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[NoMoreFun]

Before any (non victory) kingdom card could be played at most 30 times (King's court on all 10 cards). However with some new dark ages cards, such as Graverobber, Rogue, Band of Misfits and Procession, this number may be outdated. In a turn, how many times can you get a
1) Single action effect (eg how many times can you get coppersmith's effect in a turn)
2) Single action effect from the black market (only 1 card available, not in the supply)
3) Single treasure effect

Hint for 3)
Horn of Plenty/Watchtower/Cultist/Mandarin

[razorborne]

Before any (non victory) kingdom card could be played at most 30 times (King's court on all 10 cards).

I don't think you can KC a Horde. I could be wrong though.

[wuthefwasthat]

Before any (non victory) kingdom card could be played at most 30 times (King's court on all 10 cards).

I don't think you can KC a Horde. I could be wrong though.

Pedantic man notices that he said "at most", so your objection is wrong.  But then he also notices that the statement was still wrong - all the Kingdom Treasures are Kingdom Cards which could be played more than 30 times, thanks to Black Market, Horn of Plenty, Mandarin.  Then, he notices your mispelling of Hoard 

Anyways, I have...

Lower bounds for all of your questions:

1) 108
2) 43
3) 1860 

All bounds are tight or close to tight, I think.

Explanations

1)

Let me show how to play 98 Coppersmiths, since Coppersmith is fun.  The actual solution will use Rats and play 10 extra of them...

Kingdom:  Scrying Pool, University, Coppersmith, Scout (or Chapel), Band of Misfits, Procession, Throne Room, King's Court, Graverobber, Rogue

With Scrying Pool, draw your deck of 9 Processions, 9 Coppersmiths, 10 Band of Misfits, 10 Throne Rooms, 10 King's Courts, 10 Graverobbers, 10 Rogues.  (Use University to gain some stuff beforehand, so that the game didn't end on the previous turn.)

Play 9 Throne Rooms in series, and 9 Processions underneath them.  Play these on 9 Coppersmiths and 9 Band of Misfits (playing as Coppersmith).
Play 10 Graverobbers and 8 Rogues to recover the 9 Coppersmiths and 9 Band of Misfits.   
University the last Procession.  Draw everything with Scrying Pool.

Play Throne Room on Procession, playing 2 Coppersmiths.
Play 2 Rogues to get them back.  Draw them with Scrying Pool.

Play 10 King's Courts, giving 19 King's Court plays.  Play 9 Coppersmiths and 10 Band of Misfits playing as Coppersmiths.

Gain and draw the final Coppersmith.  Play it.

18 * 2 + 2 * 2 + 19 * 3 + 1 = 98

A couple arguments convince me that this is reasonably close to optimal.  In all the logic, Band of Misfits can replace Coppersmith.  A Graverogue is a Graverobber or Rogue:
 - It's never good to Graverogue back Graverogues.  Suppose you play Graverogue 2 to get back Graverogue 1.  This means Graverogue 1 was played by a Procession (otherwise, it can't help to have trashed the Graverogue.)  But we're wasting a play of Graverogue 2 (notice I don't assume anything about whether it was played by Procession or King's Court), and we might as well have not played Procession on Graverogue 1, and have an extra Procession play open.  I believe the only reason this argument isn't airtight is that you might've wanted the Graverogued card for playing up to the current chain you're in (which seems implausible to me). 
- It's never good to Graverogue back King's Courts.  This would mean King's Court was played by a Procession.  But if the King's Court were played by a King's Court, we would gain an extra King's Court play, and have an extra Procession open.  Unless we're severely limited by the number of Coppersmiths to play, this seems terrible. 
- It's not better to King's Court Processions, if we have non-chained Coppersmiths at the end, and all Graverogues are played.  Playing King's Court on Procession gives us two extra Procession plays and two less Coppersmiths.  The Processions can give us two extra Coppersmith plays, but nothing more, unless we have extra Graverogues to play.


2) 

For 43 Coppersmiths from the Black Market deck:

Kingdom:  Beggar (bane), Village, Walled Village, Black Market, Talisman, Procession, Band of Misfits, Graverobber, Rogue, Saboteur, Cache
Black Market contains King's Court, Coppersmith, Native Village.

Draw your deck with Native Village.

Do this 10 times: 
- Band of Misfits, playing as Procession, on the Coppersmith.  Graverobber, getting the Coppersmith back.  Draw it with Village.

Then, gain the last Procession and do this 10 times:
- Play Procession on Coppersmith.  Rogue, getting the Coppersmith back.  Draw it with Walled Village.

King's Court the Coppersmith.

10 * 2 + 10 * 2 + 3 = 43


3)

Let's play Copper a ton... too bad we can't do this in the same game we play Coppersmith 98 times!

Kingdom:  Crossroads, Hermit (giving Madman), Counting House, Black Market, Ambassador (bane), Band of Misfits, Procession, Throne Room, Graverobber, King's Court, Mandarin
The Black Market deck contains Horn of Plenty, Native Village, a Haggler (to help us empty piles off of Black Market buys, mid-turn), plenty more Villages, and any other necessary helper cards. 

Play Native Village to draw your deck.  Play King's Court, King's Court, Tribute, Village, Shanty Town.  Play a bunch more random Villages from the Black Market deck.  Get to 30-ish actions (enough, because of Madman).

Do this 10 times:  Play Band of Misfits as Procession, on Black Market.  Play 60 Coppers, and a Horn of Plenty, gaining Mandarin (and something else), putting the 60 Coppers and a Horn of Plenty back on deck.  Play Madman to draw.

Play 4 King's Courts, giving us 7 King's Courts plays.  Play 4 Graverobbers, getting back 10 Black Markets, and 3 Ambassadors, returning 9 Mandarins back to supply.  Play one more Ambassador, putting the last Mandarin back in supply. 

Gain the last Procession.

Do this 10 times:  Play Procession, on Black Market.  Play 60 Coppers, and a Horn of Plenty, gaining Mandarin (and something else), putting the 60 Coppers and a Horn of Plenty back on deck.  Play Throne Room, Crossroads to draw.

Play 4 King's Courts, giving us 7 King's Courts plays.  Play 4 Graverobbers, getting back 10 Black Markets, and 3 Ambassadors, returning 9 Mandarins back to supply.  Play one more Ambassador, putting the last Mandarin back in supply. 

Do this 10 times:  Play Black Market.  Play 60 Coppers, and a Horn of Plenty, gaining Mandarin (and something else), putting the 60 Coppers and a Horn of Plenty back on deck.  Play Counting House to draw.

Play 60 Coppers.

(10 + 10 + 10 + 1) * 60 = 1860

[ghostofmars]

I think the best card for part b) of this puzzle is Fortress, which I can play at least 63 times

Playing TR and 10xKC allows 21 actions to be played 3x. The first 20 of these will be Processions and BoM played as Processions, so that we can play Fortress 60 times, directly getting it back in the hand. Then we use the last KC to play it thrice

[wuthefwasthat]

I think the best card for part b) of this puzzle is Fortress, which I can play at least 63 times

Playing TR and 10xKC allows 21 actions to be played 3x. The first 20 of these will be Processions and BoM played as Processions, so that we can play Fortress 60 times, directly getting it back in the hand. Then we use the last KC to play it thrice

Oh, wow, you're right!  Although you forgot that BoM can't play as Procession if there are one in supply.  We can fix this by playing the BoMs first, and having a Watchtower in hand.  On (the last BoM or) one of the first 8 Processions, gain a Catacombs, trash it, and gaining the last Procession on top, and drawing it with the next played Fortress.  So we still have at least 63!

Also.  It's better for part a) too, and makes the solutions simpler.  But at least we know how many times you can play Coppersmith now...


Updated answers:

1) 138
2) 63
3) 1860 


New solution for 1)

With Scrying Pool, draw your deck of 9 Processions, 9 Fortresses, 10 Band of Misfits, 10 Throne Rooms, 10 King's Courts, 10 Graverobbers, 10 Rogues.  (Use University to gain some stuff beforehand, so that the game didn't end on the previous turn.)

Play a 10 Throne Rooms, and then 10 Band of Misfits as Processions in series underneath.  This gives us 20 Procession plays, which we play on Fortress each time. 

Play 10 Graverobbers, getting back the 10 Band of Misfits. 
Gain the last Procession and draw everything. 

Play 10 Processions, all on Fortress.  Play 9 Rogues, getting 9 back and drawing them. 
Play 9 Processions, all on Fortress.  Play a Rogue, getting 1 back.

Play 10 King's Courts, giving 19 King's Court plays.  Play 9+10 Fortresses.

Gain and draw the final Fortress.  Procession it.
Play the final Fortress.

20 * 2 + 10 * 2 + 9 * 2 + 19 * 3 + 1 * 2 + 1 = 138

[ghostofmars]

I overbid the solution to 1) to 781, though I think even more should be possible. The card that is played this often is Procession.

The main idea is to create (almost) infinite procession chains. This works in the following fashion using Processions or Band of Misfits (P) and Graverobbers or Rogues (with Watchtower) (G)

assume we have n P left, 2 of which are in the trash, also 1 G are in the trash then
play P1
... play P2
... ... play P3
...
... ... ... play P(n-3)
... ... ... ... play P(n-2)
... ... ... ... ... play G(n-1) get P(n),G(n) on deck
... ... ... ... ... trash G(n-1)
... ... ... ... ... play G(n-2) get P(n-1),G(n-1) on deck
... ... ... ... ... trash G(n-2)
... ... ... ... trash P(n-2)
... ... ... ... play G(n-3) get P(n-2),G(n-2) on deck
... ... ... trash P(n-3)
... ... ... play G(n-4) get P(n-3),G(n-3) on deck
...
... ... trash P3
... ... play Card Drawer (drawing all cards put on deck)
... trash P2

result P1 stays in play area P2,P3,G3 are in trash so that n' = n-1

So we end up with 19+2*(16+15+...+1)=259 plays of procession. If we cleverly start all of these chains on a KC, we get another factor of 3. Furthermore, the two P are not in the trash in the first of these loops, so that we can add another 4 plays for a lower bound of 781 plays.

Ways to increase this number:
a) After all BoM are gone, we may gain the last procession and add it to the pool ~60 plays
b) There may be some clever trick to gain/trash Cultists to draw some of the processions so that some can be played twice. I estimate at least 200 plays.

[wuthefwasthat]

I overbid the solution to 1) to 781, though I think even more should be possible. The card that is played this often is Procession.

Awesome chain.  Of course my arguments from the earlier post fail completely when the card X is Procession itself... or Graverobber/Rogue, for that matter.  I agree that more is possible.  I suspect you can play the card drawer earlier, playing the same Processions again.  Eventually, the trash pile grows, and you make up for the loss by King's Courting some Graverobber/Rogues outside of the giant Procession chains.  Then repeat, with decreased n.

Also, updated answer for 2:

We can get at least 173 plays of a single Fortress.

Get 10 Throne Rooms, 10 King's Courts, 20 Graverogues, 9 Processions, some Scrying Pools and Ironworks, and a Fortress in hand (drawing them all with Scrying Pool).

Play a Throne Room on Throne Room. 
The first Throne Room plays 9+10 Processions in series.  This gives 20 open Procession plays, which all play Fortress.  8+10 of the Processions are trashed.
The second Throne Room plays 10 King's Courts, giving 20 King's Courts plays.
King's Court 1-6:  Plays 6 Graverogues, getting back the 8+10 Processions.
King's Court 7:  Plays a Throne Room. 
- 1st Throne Room plays Scrying Pool, drawing 8+10 Processions. 
- 2nd Throne Room plays 8+10 Processions.  This gives 19 open Procession plays, which all play Fortress.  7+10 Processions are trashed.
- 3rd Throne Room plays Graverogue, getting back 2 Processions. 
King's Court 8-12:  Plays 5 Graverogues, getting back 5+10 Processions.
King's Court 13:  Plays a Throne Room.
- 1st Throne Room plays Scrying Pool, drawing 7+10 Processions. 
- 2nd Throne Room plays 7+10 Processions.  This gives 18 open Procession plays, which all play Fortress.  6+10 Processions are trashed.
- 3rd Throne Room plays Graverogues, getting back 2 Processions. 
King's Court 14-17: Plays 4 Graverogues, getting back 2+10 Processions.
King's Court 18: Plays a Throne Room.
- 1st Throne Room plays a Graverogue, getting back 2 Processions.
- 2nd Throne Room plays Scrying Pool, drawing 6+10 Processions.
- 3rd Throne Room plays 6+10 Processions.  This gives 17 open Procession plays, which all play Fortress.  5+10 Processions are trashed.
King's Court 19-20: Plays 2 Graverogues, getting back 6 Processions.
Play Ironworks, for the last Procession.
Play Scrying Pool, drawing 7 Processions.
Play 5 Throne Rooms on 5 Processions, playing Fortress.
Play 2 Processions on Fortress.
Play Fortress.

40 + 38 + 36 + 34 + 20 + 4 + 1 = 173 plays of Fortress