I'll try to clarify:
I would call "Enjoying the experience for itself" the terminal utility assigned by your utility function to you going to the movie -- for most of us, fun is one of our terminal values, so a world-state in which we are having a certain intensity of fun for a certain length of time has higher utility than one in which we are having no fun, all else being equal.
The motivation-to-work that results from having fun is a source of instrumental utility because it increases the instrumental utility output of our future work (which is an attempt to optimize for future world-states in which we are having fun in the broad sense -- world states with greater terminal utility.)
Now, let's assume for a moment that the instrumental utility generated by you working for a length of time is much, much greater (ex: you're saving the world, or a significant part of it), than the terminal utility generated by you having fun for that same length of time. If we also assume that the effect of motivation upon the instrumental utility of your work output is somehow affected by the amount of instrumental utility that each unit of your work output has, then the terminal utility granted directly by you having fun approaches zero in comparison to the instrumental utility granted by the increase in your work output as a result of motivation-caused-by-having-fun.
Of course, this conclusion is subject to the assumptions that I made earlier. If the instrumental utility generated by the work that you do doesn't dwarf the terminal utility generated by the fun that you have, then it doesn't apply.
Okay, that makes sense. We agree. I just didn't understand your assumptions the first time.
If you consider that the utility generated by working is much greater than the utility directly generated by having fun, then the main thing that you're going to optimizing when you have fun is how much motivation the memory of having that fun increases your working capabilities. This is distinctly different from optimizing for the direct preference fulfillment generated by the fun, even if the same activities are optimal for both utility functions.
The same model works for any action A such that the utility generated by the effect of that action on another action is much greater than the utility generated by the action itself. This probably applies to most maintainance actions, such as doing laundry, sleeping, eating, but this is more obvious to us -- we usually don't see laundry as an end unto itself, but we often do pursue fun for it's own sake. I'm not advocating that we shouldn't have fun, but that we (or at least I) seem to be optimizing for the wrong thing -- direct preference fulfillment, rather than motivation.
This feels like a significant insight, but I tend to get a significant number of false positives. Any ideas on how we might use this?