This guide first appeared here.
The stats above are from rank 3 + 2 stars to Legend (61% Winrate - 35-22). However I've been playing this deck from the start of the Season with +1 Burgle,-1 Shadowstrike (made the change at rank 5).
The Thieving Rogue
I've been playing Hearthstone since beta, playing almost only Rogue, and got Legend every season after Season 2 until the end of 2015. At that point it felt a little stale and I got really bored of the miracle or oil variant. I've tried almost every Rogue deck possible and kept fighting to make a Control Type of Rogue work. When Burgle was announced I created a theorycrafting thread in this subreddit (here talking about my thoughts on the card. After playing it for the first time, I fell in love with it. At the time it was a really, really slow card where it had no synergy and no place into regular Rogue decks.
However, in control matches or at least ones that the enemy wasn't smorcing all the time it generated threats and tools to keep up with them. Sometimes these tools weren't the optimal ones to use, but having them in your hand let you have more choices(Example: Playing a stolen 3-5 against a 4 power creature instead of Tomb Pillager or playing a stolen 5 drop instead of Azure Drake because you have Backstab/Spells in hand to synergise. And other times the results where insane because of how unbalanced some other class cards work in Rogue (Example: Turn 5 Preparation -> Call of the Wild).
Long story short, with Undercity Huckster and Swashburglar being available now, as a Rogue player you have the ability to roll the dice so many more times than with just Burgle that you will get an insane result almost guaranteed while outvalueing your opponent through the card advantage these cards provide.
Yes, no healing cards needed in a Aggro Shaman heavy meta. Unfortunately, I've come to this conclusion because there is no good heal available for Rogue and from what we have seen from Blizzard there will never be one. Running Earthen Ring Farseers in a not combo oriented Rogue deck is bad. No need to talk about the other healing options.
Are 2 Tomb Pillagers, 2 Undercity Hucksters, 2 discovered Deathrattle minions and Bloodhmage Thalnos enough minions for running N'Zoth, the Corruptor? They are more than enough. Sylvanas Windrunner or Cairne Bloodhoof are too slow in Rogue especially if you don't run any heal. Running 2 copies of Journey Below instead gives you the ability to be flexible, enable combos and fill up your curve (or sometimes you're gonna pick Anub'arak vs Control Warrior Kreygasm).
Unfortunately, this card is competitive and its results will benefit you more often than not. It works really well in this deck because of the amount of spells available in the decklist + the ones you can generate with your thieving cards.
Mulligans and Matchups
A general mulligan guide for this deck is to never keep 2 of the same cards and to try to have a balanced starting hand of early minions and removal spells (You should always mulligan Preparation if you have no minions in your starting hand). Mulligan for the Aggressive or Tempo variant of your opponent's class. Also, always keep one copy of your lovely 1 drop Swashburglar and always mulligan Burgle (It's awesome but not for turn 3).
Druid (60% 6-4)
It is really important to keep up with the curve. Look for Backstab, Swashburglar/Journey Below, Undercity Huckster, Eviscerate. Keep SI:7 Agent only if you have Backstab/Coin or if you're mulliganing everything else.
Mulligan Sap/Shadowstrike unless you already have a curve with early minions. Only keep 4 Drops when playing second with a Preparation. 2 Shadowstrikes are really important in this matchup now with Stranglethorn Tigers and Menagerie Wardens. Be aggressive and don't be afraid to get low in Health.
Hunter (85% 11-2)
This deck works wonders. Swashburglar and Undercity Huckster counters their early game and Backstab -> Si7 Agent just destroys their early tempo. I find that hunters right now are really easy to predict almost more than every other class/deck in the game which makes it easy for you to counter their plays by making correct mulligan decisions. Look for your early game minions and early removals. Always mulligan 4 drops, Shadowstrikes, FoK, Saps and Thalnos. Keep Edwin VanCleef only with coin and synergy. Do not let them Houndmaster their beasts unless your hand/board allows you to. Be careful of big Unleash the Hounds, turn 6 Savannah Highmane, turn 8 Call of the Wild and also keep up with their coin use if you're going second.
Tempo Mage (100% 5-0)
This deck also works wonders. Always keep an answer for Flamewalker. Look for your early minions and keep your Eviscerates. Do not overextend and try to outvalue your opponent. Restrain yourself from playing more minions into Flamestrike and be aware of the new Firelands Portal. Versus Freeze Mage play minions on curve and hope for the best since it's a hard matchup.
Paladin (50% 1-1)
You can be a little greedy with your mulligan since they there is no aggro variant on the ladder right now. Mulligan all spells except Backstab and keep 1 4-drop. Be aggressive and try to bait their removals. If possible try to bait their Truesilver Champion charges on lesser minions than Azure Drakes or Tomb Pillagers. It's a hard matchup if they have the answers they need and if they are playing murlocs pray to the Elder Gods for an Anyfin Can Happen when you're pickpocketing them.
Priest (0% 0-2)
This is a weird matchup right now. The Resurrect variant is really strong if things go its way. Generally since you're planning to defeat them by building up a board, if they have the right answers for your minions you're gonna have a bad time. Try filling up a curve and always keep Tomb Pillager. The power of Tomb Pillager and the ramping effect of the coins can really help you extend yourself outside of Priest's control.
Rogue (40% 2-3)
This is the matchup where thieving shines the most. Stealing now becomes Draw class cards which upgrades the quality of the effect. However, Arcane Giants are now included into Rogue decks and they are a real pain. Always keep Backstab, Sap and Tomb Pillager. Sap is the most important card in this matchup and hitting it correctly can really affect the outcome of the game.
Shaman (50% 5-5)
This is an exciting or rage-inducing matchup. Your starting hand compared to the opponent's starting hand is the most important factor of the game. Always keep Backstab, Eviscerate, Shadowstrike and your early drops (Swashburglar, Undercity Huckster). Keeping Thalnos also seems to be correct because of the many 3 health minions/totems. Also keep Sap if you're mulliganing everything else. Be aggressive and if they equip the Doomhammer start racing. When facing a slower Control Shaman try baiting their AoE's and restraining yourself from overextending.
Warlock (50% 2-2)
This is a less exciting, always rage-inducing matchup. Always keep Backstab, Swashburglar, Undercity Huckster, Eviscerate, Si7 Agent. Keep Sap or Shadowstrike only if you're mulliganing everything else. Fan of Knives is a really important card in this matchup but you should always mulligan it (You should need it after turn 4/5).
If you have established a board try always clearing everything. Ignoring a 1-1 to push 5 dmg to face in the midgame should always be wrong unless you're racing and you're pretty safe in Health total. If you can clear with FoK but can also choose another play even if it is less optimal, you should save the FoK for an inevitable Forbidden Ritual (if none has been played yet).
Warrior (50% 3-3)
A 50-50 matchup. Keep Journey Below (Do not pick Anub'arak unless you're 99,99% sure it's Control) and all your early minions. Try to always have an answer for Frothing Berserker and if you have early removal spells keep Tomb Pillager. Do not play into Ravaging Ghoul and be careful of dropping below 15 health (because of Drakonid Crusher). What is more, always expect a turn 8 Ragnaros the Firelord. Be aggressive and don't be afraid of Fiery War Axe or Execute. If they have already equipped a weapon try play a suboptimal minion if possible to bait them into wasting their charges on it.
Versus Control Warrior, bait both their Brawls before N'Zoth and try to get Anub'arak from Journey Below. If you're facing the C'Thun variant of Control Warrior your only answer to C'thun is Yogg-Saron so restrain yourself from playing him before that if possible.
The fact that this deck managed to reach Legend means that in this meta/circumstances it can be competitive and because of it's random aspect makes it one of the most fun decks out there imho. Trying to make optimal use of all those cards that do not belong in your deck is like another fun mini-game inside hearthstone.
Also, when the next wing of Karazhan gets released this type of deck could get more action because of the new 5 drop (Ethereal Peddler 5-6 , Reduce the cost of the cards in your hand from other classes by 2). I'm not really sure how good this card is gonna be even for this deck because of my testing with Emperor but either way it's gonna be fun trying it. Thanks for reading.