If you host zombie modded lobbies, the following won't stick to your account unless your the hoster of the lobby.

Won't stick: prestige, level, unlock all, stats

Will stick: achievements, deathcards, and mods (depending on the mod menu)
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If you host checkerboard online modded lobbies, the following will stick depending on the mod menu.

Will stick: Prestige, level, unlock all, stats

Won't stick: mods (depending on the mod menu) and the things that will stick depending on the mod menu.
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Non-recommended lobbies: Any zombie modded lobbies (unless you want achievements and deathcards.

Recommended lobbies: Any type of online lobbies that's not on zombies.
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Hope this helps if you need a lobby for World At War.

-Renders