Rule of Three

One of the "rules" writers learn is that three successive actions tell a good story while more become boring and fewer are less interesting.  That is to say that the protagonist's first, and most obvious action must fail in some sense so that he or she must adjust, only to fail again, but for a different reason.  The protagonist finally succeeds by understanding and overcoming the reasons that prevented the success of the first two attempts. More simply put; If at first you don't succeed, try, try again.  Note that it doesn't say just try again nor does it say try, try, try, try again or even keep trying until it works, damn it!  Nope;  three time's the charm.  It's what works best and cursed be any writer who ignores it.

But why does this pattern work to the point that it almost becomes a rule?  Why does it work so well?

I think the answer lies embedded in human psychology and frankly the reader's need for drama. The first encounter with the situation should make the reader experience literary frustration of facing a seemingly intractable problem.  Hope is kindled when the reader realizes the protagonist has conceived a solution and tries to implement it. That hope is dashed when this  first "solution" not only fails to succeed but places the protagonist in a more serious or precarious situation than before. Of course, if the solution worked at this point there wouldn't be any reason to continue reading the story, except to see if the protagonist has learned anything useful.

Tension is increased when the reader is surprised to discover, along with the protagonist, that there is a second possible solution that offers an expectation of success.  This solution seems so perfect that hope is briefly renewed, only to be dashed by a second failure that sets the protagonist even further back than before. There seems to be no way out as Frustration is joined by sister Despair and the reader is sent into the depths of depression at at the protagonist's absolute certainty that there is no possibility of a solution. None whatsoever.  This is the dark night of the story's soul, the nadir where only bleak certainty of doom awaits.  "Is there no way out," they might think and feel and be left with only grudging acceptance of the way things will remain.  Forever.

Then a glimmer of light appears, a tiny spark that brightens the gloom to illuminate another way. This spark draws the reader/protagonist from a well of despond.  In a few short sentences the reader/protagonist develops a deeper understanding of the reasons for their previous failures (and it is usually something about their character or dedication).  Not only that, but through that understanding the reader/protagonist finally sees the proper course of action and at last we arrive at the third solution, the epiphany that makes the path crystal clear. With that revelation the reader is swept up in feelings of relief, of also understanding what was hidden until now. Exhalation fills the reader's mind as the protagonist unflinchingly applies the solution, succeeds, and takes the reader racing at speed into a satisfying denouement that nicely rounds out the tale, often refers back to some opening scene element, and leaves the reader in a state of complete relaxation.

That is why the "rule" of three works.