D&D General Intelligent BBEG captured PCs, now what?

He puts them in suspended animation (imprisonment, maybe) and they are accidentally released by another adventuring party 1,000 years later, after the BBEG is long dead.

Big Bad Guy lets PCs fully recharge after some long rests, and then pits PCs against each other in an arena, wearing a collar that does not allow them to attack anyone outside the arena. Rival bad guy of Big Bad Guy magically disables collars mid-combat (but make sure you let the combat go on for a few rounds - enjoy the opportunity for the PCs to beat up on each other) and all hell breaks lose in the arena when the PCs realize they can suddenly leave the arena.

I would just run a spin-off about some other characters that break out main PCs out of captivity.

Morrus said:

I dunno. Dunning-Kruger and all that.

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The villain obviously wants to highlight his vastly superior intellect by explaining his grand plan, mocking the PCs for falling for it, and then leaving the PCs' trapped in a cunning death-trap of his own design, watched over by only a single inept henchman.

Flamestrike said:

Even the smartest of people suffer from hubris.

In fact, they're more likely to suffer from it.

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So much this. The fetishising of Intelligence as the only mental stat that matters and high-Intelligence characters as having effective precognition gets wearying.

What are his other stats? If he has a low Wisdom score, he's going to come up with elaborate and intricate plans that are needlessly complex, or which are more to aggrandise himself than anything else. If he has low Charisma, then his henchmen are probably going to be weary and resentful, and he'll have made enemies.

Have the BBEG interrogate then at length, so he can become familiar with them.
Have the BBEG underlings discreetly acquire some of the PC’s hair or minor possessions.
The BBEG is now capable of scrying the PCs with 100% accuracy, thanks to a -15 to saves.

Proceed to arrange a “fortunate” jailbreak. The PCs are now, basically, unknowing spies for the BBEG.

Here is another vote for an underling giving them a means to escape - possibly the jailer.

Maybe even have one of the PC being escorted by a minion to be 'interrogated.' Give the PC a chance to overpower the escort, escape and free their fellows. I think solo makes more sense, but the party as a group could work too.

Many good ideas have already been articulated, and some of this will rehash some of them, but:
1. Being highly intelligent and having good judgment are not strictly the same thing. Perhaps this BBEG is prideful (being a drow wizard, I would be highly surprised if they weren't), and thus underestimates what will contain the characters, or (as noted very early) trusts the wrong jailers. Alternatively, perhaps there's some weird skill or unique trick that isn't well known, but which the PCs already have, that makes things work. The big problem here is ensuring that the mistake is one that could be reasonably made--e.g. the jailers might normally be reliable but something has changed recently, or the BBEG has no reason to have carefully researched every party member (or has but some bits are just too difficult to discover/predict: consider The Flash escaping from Justice Lord Batman's prison by making his heart beat faster than the machine could detect.)

2. Drow are cruel and often use surface-dwellers as slaves, sometimes for experimentation. Perhaps an experiment (from this wizard's perspective) hits Gone Horribly Right territory, where something intended to develop new tools for empowering drow ends up instead giving the party the power to escape on their own. Or perhaps the experiment appears to fail, only to manifest later, after the party has gone back to their cells. The big problem here is that you have to give your PCs a new power to do it. Doing so without (a) making them overpowered in the future, or (b) making them feel cheated if it is lost or too situationally-specific to be useful later, may be tricky.

3. Though it's always a risky move...you could have an NPC sail in and rescue them. For a price, naturally. It doesn't have to be extortionary, it could be "I risked a lot to save you, now I need your help to make sure we get out of this alive" or even "we now owe a favor to the Big Good and know it will someday get called in." But it could totally also be a not-so-great person who now thinks they have the PCs under their thumb; this then changes the plot from "how do we escape from this no-win prison scenario" to "how do we secretly throw off this jerk's control?" The problems here depend on the attitude of the NPC. If they're nominally unfriendly/manipulative, why are they only getting involved now, and why is this NPC willing to make such an enemy or take such a risk? If they're nominally friendly, why don't the heroes just pass the quest off to them, and why did they allow things to get so bad before intervening?

4. Even the best prisons are rarely escape-proof, they just usually require out-of-the-box thinking. Perhaps there's a prisoner already present who had a plan, but couldn't pull it off because there weren't enough people to do it, but the party has changed that. Or perhaps there's a specific procedure that opens a very brief window of opportunity on the regular, so the party can spend time secretly practicing for it and then make their escape. The difficulty here is ensuring that the out-of-the-box thinking is something the characters could figure out, but which the BBEG either hasn't considered or doesn't think is a problem. Keep in mind, IRL many procedures that are supposed to be super-secure are often not fully followed because they're tedious or labor-intensive. The Enigma and Lorenz ciphers, used by the Germans in WWII, were both cracked due to overlooking small mistakes in design and failing to rigorously enforce consistent procedures. The Tiltman Break in particular, which was the watershed moment for cracking Lorenz aka Tunny, only happened because a frustrated encryption officer sent a message twice using the exact same settings but shortened the message the second time, allowing the British to crack the code and extract three thousand characters of cipher key. Even if the BBEG and their minions are all top-notch, no one is totally resistant to the power of frustration and boredom, and that can create an opening.

Long story short: You really do have options, but you'll want to weigh which one will have the best potential for enriching the experience, rather than becoming a millstone around your neck.

Put them in an inescapable prison, then torture them. Have the BBEG let them know that the pain can stop if they just agree to work for him. Unknown to them, he binds them to a powerful demon, such as a balor, who will be summoned if the party betrays him. This gives them the option of working against the BBEG, but there's a significant cost for doing so. I'm also a fan of using family as hostages in this type of situation, but in this case it seems unlikely the BBEG would have enough knowledge to do this.

Option 1
Kill the PCs.
Depending on what is acceptable at your table you can be more or less sadistic in your description. A sacrifice to Lloth would be in order. But the BBEG should not make a blatant mistake such as bragging or whatever. Your PCs are done for. Period. End of the line.

Or...
Option 2
A svirfniblin under magical disguise is spying for his people on the BBEG. That gnome recognizes the potential value of your PCs and risks his position to help them escape. At the very least, the PCs should lose their equipment. The gnome will ask the PCs if they are willing to work for his people and if the players are stupid enough to say no, the gnome will leave them to their fate. But again, the BBEG should not make blatant mistakes. That trope has been overused.