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Given the following post, respond as if you're commenting on Reddit:
human
[Game of Thrones] Which three deaths would have done the most good to Westeros when Arya got to choose them?
gpt
Judging by what has already happened, and with the assumption they die when she says them, probably Edmure Tully, Illyrio Mopatis, and Tyrion Lannister. At the point in the story where Arya gets the three deaths, Jaime is captured and the Tyrells haven't joined the Lannisters yet. With no Tyrion, the city falls to Stannis, and with no Edmure then Tywin is captured by Robb.

Illyrio's death means that Aegon and Daenerys have no help from him, so Barristan never goes to Dany, and she is killed by the Warlocks, meaning no impending dragon-invasion.

Aegon loses his funding, so he can no longer recruit an army, making his invasion either delayed a lot or not happening at all. This also stops the potential plague that Jon Con might have brought with him to Westeros.

Stannis kills all the Lannisters, and Robb sues for peace so he can reclaim the north from the Greyjoys. Stannis turns his eye to the other threat to his kingdom, and reinforces the Wall against Mance, making the Wall storyline effectively the same as before.

Stannis cleanses the small council. Littlefinger, Varys, and Pycelle are all killed or flee the city.

Euron doesn't return to the iron islands, since he has captured three warlocks who tell him how they have control of three dragons in Qarth. The crow's eye turns east and Asha is elected queen of the Iron Islands, since Vic is a fool and Theon has been executed by Robb Stark, Warden of the North.

With Petyr dead/lost, Lysa Tully either kills herself and her son, or is forced out of the Eyrie by the Lords Declarant, who tell her she has to either declare independance or go swear fealty to the new king. Her nephew, Robb fosters young Robert Arryn.

After a short while all the Starks are reunited, save for Bran who seems to have disappeared with the Reeds. They are assumed dead.

Up until the Others arrive, Westeros seems to be recovering, then it is thrown into a supernatural war it cannot hope to win, Stannis dies at the front line with his phony lightbringer, and with his only heir being a child, the control of the realm passes to his Regent, Davos Seaworth.

Davos, seeing what urgent need the country is in need of help, recruits groups of mercenaries from the Free Cities. One such group is the Second Sons, led by Daario Naharis.

When all seems to be lost, the others have reached the capital, killing everyone in their way. The Starks and Tullys are all dead, as are the Baratheons and Targaryens, Azor Ahai reveals himself.

Back from stealing the dragons from the Warlocks, Captain of the Second Sons, and First Ranger Benjen "Daario "Euron "Crows Eye" Greyjoy" Naharis" Stark rides the Dragons into battle. The Prophecy is complete, and the Dragon has Three Faces. He obliterates the White Walker Army with the dragons, fights the Great Other with Ice, tempered in the neck of his brother who warged into it to become Lightbringer, and takes his place on the Iron Throne with his Paramour and fellow Second Son, Prince Oberyn Martell of Dorne. Westeros embraces gay marriage, and Benjen and Oberyn adopt Shireen, showing their support for the disabled. Westeros enters a new age of tolerance, and there is an ever-lasting peace. King Jaqen rules Westeros well, and any attempt to breach the peace is met by two words:

"Not today."

The End.

Edit: Added more tinfoil.