Do you refer to complimentary tickets to an event as Annie Oakleys? Or deadwoods, perhaps? The term Annie Oakley supposedly comes from a punched ticket's resemblance to bullet-riddled cards from the sharpshooter's Wild West shows. Deadwood is associated with the old barroom situation where you'd buy a paper drink ticket from one person and give it to the bartender. If you were in good favor with him, he might hand it back to you — that is, the piece of paper, or the dead piece of wood. This is part of a complete episode.
To expand on why the tickets are punched in the first place: back in pre-computer days, the tickets would all be printed in advance ("hard" tickets) with the top price listed. If a ticket was given away or "comped," holes were punched in them so scalpers wouldn't turn around and resell them at full price.