Tl;dr: You can get at least 444 445 actions, maybe more.
Okay, I wanted to give this puzzle a try.
Some basics:
- You want to include black market (BM) with all non-kingdom cards in the black market deck, including Young Witch.
- There are (if I counted correctly) 25 different cards giving (with perfect luck) +6 actions when King Courted, which do not rely on other cards. So this includes Nobles, Dame Molly, Madman, Ironmonger, Necropolis, Trusty Steed and Hamlet, but excludes Tribute (gives +12 actions with perfect luck), King Court (KC), Throne Room (TR), Procession (PR), Band of Misfits (BoM) and Crossroads (does not give extra benefit when King Courted (for our purposes)). I assume that we can manage our deck well enough to ensure that Tributes and Ironmongers give the maximum number of actions
- You want to start your turn with a deck consisting of all action cards available in the BM-deck, 10 cards of 2 supply piles, and 9 cards from all other supply piles, and all madmans (which can be done with Hermit in the BM-deck if we use graverobber). We can easily get those other 9 cards from the supply using Universities.
- We really want KC and Tribute in our kingdom, and probably some other village piles. If we have n piles with villages, we have 44+9n cards that we really want to KC (10 Tributes, 10 Madmans, 24 unique other villages, and the 9 other cards for each kingdom pile). Also, a Throne Room or Golem played on a cantrip can be consideres as a village (there won't be villages available for Throne Rooms, they will all be King Courted).
- We can easily draw our deck with Scrying Pool at the beginning of our turn.
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The idea is to use a KC spot for PR (Procession) -> 3 KC -> 6 villages (or something else) and then use the next KC-spot to play a Graverobber to get back three KCs (we just need to play a highway early). This gives 6 King Courted actions in exchange for a Procession and a Graverobber, both on a KC spot. This allowes us to create 4 KC-spots for just 1 Graverobber and 1 Procession. Note that we can also use Rogue instead of Graverobber (using Watchtower to topdeck the gained KC if necessary) and Band of Misfits instead of Procession. So by these playing all these cards 10 times, we can create 80 additional KC spots. If we play TR -> 10 KC we have 20 KC spots, so in total we get 100 KC spots (not counting the spots Procession and Graverobber took).
Unfortunately, this is more KC spots than we have villages. Since we already used BM, KC, PR, Graverobber, Rogue, BoM, Tribute in our kingdom, and we also want Throne Rooms, we just have 3 kingdom piles with other villages. This gives 61 villages + 10 Tributes + 9 TR (1 of them is under the KC chain) + golem = 81 spots we can use usefully in KC. This means that we can let go of 20 spots, which means that we can use Procession 10 times on something different than KC. Tribute is of course the best candidate for this.
There are pretty much side conditions which all must work out, but I'm sure it's possible. If there would be an online implementation of Dominion with Black Market, I would create a log showing the idea, because I'm quite sure you can do it without shuffle luck (Scrying Pool draws your whole deck if it only consists of actions).
Now suppose everything works out we get the following amount of actions
starting actions: 1 as soulnet points out below: +1 action for a tactician played last turn
starting KC-chain: -1 action
PR on 10 Tributes: 80 actions
KC on 10 Tributes: 120 actions
KC on 60 villages: 180 actions
KC on 9 TRs playing 26 cantrips and the last village: 56 actions
KC on Golem playing 6 cantrips: 6 actions.
Playing Crossroads: 3-1=2 actions
Total: 444 445 actions
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Edit: With cantrips I mean cards that give +1 action (including pawn). The +1 card doesn't matter. If I counted correctly there are 46 cards which are a cantrip in this sense, plus up to 10 Ruined Villaged, and I just need 32 of them, so that should be okay.
