Long run? What? Which exactly equivalent random events are you going to experience more than once? And if the events are only really close to equivalent, how do you justify saying that 30 one-time shots at completely different ways of gaining 1 utility unit is a fundamentally different thing than a nearly-exactly-repeated game where you have 30 chances to gain 1 utility unit each time?
Long run? What? Which exactly equivalent random events are you going to experience more than once? And if the events are only really close to equivalent, how do you justify saying that 30 one-time shots at completely different ways of gaining 1 utility unit is a fundamentally different thing than a nearly-exactly-repeated game where you have 30 chances to gain 1 utility unit each time?