The default assumption or the rule of thumb is that expected value is approximately logarithmic in the amount of money you have. And this is kind of a very crude approximation, but it has some nice mathematical properties like doubling gives you the same additional increment with regardless of where you are. So there's some kind of scale invariance properties. If you take alogarithmic utility model, then actually this, the bet you you propose  of 51% you double and 49% you go to nothing going to nothing is basically like, like log of zero is negative infinity.

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