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The Luck stat has nothing to do with geode drops. There's actually an in-depth anaylisis of the drop patterns given by geodes; search up "geode MOMO pattern" for the thread. The short version is this: geode drops are determined based upon your character and the contents of previous geodes, there's a semi-predictable pattern of mineral, ore, mineral, ore, etc. (hence MOMO) and it carries between geode types.
So, simply spamming omni geodes on a lucky day is actually one of the least efficient options. It's cheaper to buy bombs and collect a lot of geodes on lucky days, and then buy as many omni geodes again from the shop. If you're looking for the Prismatic Shard, open a few low-level geodes to determine the pattern, and then open an Omni Geode on every mineral stage. That maximises your chances of finding prismatic shards, and uses the cheaper geodes for the unwanted ore stages (you could use omnis if you wanted the chance for Irridium ore, but that's a very expensive way to get it when you can just use bombs and stairs in the skull caves).