Do Incentives Imply Ability to Pursue Them?

So, I was playing Bejeweled 2 this morning when I should probably have been sleeping, when something about the game play triggered an errant thought: Do I assume that because I am rewarded for doing something that I have some control over achieving that?

In particular, B2 gives you a special explosive gem for connecting 4 gems in a row instead of the usual 3. These are very useful, and get saved between levels, so they are the only way you can affect the future by your current actions outside the current level. So, obviously they are very important and valuable, especially since you have relatively little control over the game.
In fact, you have so little control, getting those special gems is nearly random. As you can only move gems if it results in a breaking combo (3+ gems in a line of the same color) you have to plan very far ahead. Sometimes you get lucky and are basically handed board set ups where you can make it happen easily, or it randomly occurs due to lucky set ups with falling blocks. In fact, usually when it happens, it is due to random blocks; planning is limited as you have no foresight of what gems you will get as you make room, and so even if you really work at it your success rate is not highly correlated with your effort. At best you can just break lots of gems and hope for the best.

So, ok, B2 rewards achievements that are largely random and not due to player behavior (at least in getting the gems; good players save those things forever.) But B2 is a pretty easy game to analyze. What about bigger games like the Total War series? What about school? Work? Are we assuming that we have control over good things happening simply because we get rewarded for them? Are we getting rewarded based on largely random, unpurposeful achievements?

I think yes. There is a fair bit of research pointing towards success being a matter largely of random interactions and associations (who you know, not what), as well as around stocks and investing (see Nassim Taleb). External rewards are often not as rules based as people would like, and often we care about the results as well as the effort and inputs. If you think Olivia Wilde is hot, you don't care how much is genetics and how much is lifestyle choices.

We can't control that too well, so perhaps it isn't worth worrying about too much. What we can, and probably should, worry about is how we approach such things ourselves. If we don't know that a certain incentive is tied to results we can not directly control, we can spend a huge amount chasing a state that we have little or no influence over. For example, cancer is bad, but whether or not we avoid seems to be largely random for most people. However, the belief that somehow we can avoid it if only we pick the optimal combination of eating only grapefruit and whole grains pounded by hand is likely to have costs far outweighing the benefits of influencing our likelihood of getting cancer. We can spend our lives doing all manner of silly things believing that if only we practice the 7 Habits of Highly Effective People we can become hugely successful.

It isn't clear to me that this is a subject we are very good at analyzing. Maybe future research is required.