I just got into Netrunner, and I'm reading up about it, and I keep seeing Astrochain being mentioned everywhere, but I can't find an explanation of it. I know it involves AstroScript Pilot Program in some way.
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"Astrochain" (or "astrotrain") is a term used to refer to the use of the scored ability of the "Astroscript Pilot Program" (APP) NBN agenda in Android: Netrunner. When scored by the corporation, an agenda counter is placed on the APP that allows:
This ability can be triggered during any subsequent paid abilities window, and is generally regarded as one of the strongest agenda abilities in the game.
The APP itself is a 3/2 agenda, meaning that it requires 3 advancement tokens to score and yields 2 agenda points when scored. Because it can be scored so quickly, many NBN decks have been constructed around scoring these agendas in particular and preferably doing so out of hand (meaning the runner will never see them in a remote server, but will only be able to grab them from HQ or R&D) - this strategy is referred to as "Fast Advance".
In faction, they are often paired with SanSan City Grids, which allow for agendas to be scored one advancement token sooner than they would be otherwise. If the Corporation has a SanSan City Grid installed at the beginning of their turn, they can pay 6 credits to rez it, install the APP, advance it twice (either via credits or with a Shipment from SanSan), and score it all within one turn. The hosted agenda counter can then be saved to help advance subsequent agendas, which can be immensely helpful if your SanSan City Grid gets trashed.
This kind of deck typically is played as a "rush deck" - where you may install a few pieces of cheap, end-the-run ICE and hope to win before the runner has a chance to fully put together their rig and break through your defenses (typical ICE choices are things like: Chimera, Wraparound, and Quandry). Once they can get in, you have to win quickly.
This strategy is so strong that the influence splashes in some decks also revolve around accomplishing this goal (scoring APPs out of hand). The most typical of these is the "Astrobiotics" deck, which includes up to 3 Biotic Labours (splashed from Haas-Bioroid at 4 influence each). With an APP and a Biotic Labour in hand, one can Biotic, then install, advance the APP three times, and score it within one turn. Of course, if you do this and also have a SanSan rezzed, you can even do something else with your last click!
APP tokens are sometimes "chained" - which does indicate that you use one APP to score another, but as has been mentioned, it is not extremely common to draw them one after another in this fashion. However, if you are able to score one or two of these agendas and sit on their agenda tokens, you are in an extremely strong position to score other agendas faster than the runner can deal with them. For example, with 1 Biotic Labour, you could install a Project Beale and advance it three times. This would typically score it for 2 agenda points, but if you had previous scored 2 APPs, you could spend their tokens to advance it twice more - yielding you 3 agenda points, and the win! (note: SanSan City Grids do not help with obtaining the additional agenda points from Project Beale)
A "chain" is just using multiple AstroScripts to advance each other.
Once you score an AstroScript Pilot Program, you can use this ability:
To advance a second one quickly. If that scores the second Astro, you can then advance a third...