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I have identified three main problems holding back my piano sight-reading, and this is the second biggest.

I can work out fingerings by trial and error, but some very experienced pianists just devise them on the fly without much thought. How can I get better at that?

I mostly play classical/romantic music like Chopin, Rachmaninoff, Debussy, Liszt, and Scriabin, as well as transcriptions of modern songs and movie themes.

Horowitz:

I dream fingerings.

I heard this Horowitz quote from one of my teachers at university. If it isn't genuine, it may as well be.

Anderszewski:

I have to find my fingerings, and I have to write them in the score –
this is actually one of the most satisfying aspects of my work at the
piano. And to think that some pianists leave this to chance or to the
inspiration of the moment... There's nothing worse than a fingering
that comes out of laziness. Fingerings have their beauty, for me, they
are the choreography of the dance at the keyboard: and to dance, one
has to learn the steps.

Obviously, the greater your facility and experience, the greater your chance of improvising an effective fingering. However, I don't believe trying to improvise fingerings is an effective means of winning greater facility and experience. Instead I would be patient, and continue to be methodical in devising fingerings. The more passages you carefully finger, the greater the chance that passages you encounter in the future will be similar to something you can already do.

Intuition depends somewhat on unquantifiable native ability, but also very greatly on experience. If your intuition is failing you, then you need to develop it by generating experience.

Well there are a few things you can do to address this.

I know its obvious but practise your scales and arpeggios. A lot of what you will sight read will include strings of consecutive notes from scales or arpeggiated chords. If you have practised these you will be surprised how quickly you "fall into" the correct fingering when you encounter those sorts of passages.

Also the more you play the more you will become familiar with the "normal" ways of playing certain passages. It seems a bit surprising at first (although less so if you think about it) but there is a lot of repetition in music between pieces. Apart from scale passages - which are all over the place - there are common chord progressions and other shapes for example the Alberti bass (look it up if you don't know what it is). These things appear again and again and after a while you will get so used to them you will, as with the scales, find yourself just using the correct fingering without thinking too much about it.

The previous paragraph can also be applied in other areas. Take the ornaments and embellishments in baroque music (Bach for example). You should find that having managed to work out how to play all the turns and trills in one thing (one of the Bach Partitas perhaps) you find similar embellishments in many other pieces and they will present less of a problem.

And, of course, just play. The more you do it the more familiar it becomes. The more you do it the more familiar it becomes. You can do this. Go for it.

If you only notate the thumb you can quickly arrive to improvise the rest of the notes' fingerings - it won’t matter a lot what other fingers you use (especially in triads and scales).

You will have more problems with creating fingerings for chromatic passages and motives turning around a note.