Let's see what occurs to me on the first read...

Shikamaru and Asuma looked at the wise-cracking Hidan, or rather his HEAD, in disbelief. Impossible.

Don't like the caps style. If it's really funny, it doesn't need to be capitalized. (Notice how Eliezer uses italics in MoR - they're there to guide your mental pronunciation of lines so you can give proper stress to what words the character is mildly freaking out about. They're not there to tell you what is funny and you should be laughing at.)

Analyze the data you have, hypothesize from there.

This is just totally out of character for Shikamaru to say. It's fine for Harry in MoR. Harry is a scientist; scientists use the words 'analyze', 'data', and 'hypothesize' all the time. But while we do see TVs in Naruto, we don't see any kind of science.

Shikamaru is a game-player. He should be thinking in game terms, vocabulary, rules, stratagems, etc.

I'm not much of a Go player, and that's the closest I get to strategy games usually. However, I know there are collections of Go proverbs and sayings; there are standard move sequences and terms; and so on. You need to be using them, or going into equivalent depth for another game.

Or you need to be going even deeper into general game playing. Sirlin's Playing to Win is one of the only books I've read on that topic, but it seemed pretty good.

To again compare to MoR, Eliezer didn't wake up one day a normal guy who decided to write MoR. It has a sense of depth and insight because he spent years learning the insights which power chapters. If you can't generate that sort of thing yourself, then you must steal shamelessly from other people and sources.

How was his brain still getting oxygen?...The world was violating nearly every law of biology Shikamaru knew about.

Ditto. Who taught Shikamaru about oxygen? Did he leave the hidden village and pick up a college degree during a filler episode or something? Much more sensible would be something like 'air' (how is it still making noise) or 'chakra'.

And he's a ninja! In Naruto, they do 15 impossible things before breakfast! This sort of line would make sense if Shikamaru didn't personally have the ability to move and kill with his own shadow.

He had his usual compliment of gear, none of which was very useful right now.

'complement', by the way. (And no compliments to your beta reader.)

Then change the rules! Said RB, giving his chainsaw a healthy tug for good measure.

'revving his chainsaw' would be funnier.

"YOU BASTARD!" Shikamaru screamed at Hidan. "You're a real big man aren't you! Offing the weak! Going for easy targets! Your cheap-ass God must be so proud. What, is Lord Jashin God of the Cheap Easy Kill now? Or-"

FWIW, I'm not fond of piling on the adjectives like that. To my ears, either 'God of the Cheap Kill' or 'God of the Easy Kill' would have been preferable to both (and of those two, I prefer the former).

Shikamaru still couldn't believe Konoha was still using pigeons for communications when there were long-range communication systems available all around them in the form of television towers. Even if pigeon travel was more secure, which he doubted, sometimes what you needed was speed.

Well, ok, I see we're pulling the same Muggle tech/magic as MoR.

Gallows Humor Shikamaru laughed darkly. He was wearing a hood, of course.

Mental figments or voices is fine, but you should try for some new twist on this.

Since it's Shikamaru, I suggest you make his shadows somewhat sentient. They already are extensions of his will, to a great degree, can act somewhat independently, there are multiple shadows, etc. This gives you a path to power up Shikamaru (the shadows become ever more intelligent and independent until, I guess, they're like shadow clones?), and also a nifty weakness (where do the shadows go if Shikamaru is tossed into a sealed room?).

The final section about death... as the other comment said, a bit didactic, a bit clunky, still kind of out of character, and cribbing too heavily from MoR for my liking.

EDIT: even if Konoha goes whole-hog on the scientific method, I wouldn't expect Shikamaru to suddenly switch over and not think a single game or strategy-like thought. I'd expect to see an off-kilter take on philosophy/technology - as filtered through the mind of a lazy strategy genius. None of that is there.

I like the premise, it's always good to have more of these stories. I can't really say much about the writing or characterization, because I'm not into Naruto. I do have two pieces of constructive criticism.

So he had the argument, the chain of events that led to Asuma's death. Now he just had to find a way to break up the argument.

How would he do that?

Of course. The Logical Fallacies. They were great at breaking up arguments.

So- assume for the sake of argument that there is an inherent flaw in the reasoning, due to a Fallacy lurking under the surface. What could it be? What likely fallacies would there be?

The way it's written, this looks like a major case of writing the bottom line first. With some changes to the wording, the actual message (something along the lines of "you haven't exhausted the solution space", maybe) would be more clear.

Also, there's a lot of really overt discussion of logical fallacies and emotional biases. If there was a way to make this more implied, for instance showing the principles in action more and describing them less, it would be more instructive and look less didactic.

This post on editing needs editing! Less whitespace please!

I have very little familiarity with the Naruto franchise. Where is a good place to start?

My first thought, upon seeing this page, was: "Shikamaru versus... the... hell yes!" click

You might say I went in wanting to enjoy it, and I did. It's hard to say just yet if this fic will be as good as all that, but chapter 1 is a very auspicious start. It's well written, has good pacing, and Shikamaru's internal dialogue is both funny and makes him easier to identify with than in canon.

My main criticism is what Normal Anomaly said, so I won't restate it.

I look forward to seeing the rest of what you guys write. Kudos on a great start!