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

[Sordelor]

Arryn and Baratheon are as good as doomed.

Freys are never all going to get killed, but they'll probobly lose their lands, and the descendants of Lord Walder will forever be ill-desposed for what they lost.

For the Tully's it's gong to be very hard to return, yet not impossible.

The Tyrells will be fine.

The Stark are very likely to get the power back.

[Heyo Winter Comin']

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.

You shut your mouth!

[thelittledragonthatcould]

• 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.
  

• There are Lannisters from a lesser branch but it is the same scenario with the Arryns
  

You do realize that the current heir of the Vale is Harry Hardyng who as the son of a Landed Knight(not Noble or even Masterly) is pretty much a nobody. The Lords Declarent are more than happy with him as the heir despite the fact that if Ronin had a couple of brothers he would of been a nobody.

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.

They would just change their name from Frey to Lannister if they were to inherit Casterly Rock. It is not really a big deal just like Bran would of changed his name to Tully if Edmure died without an heir and Cats side inherited Riverrun.

[Golden&Crimson]

Why some people keep counting the Freys among the Great Houses?

House Frey isn`t a Great House.

Currently we have the following Great Houses:

- Lannister

- Tyrell

- Baratheon

- Arryn

- Greyjoy

- Martell

- Bolton

- Baelish

- Targaryen

- Tully

- Stark

Freys are at the same level of Manderlys, Harlaws, Royces, etc. They aren`t at the same level of a Lannister or Stark.

[Blede]

But... the king's decree...

"Harrenhal is a ruin, haunted and accursed," he objected, "and Baelish... the man is a coin counter, no proper lord, his birth..."

I think some people associate the titles of Lord of Riverrun and Lord Paramount of the Riverlands, and are as confused as Ser (Lord ! LORD !) Emmon Frey when Jaime told him he wouldn't rule over Lord Walder. As for me, I mentioned them only because everyone is doing so.

[Fat Mac]

Legally in Westeros, the great Houses are

1. Lannister

2. Baratheon

3. Tyrell

4. Martell

5. Arryn

6. Greyjoy

7. Bolton

8. Baelish

At this point, Bolton and Baelish are the most likely to go out. They are "villains" and will soon be defeated most likely by Stannis and Sansa, respectively.

The others I think will survive. Come on people, the Lannisters and Tyrells number in the dozens, and the Arryns and Greyjoys have cousins that carry the name out the wazoo.

Baratheon is in danger, but I don't think all those bastards Robert had are in the story for nothing ;)

[thelittledragonthatcould]

Baratheon is in danger, but I don't think all those bastards Robert had are in the story for nothing ;)

Their purpose was to let Ned play Sherlock and discover the mystery of the Twins incest.

[Seneti]

• 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 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.
  

I agree with almost everything in your post, except for the quoted parts. I'm sure Lord Walder is going to bite the dust soon enough, leaving 20+ sons fighting for power + LS happily hanging every Frey she comes across. House Frey will crumble soon enough and the hostage situation will solve itself. As for the Tyrells: they have shown the remarkable ability to take every single blow with as much grace as anybody can and still gain something from it. I'm sure they'll be able to weasel their way to the end of the Game (they won't win, but they won't lose either).

[Fat Mac]

Their purpose was to let Ned play Sherlock and discover the mystery of the Twins incest.

I doubt it. Two of his bastards (Edric, Bella) were introduced after that point, and even Mya didn't have a role in that. Not to mention Gendry became a supporting character in Clash and Storm, with a guest appearance in Feast. I'm not saying any of them will be king or anything, just that I'm assuming at least one of them will have future political relevance.

[LS1Transam]

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.

If I'm not mistaken, the original title for this next book was going to be "A Time for Wolves" so that at least hints at a Stark resurgence

[The Crow's Third Eye]

It would be rather fitting for the main branch of House Lannister (i.e. the Lannister's of Casterly Rock, not of Lannisport) to suffer such a loss that they either are ruled out in the male line or at least no longer considered to rule the Westerlands. Kind of a parallel to the Reynes of Castamere. Not that this is likely, would just be fitting. But to me I think the House in most danger of some kind of fall is the Tullys. We only have Edmure and le Poisson-Noir remaining, and our favourite fish doesn't seem inclined to marry anytime soon. Also, Edmure's son/daughter is likely going to be declared a Frey, thus ending the Tully line

[littleRickon]

For many of the houses in danger, there seems to be at least one possible survivor, and many of them have been introduced as highly likable characters throughout the series. Now, I doubt that the story will end with the "nice" offshoots of every line in power, but it could well be that some of those are coming into their rule

Stark: Rickon is most likely still alive and kicking, and should be able to continue the line. Of my list here, he is probably the least likable, although I obviously sympathize with him. I think he will be a black raging angel of revenge.

Tully: Edmure, while presently a hostage, is also the one leader who has shown his unlimited (and probably unwise) support and compassion for the smallfolk. The scene where he let his people into Riverrun will reap some late benefits when the most powerful force in the riverlands after the collapse of the Lannisters will be the Brotherhood. I don't think they forgot. The BwB likely both know that Edmure is being transported to CR (Tom o'sevens is in Riverrun) and could very well take back the castle from the Freys once the Lannister reign is over.

Baratheon: Stannis, however much I like him, will not continue the line. It has to be a bastard of Robert's, and we know 2 of them that both seem very nice guys and have to have some part in the story to come. Edric, and more likely, Gendry. Someone needs to legitimize them, but as long as we don't know who ends up on the IT, we can't rule that out.

Arryn: Harry. He is called the heir for a reason. Would be a bit ridiculous if everybody in the Vale called him the heir but nobody would respect him continuing the line. Will he be a weak leader, to be manipulated by stronger parties in the Vale: most likely. Will he continue the line: sure!

Lannister: I can fully anticipate their downfall as a dominant force in the GoT, but they don't need to go extinct. Genna is still out there and her children could very well continue the Lannister name.

The ones I actually see as most precarious are the Freys. Of course there are a lot of them, but the whole realm seems to be on a merry Frey-hunt and their ranks are dwindling. They also deserve some epic payback story-wise for the RW, and I think GRRM is going to give us the end of their line before we get the end of the books. That they were so many to start with will just make it all the more tragic/ironic.

Boltons, not so sure there. Roose seems like a real player, he might just pull something out his sleeves that nobody could have seen coming...

[Arthur Lannister]

House Stark already had lost the game unless Rickon comes back and try to reclaim his family's lands.

House Bolton is doomed due to lack of competent heirs and lack of popularity.

House Frey is doomed if Walder Frey dies and his sons would fight each other to succeed him.

House Lannister is collapsing unless Daven, Martyn, Damion, Lucion, or any other competent Lannisters save their fortunes.

House Tyrell is doing fine for now.

House Baratheon is doomed unless Stannis legitimizes Robert's bastards.

House Martell is doing fine for now.

House Arryn is doing fine under Littlefinger's manipulations for now.

House Tully might recover should Edmure and his family reclaim their lands.

[KingMaekarWasHere]

I think that it will be the Lannisters because Kevan is gone now, his brother that some think is still alive has not been seen in years, Tywin is gone, Cersei is a woman so all her children count as Baratheons, and Jaime is in the Kingsguard. That I believe leaves Lancel and several other Lannister men, and since Tywin likely made most of the lions feel sub-serviant to him and his three children, well that might mean that certain amounts of self-esteem flew out the metaphorical window years ago for the cadet branches. Not to mention that Lancel joined up with the Warrior's Son I believe, which is pretty much like a Kingsguard for the worshippers of the Seven, so he can no longer have legitimate children or lands.