Surprise!

Mavis fails to impress Simon Cowell when she dives into a tiny paddling pool held by a bear.

Esy recently raised the topic of surprise.
And I overheard my son and mother discussing Indiana Jones the other day. They both agreed that they liked the surprise bits best - the parts where Indy is progressing through some catacomb or another and then a decomposing corpse pops out of the wall.
So let's have a look at this surprise, and ask ourselves how much of a surprise it actually is.

First of all, it's logical. When one is hanging out in tombs, one might reasonably expect to discover the odd skeletal remain here and there.
Or, to put it another way, I wonder what the effect might have been on my son and mother if Indy was brushing away the cobwebs to suddenly be assaulted by a giant egg whisk.

Sunset Bickham won't forgive you if you go egg-whisky on him:

Because fiction is make-believe, it has to be more logical than real life if it is to be believed. In real life, things may occur for no apparent reason. But in fiction you the writer simply cannot ever afford to lose sight of logic and let things happen for no apparent reason.

So why do corpses pop out of walls?

In Raiders of the Lost Ark, (and this is from memory here) Indy stands at the entrance to a tomb and his guide explains that nobody ever comes out alive (premonition/suspense). Indy recalls some archaeologist who went into this tomb and was never seen again.
Sure enough, his guide activates a trap and the cadavre of said archaeologist springs out on spikes.
Surprise!
This scene has many functions, all of which are bound by logic.
It warns the viewer to expect corpses - it suggests the boundaries of the movie (preparation/establishment). And with this knowledge comes suspense (through expectations).
It shows the viewer that Indy is cleverer than this other eminent archaeologist, simply because Indy has avoided this trap. Also, Indy is more familiar with such expeditions than his guide - Indy is savvy. These are shows. Rather than the guide saying 'Gosh Indy, you're probably the best archaeologist around,' this exact same information is demonstrated.
The functionality is wrapped up in surprise.

Surprise is like an electric shock. It's sure to wake the viewer or, if he's already awake, to keep him alert. Surprise spikes the emotional topography. Surprise is not there for it's own sake, and the audience will not thank you if you cheat them.

At number 23 in his how-to book, The 38 Most Common Fiction Writing Mistakes, Sunset Bickham explains why we shouldn't drop alligators through the transom.
Legend has it that some writer had her detective interrogating a beautiful woman in his office, and then couldn't think of a way to end her scene with a disaster. So the writer had an alligator fall through the transom.
You can almost feel Sunset shaking with anger:

That's the worst kind of cheating, the sorriest kind of writing!

Why Mr. Bickham?

Because it didn't answer the scene question.

Somewhere in that book, and probably in every other how-to book on my desk, you'll find a diatribe on the evils of deus ex machina. The Ancient Greeks loved their plays. The playwrights built all manner of conflict and obstacles into their plots. And then, at the end of every play, an actor would be lowered on a winch, proclaiming to be whichever god, and then righting all wrongs with the wave of a hand.

It's like Quidditch. You can battle for ages, winning points with cunning and broom-flying exploits and teamwork and tactics, the points swinging from one team to the other, and then some little git catches that golden snitch and the game's over and nothing else in that match mattered after all.

You'll also find in these books tirades against coincidence. However, Robert McKee proposes an exception, where an Antiplot is created, not from causality, but from coincidence, the distinction being (essentially) that causality creates a chain-reaction through to the climax and expresses the interconnectedness of reality, whereas coincidence fragments the story into divergent episodes and expresses the disconnectiveness of existence. He uses After Hours as an example of such an Antiplot. (Robert McKee: Story.)

Thinking over my own conclusion, I reckon this is the recipe for a satisfying reveal:

The more obvious (and logical) the reveal seems, the more satisfying it is.

I think this distinction clearly separates Saw from its weaker sequels (weakquels?).
The final revelations in Saw are unexpected. However, they instantly feel extremely obvious and natural and effortless and unforced.

When presented with a reveal, the viewer will want to trace its history. The reveal suddenly makes sense of all that has gone before: those little pieces of dialogue that didn't quite sit right (Rachel tells her father to leave her splinter be because her body will push it out when it's ready - War of the Worlds); those characters who lurked in the shadows and seemed to have little purpose (Sweeney Todd); those props that were briefly brought to the fore and then subsequently neglected (let's say ... Chekhov's Gun!).

It's all there! Every ingredient is in place! But the author hides them with misdirection or imbues them with insignificance, or he might present the elements plainly and simply choose to conceal the connections.

N.B. In my post Utopian Dominoes, I argued that we need to feel something is significant in order for it to register. I would amend this slightly by suggesting that everything is automagically given significance by nature of its inclusion. Therefore, even when we pretend that a plot device is insignificant, a part of the reader's brain assumes that it isn't so. And this is possibly why I have trouble with MacGuffins.

Surprises are an essential, inescapable ingredient of plot. They can get the pulse racing, and they can inject a freshness into a story and they can even change the course of the hero's quest. But they are also subject to the strict regimes of logic and clever preparation. The logic pleases the reader's brain, assuaging any notion of cheating, even offering gold stars for cleverness should the reader have pieced an amount of the puzzle together. The preparation facilitates the logical revelation and, where visible, provides suspense.
That one memorable aha! moment might have been crafted from an entire novel's worth of preparation!

There will be more thoughts to come, perhaps when I discover a satisfying way to classify surprises.