 What exactly have we done here? We’ve given our agent choices over lotteries, instead of directly over resolved outcomes, and observed how much extra risk of death he’s willing to run to change the odds of getting one form of death relative to an alternative form of death. Note that this cardinalizes the agent’s preference structure only relative to agent-specific reference points W and L; the procedure reveals nothing about comparative extra-ordinal preferences between agents, which helps to make clear that constructing a vNMuf does not introduce a potentially objective psychological element. Furthermore, two agents in one game, or one agent under different sorts of circumstances, may display varying attitudes to risk. Perhaps in the river-crossing game the pursuer, whose life is not at stake, will enjoy gambling with her glory while our fugitive is cautious. In analyzing the river-crossing game, however, we don’t have to be able to compare the pursuer’s cardinal utilities with the fugitive’s. Both agents, after all, can find their NE strategies if they can estimate the probabilities each will assign to the actions of the other. This means that each must know both vNMufs; but neither need try to comparatively value the outcomes over which they’re choosing.