts! Need to make a decision by Saturday about whether to buy a ticket :)
Labels: double effect, ethics, lottery, statistics
posted by dmowen @ 21:42
8 Comments
8 Comments:
Capitan, I believe your math is wrong. The formula you used indicates that not only do you have to pick the right numbers, you also have to pick them in the right order which I don't think is the case (but I concede I'm not sure). If I were very helpful, I'd correct your formula, but I can't remember it off the top of my head. Good luck!
Yes I, too, am thinking that it's "54 choose 6" (with that bracket-y math notation) which equals 54!/[(54-6)!6!] not 54!/(54-6)!, because the order of the numbers doesn't matter. This would explain the difference by a factor of 720.
Anyway, thanks for sharing your thoughts, I enjoyed reading them.
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