There is a demonstration of exactly this in Eliezer's post from 2008 about the Allais paradox.
(Eliezer modified the numbers a bit, compared with other statements of the Allais paradox that I've seen. I don't think this makes a substantial difference to what's going on.)
In Eliezer's formulation, I pay him two cents, and then he pays me tens of thousands of dollars. That doesn't sound like a very convincing exploit.
And if we move the payoffs closer to zero, I expect that the paradox disappears.
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