RobinZ comments on The Prediction Hierarchy - Less Wrong

21 Post author: RobinZ 19 January 2010 03:36AM

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Comment author: Bugle 20 January 2010 01:26:45AM 0 points [-]

My grasp of statistics is atrocious, something I hope to improve this year with an open university maths course, so apologies if this is a dumb question:

Do the figures change if you take "playing the lottery" as over the whole of your lifespan? I mean, most of the people I know who play the lottery make a commitment to play regularly. Is the calculation affected in any meaningful way? At least the costs of playing the lottery weekly over say 20 years become much less trivial in appearance

Comment author: RobinZ 20 January 2010 03:11:52AM 0 points [-]

As mattnewport and LucasSloan point out, it doesn't change the actual numbers - a bad bet multiplied a thousandfold is still a bad bet - but it does change the wrong numbers: buying a thousand tickets for a 0.01% chance of a million dollars is a losing bet again.* More evidence that the ignorance argument fails.

* How I calculate this (changes in italics):

According to your calculations, "none of these thousand tickets will win the lottery" is true with probability 99.9975000312185%. But can you really be sure that you can calculate anything to that good odds? Surely you couldn't expect to make forty thousand predictions of which you were that confident and only be wrong once. Rationally, you ought to ascribe a lower confidence to the statement: 99.99%, for example. But this means a 0.01% chance of winning the lottery, corresponding to an expected value of a hundred dollars. Therefore, ... these thousand tickets still lose, because you spend a thousand to win a hundred.

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