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Emile comments on Open Thread, May 1-14, 2013 - Less Wrong
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Yet Another Comment Not Answering Your Question ....
A lot depends on whether this "large sum of money" is more or less than five million dollars.
I guess that in most ordinary situations the utility of $5M isn't anywhere near 1M times the utility of $5.
Even with positive expected value, you may be better off passing up the bet depending on your tolerance for variance and the local shape of your utility-of-money function.