WHY THE FUCK DIDN'T SANSA TELL JON THAT THE SOLDIERS FROM THE VALE WERE ON THE WAY AND INSTEAD ALLOW HUNDREDS (OR THOUSANDS) TO DIE?
Admittedly, it's a good question, one that any decently intelligent viewer should ask. Some of my friends stopped there and concluded that it was a plot hole. Ruined the episode. What were the writers/directors thinking?
In this instance, those friends were wrong. Not stupid, just wrong. However, they crossed the line into stupidity once I explained to them what really was going on and they refused to admit that they had been wrong. Don't be stupid or wrong. Here's what happened and why:
In short, Sansa knew that the knights of the Vale were coming and purposely instructed them to intervene only once the Snow forces were about to lose, which was by far the most likely outcome to materialize.
The thinking behind Sansa's strategy is evident from the conversation she has with Jon Snow the night before the battle (and perhaps from some additional indications I will mention). Note this critical dialogue:
SANSA: You've known him for the space of a single conversation, you and your trusted advisors, and you sit around making your plans on how to defeat a man you don't know. I lived with him. I know the way his mind works. I know how he likes to hurt people....You think he's going to fall into your trap. He won't. He's the one who lays traps... He plays with people. He's far better at it than you. He's been doing it all his life...
JON: Alright, tell me. What should we do? How do we get Rickon back?
SANSA: We'll never get him back. Rickon is Ned Stark's trueborn son, which makes him a greater threat to Ramsay than you, a bastard, or me, a girl. As long as he lives, Ramsay's claim to Winterfell will be contested, which means he won't live long.
JON: We can't give up on our brother.
SANSA: Listen to me, please. He wants you to make a mistake.
JON: Of course he does…
SANSA: Just don't do what he wants you to do...
JON: We're lucky to have this many men.
SANSA: It's not enough.
JON: No, it's not enough. It's what we have. Battles have been won against greater odds.
SANSA: If Ramsay wins, I'm not going back there alive.
JON: Do you understand me? I won't let ever let him touch you again. I'll protect you, I promise.
SANSA: No one can protect me. No one can protect anyone.
There are a bunch of things that we can take away from this conversation regarding Sansa's estimation of Jon Snow: (1) Jon is underestimating Ramsay. (2) He's not as good a strategist as Ramsay. (3) Jon's forces can only be victorious if they are unpredictable, forcing Ramsay into a mistake. (4) Jon is incapable of formulating an unpredictable strategy, partially because (5) he's substituting optimism and idealism for military strategy (e.g., "We can't give up on our brother...Battles have been won against greater odds...I'll protect you, I promise").
Given this outlook, Sansa knows that she needs to engineer the unpredictability and display the ruthlessness that Jon is incapable of exhibiting. And this she does. In spades. For her gambit to work, however, Jon Snow must be kept completely in the dark.
Ramsay's battle strategy is brilliant and methodical, as Sansa knew it would be. Ramsay wields his forces like a chess master, allowing his cavalry (i.e. "pawns") to inflict maximum carnage before sacrificing them to his own archers, knowing that the arrows will also devastate enemy soldiers. Once the cavalry and the archers have wrought their damage, and only then, Ramsay springs his infantry trap, releasing his archers to surround Snow's forces in a vise from which there will be no escape.
But here's the catch. In springing this brilliant, effective trap, Ramsay COMPLETELY EXPOSES BOTH HIMSELF AND THE CASTLE TO ATTACK. It's undeniable. Check out the arrival of the Vale forces. Ramsay is on his horse with, literally, only two other mounted soldiers near him. No archers, no rear-guard, nobody. All of Ramsay's men are on the battlefield, primed for the kill - the kill that would undoubtedly have taken place if not for Sansa's incredible, successful gamble.
So why didn't Sansa tell Jon about the Vale troops? Don't you see? She couldn't! If Jon had known they were coming, he'd most likely wait for the Vale soldiers to arrive and draw up battle plans for the (newly) enlarged army. Conventional, unimaginative, battle plans that Ramsay--once he sees the new soldiers arrive--would easily anticipate and counter. The only way that Ramsay would make a mistake, the only way, was to spring a genuine surprise on Ramsay, with no warning and no compunction about the lives the strategy would cost.
And that's the incredible irony underlying Sansa's strategy. She "out-Ramsays" Ramsay. The show makes a point of contrasting Ramsay's willingness to shoot his own soldiers with Davos's (=Jon's) unwillingness to do the same. But Sansa goes even further than Ramsay. She is willing to risk Jon's entire army--and Jon himself!--because, she is convinced, only (the pretense of) impending victory would induce Ramsay to lower his defenses.
This post is lengthy enough. I'll try to add some evidence and color in a new post soon.
Thanks for reading!