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Stuart_Armstrong comments on The Ellsberg paradox and money pumps - Less Wrong
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How does the central limit theorem apply here? If you have a lot of independent deals of the form 1/2 +- 1/4, say, then when confronted with a million such bets, their value is very close to 1/2. I don't see how your model deals with these kinds of situations - randomising between +- 1/4 and -+ 1/4, maybe? Seems clumsy.
If you mean repeated draws from the same urn, then they'd all have the same orientation. If you mean draws from different unrelated urns, then you'd need to add dimensions. It wouldn't converge the way I think you're suggesting.
The ratio of risk to return goes down with many independent draws (variances add, but standard deviations don't). It's one of the reasons investors are keen to diversify over uncorrelated investments (though again, risk-avoidance is enough to explain that behaviour in Bayesian framework).