Somethings very wrong with the crossplay coding in this game. It is so common to feel like the opposing console is seeing you before you see them. I highly doubt that’s just coincidence knowing Bungie over many years you all prolly have inferior crossplay coding compared to other games way worse than we all realize
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Could be copium but I’ve felt the same on occasions so I restart my console and notice it less. Might be worth it to periodically restart the game after longer play times.