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Vaniver comments on Iterated Gambles and Expected Utility Theory - Less Wrong Discussion
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To be clearer, utility is approximately the logarithm of your wealth, not of the change to your wealth. So there's a hidden number lurking in each of those questions--if you have $100k (5) of wealth, then option A brings it up to $100240 (5.00104) and option B brings it up to either $101000 (5.00432) with 25% probability and leaves it where it is with 75% probability, which works out to a weighted average log wealth of 5.00108, which is higher, so go with B.
But if your wealth is $1k (3), then option A brings you up to a weighted average of 3.09 and B brings you up to a weighted average of 3.07. So go with A!
(The breakeven point for this particular option is a starting wealth of $8800.)
I am confused. Pick B every time? Even although the weighted average of A is better in the second case? That's supposed to be "So go with A!" right?
Typo fixed; thanks!