Which will be the first Great House to lose the game for good?

[bloodsteel bitterraven]

Starks, Arryns, Baratheons, Tullys and Lannisters are pretty much destroyed. The next one to suffer will be the Greyjoys. Euron is up to no good.

[grand old duke of stark]

I don't think the Freys ever were in the Game; they just helped out the Lannisters by crippling a major contender. The Boltons are questionable too, though they;re obviously of more Westeros-wide importance. HOuse Greyjoy may well be knocked out of the Game. Victarion will be Moqorro fodder probably and since so many have it in for Euron, he's likely to be assassinated (preferably by Damphair).

Yara may well rule, but she'll eschew the Iron Throne, possibly supporting Stannis.

House Baelish will go, the sooner the better. A one-man house with the ambition of hundreds, it cannot stand long. If Doran dies and if Arianne is more interested in ruling than fighting, she'll withdraw from kingdom politics.

That leaves the Game to the resurgent Starks (+Tully and maybe the Vale), Targs, fAegon, and Stannis. And the Others.

[Alhazred]

The Martells are doomed. From the Sea the Dornish came, and to the Sea they shall return. All that sand is going to get washed away in a catastrophe.

However, anyone writing off House Arryn, because of Sweetrobin, is delusional. The fact that everyone writes off Sweetrobin is just setup for a major comeback.

[BanzaiZ]

Of the Great Houses, unless Edric is legitimized, I don't see the Baratheons continuing to exist. Tullys are on the chopping block, and the Greyjoys are fighting with the Lannisters to be next in line.

There seem to be enough Arryn descendants left that could just take the Arryn name, so I don't necessarily see them dying out the way some of the other Houses are going, especially since they aren't even at war with all of the heirs being mutilated, murdered, ala Theon and Robb. The entirety of the Tyrell history seems to show them always managing to land on their feet, so I don't see them being annihilated, though I don't see Mace surviving. House Martell is a little iffy, it depends on how the DoD v 2.0 goes down, I think. House Stark seems all but set up for some sort of re-emergence. Jury is still out on House Targaryen.

[Lord Ronin]

Besides stark? Bolton will be wiped out, and I think the arryns too...also the freys are due

[Spencer Snow]

Pretty much any of them besides Stark. I think Tyrells are going to go out hard and soon, also Freys or Bolton.

[jordanmp16]

Could be argued that he's already done this with House Stark. Lord; dead. Heir; dead. Lady; undead. Remaining children either presumed dead or scattered to the four winds. Castle; burnt. Lands; gone.

I know everyone wants/expects a resurgence of the Starks...but that doesn't mean it's going to happen.

[RhaenysBee]

Arryn. Then Stark. I'm not sure about the rest.

[SanderOfTheFaith]

It already happened to Lannister? Tywin and Kevan are dead. Cersei is F'ed as well, Jaime is in the kingsguard and Tyrion is wanted. Who is competent enough to overcome a downfall?

[raegal_targaryen]

None of the living relatives is called Arryn.

what about the arryns of gulltown HMM.

[Blede]

None. In the end all the original Great Houses will survive, and will be back on their starting positions, as they always did. Because the Game is eternal.

Even the hated Freys and Boltons will survive in the end: with so many factions inside House Frey, one is bound to join the winning side and will be spared (maybe losing some lands like the Conningtons after Robert's Rebellion), and the Boltons through Fat Walda's son/daughter, maybe fostered at Winterfell to ensure his/her future loyalty. This will be (part of) the bittersweet ending.

[juanml82]

It already happened to Lannister? Tywin and Kevan are dead. Cersei is F'ed as well, Jaime is in the kingsguard and Tyrion is wanted. Who is competent enough to overcome a downfall?

Genna and Tyrion. Unfortunately, Genna took the Frey name, but one of her sons, either Lyonel Frey or Red Walder can take the Lannister name and continue the dynasty.

Tyrion is also likely to make a comeback and, should he assume the position of Lord of the Westerlands, he'll have a choice for a wife to continue the line.

I don't see the Martells going down. They can always keep Trystane safe and, worse come the worse, if they align themselves with a winner, there are plenty of Sand Snakes to legitimize.

The Greyjoys might not be extinguished, but the Ironborn might very well oust Euron once the Reach defeats them.

[The Dragon Queen]

Arryn, Bolton and Freys for sure! Tully and Baratheon (maybe?) the Starks kids are Tullys too and Shireen might survive or maybe one of Robert's bastards could be legitimatized in the future?

[Ser Luke.]

Lannisters for sure. They've been in huge trouble since the end of ASOS

[Pod The Impaler]

House Arryn seems in the most danger. Only the Gulltown cadet branch might survive for long.

Of the lessers:

House Bolton is not in great shape. Roose should have kept Walda far away from Ramsay, seriously.

The Freys are going to be devastated, but there's so many of them.

[Petyr Patter]

Keep in mind, you don't have to kill all the members of a house to end the house. You just have to take away its lands. Then, the "house" is just a name, and its members might as well be peasants or mercenaries. Lannisport is apparently filled with Lannisters who can't trace their lineage to a Lannister of Casterly Rock and thus lack noble status.

Hence, is some ways House Tully and House Stark are already "lost the game." Except, obviously, they haven't. Heirs are still alive and a rebalance of power might very well bring them back their lands. House Arryn is certainly in danger of losing the Erie should little Robert die. The Boltons are also low on members, are in harms way, and likely to not be viewed favorably by any new leadership. Or, old leadership as the case may be.

Still, the House I think will lose overall will be the Tyrells, or at least loose Highgarden. I don't think all the members will die, but they've taken their status as Lords of Highgarden for granted to long, and it may come back to bite them.

[Arya kiddin']

The first to kick the bucket will be either Tyrells or Martells. If you consider the ones that don't have paramouncy as well, I believe Boltons and/or Freys.

[thelittledragonthatcould]

Keep in mind, you don't have to kill all the members of a house to end the house. You just have to take away its lands. Then, the "house" is just a name, and its members might as well be peasants or mercenaries. Lannisport is apparently filled with Lannisters who can't trace their lineage to a Lannister of Casterly Rock and thus lack noble status.

The Lannisters of Lannisport are a seperate Noble House to their Caterly Rock cousins much the same way that there are two 'noble' House Flints in the North and a 3rd from the mountain clans who are not classed as 'noble' or two noble Royces in the Vale, two noble House Vances in the Riverlands. There are even Houses like the Daynes and Fossoway who have a Noble House and a Masterly House and exist independently of the other branch.

[franbatista123]

House Bolton and Frey in the next book, perhaps House Tyrell too. The thing with House Arryn is that there are plenty of distant relatives who can just change their name to Arryn, thus continuing the house. House Targaryen will have to be extinct, but not until the last book.

[Weirwood Druid]

A check up with each of the big houses:

House Arryn:

• essentially already dead, only SweetRobin is left.
  
• There are still some Arryns from the lesser branches but it will be hard to put them in place of succession, them having never dealt with real power and it will be sour for all the houses such as Ironwood and Royce who are then suddenly ruled by someone who only a while ago was a nobody.
  

House Stark:

• Dead to most people from westeros, no lands, ancestral seat destroyed and the Stark children scattered, on paper however they are alive and well with a big potential to come back.
  
• Sansa Stark's marriage to Harrold gives the Starks a powerful possibility to take back their lands
  
• Rickon can return with the help of Manderly
  
• the support of Bolton is highly dubious, it is only a matter of time before the Northern lords realise it is better to sacrifice your heirs who are stuck at the Twins and go down fighting than slowly die out under the reign of a psychopathic monster as Ramsay snow,
  

House Tully:

• In a worse state than House Stark, has far little chance of returning back to power.
  
• Edmure is captured and his upcoming child is danger of getting killed, only through plotting of the BWB, Blackfish and River lords who are willing to take the risk can he return back to power, maybe the Vale can help too.
  
• Blackfish can also be a heir, but seeing he has no interest at all in women we can assume there will be no new heirs through him
  

House Greyjoy:

• Euron Greyjoy seems only to have bastards and no interest in siring a real heir except with Danny, who may be barren.
  
• The Greyjoys also play a high risk game, having no real allies and being disliked by almost everyone they really must throw everything they have, if they lose... I doubt the next conquer will be as merciful as Robert Baratheon.
  
• Victarion has no luck with wives, the man maybe sterile
  
• Aeron is a priest and so sour and humourless that he can turn any woman sterile with a mere look
  
• Asha Greyjoy has no chance because of her sex
  
• there are lesser branches of the Greyjoys but they have even a less chance than those Arryn as the Ironborn only select heirs through a kingsmoot/or by their own approval
  

House Baratheon:

• In a terrible position just like House Tully, only Stannis is left and he only has 1 daughter
  
• I have strong doubts Stannis makes it through the end of the series, seeing as he now is already a shadow of his former self.
  
• Robert has many bastards but who will legitimize them?
  

House Lannister:

• Kevan Lannister's death sealed House Lannister doom, he was the only one who could save them.
  
• Cersei is very destructive and will most likely not see the end of the series
  
• Jaime is of the kingsguard and there for can't inherit the Rock.
  
• Tyrion is banished and cursed as a kingslayer and a kinslayer, even if he returned to Westeros I doubt the Westerland lords would accept him, it will most likely be a Roose Bolton scenario
  
• Genna's children carry the Frey name and since everyone hates the Freys now it isn't wise to let them inherit it, also there is that plot of the BWB in Riverun.
  
• There are Lannisters from a lesser branch but it is the same scenario with the Arryns
  
• Maybe Tyrek will inherit it all, through a Varys ploy.
  

House Tyrell:

• So far they have taken the least amount of damage when it comes to personal loses in the wars, I think that is going to change as Mace isn't really smart and they are walking a tight rope with the unstable Lannister alliance and the Greyjoy threat and of course the revived Faith Militant can cause plenty of problems. They are secured when it comes to heirs, there are many side branches with bigger reputations to inherit it all.
  

House Martell:

• Also pretty stable despite the deaths of Oberyn and Quentyn, House Martell is pretty sturdy when you look at their history I also think they will survive these series of conflicts.
  

House Targayen:

• A combination of House Arryn and House Stark; they lost all their lands, their orginal homeland is destroyed and the only heir is Danny who may be barren, there is also Aegon but if he is real or not can't be detemined of yet.
  
• If there is still a Blackfyre he/she can also inherit it.
  

House Arryn and House Targayen are good bet, Baratheon and Tully too.