I’m not sure there is a way to make sense of such utility-definitions. What fixed question that relates to utility value is being answered by observing the result of a random number generator? Original state of the world is not clarified (both states of the random result were expected, not correlated with anything interesting), so state of knowledge about utility defined in terms of the original state of the world won’t be influenced by these observations, except accidentally.
I’m not sure there is a way to make sense of such utility-definitions. What fixed question that relates to utility value is being answered by observing the result of a random number generator? Original state of the world is not clarified (both states of the random result were expected, not correlated with anything interesting), so state of knowledge about utility defined in terms of the original state of the world won’t be influenced by these observations, except accidentally.