The Olympia can be found frequently throughout the level "Payback," in which it is considerably effective, but still suffers the same problems as it does in multiplayer, specifically, lack of range and constant need to reload, meaning that on higher difficulties, this weapon will be largely ignored and longer range weapons will be used.
The Olympia is a part of the default CQB class (primary weapon), along with the perks Hardline, Sleight of Hand, and Tactical Mask. Although the reloading time of the gun is not long, users will be doing so often. Lightweight and Marathon are also beneficial due to the fact the Olympia (as with any shotgun), is best used as close to the enemy as possible, and these perks both aid in that.
However, it is ill-advised for an Olympia user to charge headlong at the enemy, as the enemy will most likely be using weapons with far greater range and/or rate of fire. Instead, players should attempt to outflank the enemy and use cover whenever possible in order to take enemies by surprise. The Olympia excels in maps where the user can readily flank the opposition. As of patch 1.06, all shotguns cancel out an enemy player's ability to enter Second Chance. This was put in place to balance the shotguns inconsistent headshots against users of said perk.
With or without Sleight of Hand, it is advised to reload after every shot (as long as it is safe to do so). This is because it sometimes requires both barrels to dispatch an opponent, and also because enemies sometimes travel in groups. It could be said that the Olympia requires more skill to master than most weapons, because both shots must be managed carefully. An alternative to Sleight of Hand would be Steady Aim, as this allows the user to hit enemies with more consistency than with Sleight of Hand. Furthermore, Reload Cancel works very well with this gun.
Even though the Olympia's damage drop off is farther than the other Shotguns, the Stakeout has a better (but not by a lot) range both in pellet range and one shot kill range because of it's tighter spread. However, the Stakeout is pump-action. The Olympia has a better chance at taking a follow up shot should the first shot not kill in one hit. Also, because of the Olympia's wider spread, it is a superior shotgun for clearing a room/area of multiple targets, provided that all the targets are grouped together, an example being the second floor windows on Nuketown.
The Olympia is available in Zombies as an easily available weapon, with it spawning near the player spawn in Kino der Toten, Ascension, "Five", and Call of the Dead. In all maps, it spawns in the room you start in. It costs only 500 points, the amount you spawn with. It functions much like the Double-Barreled Shotgun in the World at War maps, though it is cheaper and available right away at the cost of being weaker and having less ammo than the Double-Barreled. If aimed well, one shot of the gun will kill the Hellhounds in the later levels. Although it is very effective, after round 6 it loses its one shot kill ability. It can be a very useful gun with Juggernog and Speed Cola. Double Tap Root Beer seems to have little effect being only two shots to fire, if the player is mainly close range Juggernog might be more effective, if the gun is just back up then Speed Cola is better, but it isn't recommended to keep the Olympia at rounds 6-7, unless you have it Pack-a-Punched.
If upgraded via the Pack-a-Punch Machine, the Olympia becomes "Hades", with an increase in power, range, as well as switching to incendiary rounds with 60 extra rounds. Plus, its reload speed seems to increase (not as much as Speed Cola would). "Hades" kills the zombies effectively until around rounds 19-20 and is a good window watcher weapon. It also kills Hell Hounds one shot to head, no matter which round.