When does gambling reduce risk?
Suppose that you face risk. It is obvious that taking gambles whose outcomes are negatively correlated with the outcomes of your other gambles can reduce your overall risk ('hedging'). My question, however, concerns **uncorrelated** gambles - can these reduce your overall risk, and if so when?**Edit**: to be clear, I am asking about when you can reducing your risk by taking **additional** uncorrelated gambles, not simply by replacing some gambles in your portfolio with others.