When setting up MAME360 options.ini file, you can have trouble setting the roms path as well as other paths. Here is a trick to get it to work no matter what device you are running MAME360 from.
Setup your options file like this example.
rompath = game:\roms
samplepath = game:\samples
cfg_directory = game:\cfg
nvram_directory = game:\nvram
memcard_directory = game:\memcard
input_directory = game:\inp
state_directory = game:\sta
artpath = game:\artwork
snapshot_directory = game:\snap
diff_directory = game:\diff
ctrlrpath = game:\ctrlr
comment_directory = game:\comments
cheat_file = game:\cheat.dat
title_path = game:\titles
autoframeskip = 0
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Another trick is that when installed rom games, you just have to copy the whole zip file to the roms folder. You don't have to extract any of the files. MAME360 does this for you.