Bugle 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: mattnewport 20 January 2010 01:36:38AM 2 points [-]

If by 'do the figures change' you mean 'does it ever become a good bet' then no.

Comment author: LucasSloan 20 January 2010 01:37:16AM 1 point [-]

Your odds of winning once go up as you increase the number of tickets you buy (# of tickets purchased * Chance of winning per ticket). The expected value of a given ticket remains the same. All you are doing is focusing more money away from other possibilities. If you buy 5 tickets a week for your entire life, and the odds of winning are 1 in 100 million, then you have a 0.000169 chance of winning the lottery, but you could have spent your 16 thousand on a new TV or a vacation.

Comment author: orthonormal 20 January 2010 01:42:54AM *  1 point [-]

It comes out to about the right number in this case, but your math is wrong. The expected number of times you win in n trials at probability p equals np, but the probability of winning at least once is slightly less at 1-(1-p)^n.

Comment author: LucasSloan 20 January 2010 01:45:06AM 1 point [-]

Yes, thanks for the correction.

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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