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Regardless of the kind of ticket or service level they purchased, any United traveller may fly standby on an aircraft leaving within 24 hours of their scheduled departure without paying a standby fee.

It might also be possible for you to reserve a seat on a different flight rather than just standing by for one:

Premier members, who also have MileagePlus elite status, are able to confirm a seat for the same day with the same departure and arrival cities as their original ticket. If the new seat is in the same fare class, they are not required to pay a fee. A fee differential could be charged if no seats are available in the fare class that was ordered.