Huh. This might just be the best general-purpose recursion card printed since the original Déjà Vu.

Overall, it's probably lost a little bit of power - it's no longer quite so amazing for virus decks in particular. (Which is probably just as well, even if Noise: Hacker Extraordinaire is no longer around.) But getting back an arbitrary card from archives is still an extremely powerful (and uncommon) effect, so this will clearly still see plenty of play.

There are some really interesting aspects of this card though!

• First off - it's a run event now. This does some fun stuff to the card's power level. On one hand, it means that it kind of saves you a click over the old Déjà Vu, as long as you were planning on running this turn anyway. (And didn't need the card you want back to do it!)
• On the other hand though, the fact that it requires a successful run also gives at least some counterplay to the corp. If you don't have any un-iced servers on the board, this card is a a little harder to play. (Defend your archives, people! Even if you're not playing Jinteki: Restoring Humanity, runners have entirely too much mischief they can apply if they get unfettered access to a central server!)
• It's a run event that triggers off of a successful run, but it does not replace your access or anything. So it combines nicely with all the "instead of accessing" triggers, like Security Testing, Zenit Chip JZ-2MJ, etc. It also plays nicely with many multiaccess tools like WAKE Implant v2A-JRJ or The Twinning. And of course, all the general tech that triggers off of successful runs, like Pennyshaver, etc.
• It has fun synergy with a lot of cards that you might want to play after a run. Emergency Shutdown after using it to run on HQ for example. Or En Passant. And of course the fun one - You can use the run from Katorga Breakout as one of your three required central runs, and then use the retrieval effect to get back your Deep Dive (or other "run all 3 centrals first" card of your choice), while still having enough clicks left to play it!

All in all - a very solid card in Anarch. It's powerful, but feels fair. It's an effect that other factions are going to desperately want (especially in startup, as of this writing, when program recursion is harder than usual) but the 3 influence cost will probably make it difficult to justify splashing more than x1 or x2.

All that Bwob said is correct.

First, I'll look at it from the point of view of the Startup Format : it is the ONLY recursion card for runners in startup. This card means you pay 2 to make a run and exchange this card for something else. In startup, a good "something else" could be Chastushka for example.

In any deck in startup, this card could be your replacement for multiple tech cards or a 4th card of that your deck is build around, like Spark of Inspiration, The Maker's Eye, Chastushka, Inside Job, Emergency Shutdown.

In standard, it is a tougher proposition to use this card or Labor Rights. If you want 4 to 6 copies of one card, the Katorga Breakout is better. If you want to do late recursion to lenghten the deck or if you want to sift your deck, then Labor Rights. Tempo wise, it is better than Harmony AR Therapy and it require less support than Rip Deal. But at 3 influences, I think only one copy would be used out of faction.

Hence, I think having one copy of Katorga Breakout is good for any combo deck. In the Startup Format, it is a great card that will protect you from losing any essential cards from damage (looking at you, Jinteki: Personal Evolution).

The art fit the name and is nice, if somewhat cartoonish (those picks seems disproportionally huges) and it makes me wonder what Esâ Afontov: Eco-Insurrectionist is holding in hand. The quote is inspiring and fit really well with the effect and the name. Well done!