I've been working on my Lannister deck again lately and it occurs to me that this perception of Lannister's overwhelming draw dominance is not entirely accurate. For a start let's look at what they do have.
Golden Tooth Mines- The card that all others are compared to. Sure, it nets you a guaranteed card per turn while it lasts, but does nothing else.
Qyburn's Collectors- Much more viable now that First Snow of Winter is gone, but paying 4 still irks.
Hornvale- Not worth talking about. (As wel as the equivalents for all the other houses)
Summer Tax- Solid card, but really only a replacement effect.
Tommen- Yup, great card, but do watch for other kings.
Tyrion Lannister- Solid draw, but hard to justify running over shadows Tyrion.
Insidious Ways- All around solid.
Gold Cloaks- In Lannister, usually just a replacement effect. They really shine more out of say.... Targ.
For reference, how about Martell (and yes, I'm going to include reveal):
Desert Exiles- Ok, really only in the Reinforcements deck that I've never seen materialize.
Bronze Shield- Good card, but just replacement during Summer.
Fleabottom Scavenger- Holy crap this card is good. Up front 3 card boost and claim soak? I've had it be amazing so many more times than not.
Dornish Paramour- Solid just like Insidious Ways.
House Messenger- Solid and gets around the cap.
House Dayne Skirmisher- Only 1 draw, but 1 discard makes it a 2 card tempo change. (Granted you do have to kill him....)
Viper's Bannerman- Expensive but potentially 4 non-cap-able cards.
In playable cards, I'd actually give the nod to Martell at the moment as two of theirs get around the cap and one other gives a three card boost up front. Now, I'm not going to argue that these houses are in the lead, but as a very quick run down:
Stark- Sansa, Guard at Riverrun, Blackfish, Eddard, Storm Dancer, (plus To be a Wolf for great search)
Targaryen- Xaro's Home, Maegi Crone, Tears of Lys, (plus Street Waif and Dany's Chambers for great recursion)
Greyjoy- Kingsmoot, Scurvy, LIV, Fishmonger's Square, Drinking the Sea
Baratheon- Battle at the Wall, Renly, R'holler's Blessing (plus some pretty solid discard effects lately)
Neutrals can be used to varying effects in certain houses and certain builds. Gilly, Sam, and The Kings of Summer in Baratheon or Targ, Sam in Greyjoy or Stark, King's Landing in Lannister, Stark, Targaryen or Baratheon Shadows builds, etc. As well as a handful of replacement effects that can be scattered around.
Yes, in the end it does look that Greyjoy and Baratheon are further behind the rest of the pack in playable draw, but is Lannister really as far out in front as general talk here makes it out to be? I don't think so. At least not so far out in front that isn't a reasonable amount for a house that is supposed to have draw as one of their strengths. They may have GTM as an auto draw each turn, but it does nothing else and takes longer to ramp up than Martell draw. I think we're much closer to reasonable parity on these effects than most people have noticed.