Through declumping, you are manipulating the probability of not drawing multiples of particular cards in your favor. You are making the probability distribution of drawing certain combination of cards more predictable.
You don't need to check where you're putting the card to understand what you're doing to the probability distribution of drawing the particular cards that you're declumping. That's why people declump, because even though they don't know exactly where they're putting the card (and they don't know exactly the math behind what they're doing), they do know that making the distribution of cards in their deck more favorable, such that the distribution of cards that they're going to draw is not only more predictable, but aligned with what they want.
But that's my point. You don't know that you are making the distribution more favorable. You are putting it in a new place. You might take apart two Junipers, then put one of them next to another Juniper. I understand the weakness of this point, but really, the important thing is as follows.
It doesn't matter whether you declump the Junipers or not, the next card has the exact same probability of being a Juniper provided you shuffled enough. It doesn't matter what you've done, if you shuffle enough there is always the possibility that a Juniper is next. If you ever think that a Juniper is not next you've stacked your deck.
The only thing declumping does is make you feel like you've separated the cards, which, if you actually did, is stacking. You can declump, shuffle and still end up with 3 Junipers in a row, that's just how it works.
Going to have to call you on this. No, no it wouldn't. That's not how random works. If anything, it's now less random, as you've taken indirect control of the positions of the card(s) you moved. Indirect, since you do shuffle your deck afterwards, but control nonetheless. You're not going to achieve computer-levels of randomisation; 7 shuffles doesn't make the deck completely or perfectly random, only sufficiently so.
But you guys' arguments actually support my original point: declumping doesn't matter if you shuffle sufficiently, and the whole thing about insufficient shuffling feels like it's just an issue of paranoia and distrust to me. If your opponent declumps and you don't feel comfortable with their shuffling, take it into your own hands. Riffle it a couple more times. Problem solved.
There are a couple of major flaws in some other arguments this thread makes. The biggest one being the whole "seven riffles" thing. The idea that 7-8 riffles gives "optimal" randomness is a misrepresented mathematical experiment designed for 52-card poker decks. There are two important differences between poker decks and Pokemon decks... firstly, the latter is 60 cards; secondly, the latter usually has multiples of the same card, while the former most certainly does not. Statistics and probability are sensitive things - these differences really alter the numbers quite a bit and can make things very difficult to predict or compute. The 7-8 riffles argument is just out of place here.
But even aside from that, you guys DO know that the "randomization" of a deck, compared against the number of riffles, is asymptotic, right? That means each riffle shuffle consecutively has less and less of an effect. So while 7 might produce optimal results for a casino dealer who can take his time while his players take a drink and chat, I'd think 3 - maybe 4 (I've seen players do 7 fast, good riffles, but let's be generous to the slower-handed players out there) - should be enough to really shake up the cards and prevent you from guessing what comes up next.
I actually like this perspective. Maybe instead of Junipers, I see 2 or 3 energy together, and I leave them that way because I'm preparing to Celestial Roar. Or maybe two or three rare candies together than I don't need anymore are clumped together, and I'll leave them that way hoping they stay far away from the top of my deck. The point is, even having knowledge of a clump can affect your gameplay.
This is a much more educated way of looking at probability and randomness. For functional purposes, randomness really has a lot less to do with the actual ordering of the cards, and more to do with how much you know about that ordering. Whether you do or don't declump, once you've searched your deck, your deck isn't random anymore, and you need to shuffle it to return it to the appropriate state of randomness.
Therefore you could make the argument that declumping is actually completely irrelevant to randomness.
Again, this entire thing feels to me like it comes down to distrust and paranoia, and some stuffiness from people who don't want to take matters into their own hands.
If your opponent reorders their deck or really does ANYTHING that makes you uncomfortable, just shuffle their darn deck.
If you're worried about being called out on it for taking too long, call a judge over and ask THEM to shuffle.
The rules are not your enemy, people.