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Daenerys Targaryen, Tyrion Lannister, Grey Worm, Varys & Missandei of Naath (GOT) - Credit if using
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Daenerys Targaryen, Tyrion Lannister, Grey Worm, Varys & Missandei of Naath (GOT) - Credit if using

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being master/mistress of whispers must be so funny because you send spies on people on both sides of beef and make riddles with mysterious appearances, and also being hated but needed all the same. it’s like being the friend in a group that’s abusing the “i told you” button at every death twice a week
the person who nobody wants to invite but appears in the room before anyone even turned the keys, just to say their scenes are so entertaining because it’s not me they’re talking. because i’d be stressed. no i don’t want to learn about the queen’s affairs thank you very much i just want a fair sum of money and live happily after
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Daenerys Targaryen, Tyrion Lannister, Grey Worm, Varys & Missandei of Naath (GOT) - Credit if using
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Daenerys Targaryen, Tyrion Lannister, Grey Worm, Varys & Missandei of Naath (GOT) - Credit if using
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Daenerys Targaryen, Tyrion Lannister, Grey Worm, Varys & Missandei of Naath (GOT) - Credit if using

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Would Varys have freed Tyrion himself without being coerced by Jaime? If he is being eyed as a potential recruit for Dany/Aegon.
Hard to say. On the one hand, Varys sure did have a whole end-to-end escape route lined up on very short notice, from Tyrion's cell right to Illyrio's manse. It's the ship connection that's more interesting to me than the tunnels - it requires more logistical coordination, which takes more time in a society without even telegraph lines. It's not as though Varys can call a rideshare service or bundle Tyrion anonymously onto a train. Ships might be coming in and out of King's Landing regularly, the King's Landing-Pentos route might be one of the most common shipping lanes in the area full stop, but Varys still needs a reasonably trustworthy captain.
Of course, it's also part of Varys' job to be able to do this sort of thing. If anyone could get Tyrion out of the dungeons and headed to the Free Cities with only half a day to plan, it's Varys. That's exactly why Jaime outsourced that aspect of the plan to him. It doesn't necessarily speak to Varys having a route lined up for Tyrion specifically in advance. It's just consistent with the theory.
On the other hand, the fact that Tyrion's in that cell, awaiting execution for regicide, means freeing him is very high risk for Varys. I think faking Tyrion's death would be a very hard sell, while an obvious escape raises different red flags. As we see in AFFC, freeing Tyrion in such a way means that Varys is an immediate and very obvious co-conspirator. He has to leave his position, forfeiting his ability to feed curated information directly to Cersei (and other functionaries) and forgoing his invites to high-level political meetings just when the regime's going to be making some important decisions that will affect how they respond to Aegon.
I lean towards no, Varys wouldn't have, not ahead of a death sentence and not at that time (if either factor changed, I think he would have taken the risk) - but it's a lean only. And it's certainly true that Varys adapted and made the best of the circumstances he found himself in.
I wonder how many full time jobs Lord Varys had in the Red Keep
Do you think that if Tyrion hadn’t been framed for Joffrey murder then Varys would have eventually murdered him? Varys needed the Lannisters as incompetent and cruel as possible to make Aegon seem appealing and Tyrion being the most competent of the Lannisters makes him a liability.
I doubt it would have been option one, or option two. It would have been a numbered option though. Probably option three or option four.
Varys can see as well as anyone else in the Red Keep that Tyrion is unpopular. Not just with the general population of King's Landing but within his own family. In ASoS Tyrion is marginalised politically within the regime; the danger for Varys would be that Tywin held his nose long enough to make good use of Tyrion as Master of Coin. Especially if Tywin came to that conclusion because he has to ship Cersei off somewhere she can't do much damage, and he needs at least one kid to be present and competent.
But Varys is also aware of Tyrion's relationship with Shae. That relationship is a very convenient lever to keep Tyrion distracted and, if needed, it could be revealed for whatever political consequences to Tyrion (and whatever other consequences to Shae, none of which are going to be fair, some of which could be lethal).
Varys knows Tyrion's got severely mixed feelings about his family and identified him as a potential recruit. Giving Tyrion the Ser Barristan treatment has got to be the preferred option even if Joffrey wasn't murdered when he was. Next best after recruiting him is disgracing Tyrion and getting him sent away; he can be recruited or used later in life that way, and in the short term he won't be there managing the accounts for the Lannisters.
Murder wasn't option one even with Ned, who is absolutely not a recruitment prospect at all. Varys isn't out there killing people because he thinks it's fun. He kills people because he believes he needs to, and he has a pretty high bar for that assessment. Hell, Varys even ships Gendry, Robert's bastard son, a young man of fighting age, out of the city to get him out of Cersei's range. So with all that in mind, with Tyrion, I think Varys would prefer to try a few other options before setting the little birds on him.