Each house starts at their assigned positions on the board and with their assigned house cards. Each player chooses one card to keep in their hand while passing their remaining cards to the player on their right or left. Starting with Baratheon, the Baratheon cards pass to Martell, Tyrell, Lannister, Greyjoy, and Stark before the final unchosen Baratheon card returns to Baratheon to complete their hand of 7 (this order can also be reversed and it creates a very different dynamic). No matter which direction you pass in, each house keeps what the player determines is its "best" card, and the card that the rest of the realm passes on, or the "worst" card, eventually makes its way back to its original house. Each house ends up having two of its original cards as well as one card from every other house. The result is that each game presents each house with a unique set of house cards and an endless supply of new and challenging match ups.
Just as a quick example, say you have been assigned house Stark and you will be passing your hand to Greyjoy. Most likely you will elect to keep Roose Bolton rather than Eddard. Even on the off chance you value Eddard and his two swords over Roose's ability to return your entire hand after losing a battle, electing to keep Eddard would result in Greyjoy being able to pair Roose with Balon, a potentially unbeatable hand. So the only real choice in this scenario is to choose to keep Roose. Let's look at a few different scenarios depending on which card Baratheon elects to keep.
If Baratheon chooses to keep Stannis, Stark can now choose from Patchface, Melissandra, Sallahdor, Brienne, Davos, and Renly. If Stark chooses Salladhor, he has a great way to defend against a potential Greyjoy sea invasion and may be able to thwart it entirely. Alternatively Stark could select Patchface, creating a Roose/Patchface combo that could devastate an opponent's hand, the prospect of which may deter an attack in the first place. Selecting Patchface also prevents him from passing to Greyjoy, meaning that Roose is safe unless successfully baited out, something that Greyjoy will have a much harder time doing without Aeron. Sallahdor could end up with Greyjoy, giving him a kind of defensive replacement (albeit with some tantalizing offensive opportunities) for Victarion.
Baratheon might very well choose to hang on to Sallahdor as his defensive backbone. This leaves Stark with the choice of the devastating Patchface/Roose combo or a Roose/ Super Stannis +5 combo. Not to be forgotten are the implications for Greyjoy's hand. If Stark goes for the Roose/Patchface combo in a scenario where Baratheon kept Sallahdor, Greyjoy is looking at a potential first three cards of Balon, Eddard, and Super Stannis, a Squidy nightmare for the realm.
The brief discussion above illustrates all of the choices that having a draft would present to a player before the game has even started. Thematically, it's in line with the family infighting and shifting individual loyalties that are common place in A Song of Ice and Fire. I'd be interested to see what other peoples' takes are on drafting and am curious as to if drafting has every been discussed as a potential option for the site much as random start position is.
Can't wait to see what hand combinations other users come up with. Best of wishes to all the Lords and Ladies, and a pox upon the Lommys and their filthy green hands. --- Dave the Sweetling