An impromptu, gimmick-free, borrowed deck miracle. A location and divination of a selected card under test conditions. Read on.

Imagine:

The magician introduces a deck of cards. The spectator can thoroughly examine it, after which they can freely shuffle it for as long as they want in any way that they want.

Once they're done shuffling, the magician invites them to look through the deck (faces towards themself, backs towards the magician) and select any two cards that they like. Let's suppose they select the two black A's. They turn these face-up and leave them on the table.

Next, the magician instructs the spectator to select another card - this time without looking through the deck. So the spectator pulls out a random face down card. The magician tells them not to look at this card yet - it will be a mystery for the end. They are then asked to sandwich the unknown card between the two face-up black A's. With that done, the magician tells them to bury the trio anywhere inside the deck - the magician looks away as they do so. Finally, they are asked to give the deck as many complete cuts as they want so even they don't know where the trio ends up.

After all that, the magician turns back around, takes the deck from the spectator, and immediately brings it behind his back. (Alternatively, the spectator can place the deck behind the magician's back into his hands while he's still looking away.) Whilst holding the deck behind his back, the magician explains that he has an uncanny ability where he can find face-up cards without being able to see any of the cards. He explains that he will find the unknown selection by feeling for where the two face-up cards are. Furthermore, the magician explains that he has a second uncanny ability where just by touching a card he can reveal what it is.

The magician claims that he's found the unknown card and slowly begins to reveal its color, its suit, and finally its value. He claims it's the 9D (for example).

Finally, the magician brings out the deck in one hand and the selection in the other hand. The spectator turns over the selection and it is indeed the 9D. Then, the spectator spreads through the rest of the deck and sees that the face down card is missing from between the two black A's, proving that the card the magician located behind his back is indeed their selection!

Some important conditions of note:

The effect uses a regular deck of cards (which could even be borrowed).
There are no gimmicks of any kind in play - this is 100% impromptu. Aside from the borrowed deck, nothing is used.
From the moment the spectator shuffles the deck to the moment they lose the trio inside the deck, the magician doesn't touch the cards. He especially doesn't touch the two face-up selections and the unknown selection.
This method works even if all the cards in the deck are perfectly straight (without any natural bends) - this is to rule out one possible method that some people may have thought of when reading the description above.