I'm interested in hearing about counting techniques used by advanced pianists. I don't really know if there is standard method used by more advanced players. Let me say what I do and solicit comments and alternatives.
The first problem that comes up is assigning the beat/count location of a particular note. This is not a big deal for quarter notes, but what about for 32nd's or 48th's, etc. in a complex rhythm. What I came up with is to count with these sounds:
For quarter notes: 1 2 1 2 etc.
For 8th notes: 1 n 2 n etc.
For 16th notes: 1 ah n ah 2 ah n ah
So far I'd guess this is pretty standard, but to count denser/shorter notes I have an alternative for 16th notes & beyond:
16th's alt.: 1 be doe tay 2 be doe tay etc.
32nd s: 1 ah be ah doe ah tay ah 2 ah be ah doe ah tay ah .
For both these cases the core sound syllables (be, doe, tay) were chosen for being able to roll off your tongue QUICKLY, and to have different leading consonant and trailing vowel sounds, which I found helps avoid getting mixed up. Having "sounds" for counting 32nd notes makes counting the first page of Beethoven's Pathetique sonata a lot easier.
To count 2 counts of triplets use: 1 be doe 2 be doe .
To count 2 counts of six-tuplets use: 1 ah be ah doe ah 2 ah be ah doe ah ,
or (for grouping in 3's): 1 ah be doe ah tay 2 ah be doe ah tay .
So the first part about counting is the assignment of count sounds to the various notes as indicated above. The next part is how to accommodate music that is alternately sparse and dense in notes per second. I think it's too hard to (e.g.) count in 32nd notes for a beat that is a simple quarter note, just because the preceding beat was in 32's. So I use a hybrid like in these examples:
1 n ah 2 1 2 1 2 n 1 2 ,
1 n 2 1 2 be doe tay 1 2 be ah doe tay 1 ah be ah doe ah tay ah 2 .
1 n 2 1 be doe 2 be doe 1 be doe tay 2 be doe tay.
Note that, e.g., "be doe" can represent two 16th notes in places or two notes of a triplet in other places, so the pianist needs to be aware of the different time values being used and to insure that the underlining 1 2 1 2 beat is maintained.
These are examples. For simple rhythms of regular (e.g.) 16th notes, I don't count the 16th notes separately, only the quarter notes, but for an irregular pattern of 16th notes I would count them on a finer scale, though not necessarily finer than 8th notes.
I am definitely interested in hearing how others count in sounds a mix of dense and sparse notes, and a mix of triplets and (e.g.) eighth or quarter notes.
Some say they stop counting once they know a piece. I think for difficult passages, it still helps me to always count to avoid racing ahead.
Lastly, a rare piece (e..g., Chopin Nocturne in Db Major Op. 27-2) needs sounds for 6 or 12 notes in a beat, so I use "my so" for the 2 additional sounds; e.g.:
1 be doe tay my so 2 be doe tay my so 1 ah be ah doe ah tay ah my ah so ah 2.
These sound syllables are pretty much gibberish, but you can get used to them if you go for a walk and start using them in time to your steps (plus vary the "density", include triplets, etc.).