Formicary is a good Weyland sentry. It's no Archer, Surveyor, or Colossus, but it is a cheap sentry you can slap down on your remote and then have magically defend your centrals when you need it to. Its sub isn't the greatest in the world, it lets the Runner pick their poison after all, and its rez-to-break ratio isn't all that great either, but it's effect is punishing enough that Runners would rather just end the run if they facecheck it and its effect practically begs the Runner to facecheck it when they least expect it to. I think 2 creds for it is a steal, honestly. Also, Formicary was the central part of a hilariously degenerate combo that led to the first banned NISEI card. Since it had the exact same trigger as Cayambe Grid you could choose to let Cayambe fire first, then Formicary, then Cayambe again after the runner breaks the Formicary, then any other Formicary you had laying around, then Cayambe again, and so on. It was not unusual to force the runner to pay 30+ creds on a single run. That was a wild time.

(I've been meaning to write some "banned/rotated card retrospectives" for a while. This one's my first.)

Ah, Formicary. A card that started its life as a way to give the Runner a mildly annoying surprise when they ran an apparently unprotected server, and ended up as part of way too many degenerate combos. There's an entire official article about why this one card was banned, which basically summarises to "trying to ensure that newly designed cards didn't combo too degenerately with Formicary ended up being too restrictive on the card designs".

The basic idea behind most Formicary combos is that you trigger a "the Runner approaches the server" ability of another card, then after that's resolved, use a long-distance Formicary rez to cancel the approach, thus allowing the original trigger to trigger a second time once the Runner passes the Formicary. There's are quite a few possible effects you could use with this, but most of the combos weren't being actively played at the same time, so it's worth looking back at just how much chaos this one card caused:

• Formicary + Cayambe Grid. This makes the Runner pay the Cayambe Grid tax twice, and in the typical Cayambe Grid deck, the tax is enormous and trying to pump it up out of reach is one of the main things that the deck does. Cayambe Grid got banned in June 2020 with minimal explanation: the ban was apparently a targeted ban to kill one specific deck that was extremely unfun to play against, but the balance team didn't specify which. I do think the "the ban was to kill Formicary + Cayambe Grid" theory is plausible, though.
• Formicary + Manegarm Skunkworks. This was basically the same idea as with Cayambe Grid, but didn't cause as much friction, and wasn't played that commonly. Most likely this is because people preferred to combo Manegarm Skunkworks with Anoetic Void instead (although there was nothing actually stopping you from comboing all three cards together, but people preferred not to bother with that in tournaments, most likely for influence reasons).
• Formicary + Dedication Ceremony on Reconstruction Contract in Ob Superheavy Logistics. This uses up three cards and requires a specific identity, and only works in Eternal, but is effectively an automatic win (barring specific removal cards like Pinhole Threading), and is much simpler than the typical Netrunner win combo. The basic idea is that Dedication Ceremony costs 1, and most ambushes cost 0, so once the Runner is locked into breaching Dedication Ceremony's server, you can trash it to move the counters (as long as there's a legal target anywhere, e.g. you have advanceable ICE), use Ob to install an ambush from R&D in the server the Runner was accessing, and then choose the newly installed ambush as the card to put the Dedication Ceremony counters on. Many players' immediate reaction is "does that work?", and the answer is "yes, as long as you don't destroy the server mid-run by removing all the cards in and protecting it", which generally implies that there must be ICE protecting the server. The Runner might well jack out – but then you could wait until your own turn and choose a different card to search for and put the counters onto, making for a nearly automatic win because you can choose between, e.g., Project Junebug and Clearinghouse based on whether the Runner accesses or not. Ideally, you'd want 6 counters rather than just 3, using double Dedication Ceremony (because that makes both Project Junebug/Cerebral Overwriter and Clearinghouse definitively lethal against normal hand sizes), but that takes an entire turn to set up; adding Formicary to the mix therefore lets you set up the combo using only 3-click turns via allowing you to ICE the server clicklessly if the Runner decides to run it. This sort of combo isn't the only reason Ob was added to the Eternal points list (first at 1 point, then 2), e.g. Ob also combos with Estelle Moon which is one of the most broken cards in Eternal, but it can't have helped.
• Formicary + HB "derez matters" cards (e.g. Stegodon MK IV, Brasília Government Grid). One of the main drawbacks of Formicary is that its trigger typically only works once, because it needs to be derezzed to trigger but rezzes itself when it does. One of the main drawbacks of the HB cards is that you need to find ICE (sometimes even off-server ICE specifically) to derez. As such, the cards cancel out each others' drawbacks, with each giving you more uses of the other, in a self-sustaining cycle. This is what finally ended up getting Formicary banned.

Also, there's one card theoretically combos with Formicary, but where the combo wasn't really the problematic part: Formicary + Nanisivik Grid. The idea is that you can use one Nanisivik trigger to, e.g., trash a program (the Runner's killer could be a good choice, as that makes Formicary more expensive to get through), and then if the Runner runs back through, use a second Nanisivik trigger to end the run. It turns out that Nanisivik Grid was broken enough on its own, however, that the Formicary combo was overkill (you put one Nanisivik Grid on Archives and it makes it almost impossible to disable any of your Nanisivik Grids, including both itself and ones placed elsewhere).

Some non-combos include Letheia Nisei and Mti Mwekundu: Life Improved, which are only usable once per run even if you use Formicary to interrupt the trigger.

I can see why the card got banned. In most of the combos above, at least one piece got banned (or for Eternal-based combos, pointed); the only exception is the Manegarm Skunkworks combo, and that's a card that lots of casual players surely were wishing would be banned (Skunkworks combos were part of what was the best archetype in Standard for quite a while). Perhaps the lesson here is that, when you find a degenerate combo, maybe it's both halves that are banworthy!