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LucasSloan comments on The Prediction Hierarchy - Less Wrong
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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
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.
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.
Yes, thanks for the correction.