The noun is spelled “pickup” as in “drive your pickup” or “that coffee gave me a pickup,” or “we didn’t have a real date; it was just a pickup.” If it’s a thing, use the single-word form. But if it’s an action (verb-plus-adverb phrase) then spell it as two words: “pick up your dirty underwear.”
There’s also the adjectival form, which has to be hyphenated: “Jeremy tried out one of his corny pick-up lines on me at the bar.” According to this rule, it should be a “pick-up game” but you’re unlikely to get into trouble for writing “pickup game.”
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