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We give elementary examples within a framework for studying decisions underuncertainty where probabilities are only roughly known. The framework, ingambling terms, is that the size of a bet is proportional to the gambler'sperceived advantage based on their perceived probability, and their accuracy inestimating true probabilities is measured by mean squared-error. Within thisframework one can study the cost of estimation errors, and seek to formalizethe ``obvious" notion that in competitive interactions between agents whoseactions depend on their perceived probabilities, those who are more accurate atestimating probabilities will generally be more successful than those who areless accurate.

Gambling under unknown probabilities as a proxy for real world decisions under uncertainty