My part covers some fine examples of good accompaniment patterns that demonstrate some points I wanted to mention.
SlidesThere's not much in the slides, so I'll be converting the info to post form and updating this message accordingly.
It depends on the trackUltimately, the kind of accompaniment you want to write will end up differing based on the track itself. Write in what you feel is a good representation of the original. That said, here are some things you can think about...
#1 - Craft a similar textureSometimes trying to write in something exactly resembling the original piece doesn’t work super well, due to accompaniment being driven by percussion or consisting of multiple distant parts. In such cases, crafting a left hand part that captures the rhythm, the chord, and the general contour of the original can get the point across without matching voices exactly.
"Great Canyon" from Pokémon Mystery Dungeon: Blue/Red Rescue Team by Bespinben
Note how the bottom staff is relatively easy to play, matches the important bass notes and emphasizes the same rhythms through the way it moves up and down.
#2 - Vary it upMany pieces have a wide range of textures and dynamics, so don't feel constrained to writing an accompaniment that is consistent the whole way through. Think about how you can use a variety of techniques to build up and release tension.
"Battle III" from Octopath Traveler by Static
This excerpt is a great example of using patterns from single notes, to alternating bass and offbeat dyads, to octaves and broader up-and-down patterns to carry the arrangement from the piece's tamest section to its climax.
#3 - Pedal can take single notes, octaves, and power chords a long wayWith a grand orchestral accompaniment, there may be a temptation to write something grandiose and difficult. But all things considered, some very simple accompaniment patterns can end up sounding full and rich with the use of pedal. Single bass notes, octaves, and power chords can help fill in the texture even when they exist to underscore the root of the chord.
"Fire Emblem Theme" from Super Smash Bros. Brawl by Latios212
See how in this piece, the powerful low bass notes coupled with the chords in the right hand make the arrangement sound full without any motion in the left hand aside from chord changes.
#4 - Maintaining driveSome pieces maintain an extremely high level of energy throughout which may seem difficult to maintain by using one hand on the piano. When necessary, don't hesitate to keep the motion going - but it doesn't have to be all chords all the time. Single notes or arpeggios interspersed with powerful chord strikes to emphasize the rhythm can do this very well.
"You Will Know Our Names" from Xenoblade Chronicles by Maelstrom
In this example, the "chorus" of one of the most powerful battle themes out there, the left hand part consists of single notes and some chords, with hardly any rapid up and down motion. Though it may be fast, such an accompaniment is not very difficult to play and provides a great backing to the melody.
#5 - Just what’s in the originalMany of the examples above are of rather busy or intimidating pieces. Sometimes, though, the original track will lay out exactly what you need without the need for any additional embellishments. When considering how to write an accompaniment part, don't discount what's in the original verbatim if it's workable for piano.
"Goron City (Day)" from The Legend of Zelda: Breath of the Wild by Olimar12345
Here, the low left hand part stands on its own - and with the right hand melody so low, the two voices work together to paint a good picture of the original.
#6 - Left hand isn’t everythingIt's important to keep in mind what the right hand is doing. While the left hand accompaniment sets the foundation of the arrangement, it's not something to be written entirely independently of what the right hand is doing. There's a trade-off of how much harmony and detail to include in the left hand vs. the right.
"Egg Planet" from Super Mario Galaxy by Sebastian
In this arrangement, the left hand just rhythmically plays C in the bass for the majority of the A section, which would sound pretty bland on its own especially compared to the lush orchestral Galaxy sound. But given that the right hand contains all the harmonies and plays them along with the melody, the two parts come together to form a complete-sounding piano piece.
See what other arrangers and performers are doing!These are just some random pointers and pieces of info that can help you experiment on your own. But as I've implied with these examples, possibly the best way to learn is to go out there, see what other arrangers are doing, and incorporate different ideas into your experimentation when arranging. Look at sheets on site and other sheets arrangers have in submissions, and try them out on the piano. See what kinds of accompaniment patterns you like or don't like the sound of, and what parts you think are easy or hard to play. Remember to take your time to figure out what works best, and to have fun!
