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[AJD]

I play Action X from my hand.

Once Action X is finished resolving, the gamestate is exactly the same—it is as if Action X had been an Action card that said "do nothing". All cards are in the same places they were when I put Action X in my play area, I have no more (or fewer) coins, actions, or buys, etc.

But! Action X didn't actually do nothing! During the course of resolving Action X, a single card ran around the mulberry bush, passing through four distinct locations and stopping in the fourth, right back where it started.

How did this happen?

[eHalcyon]

X is Procession.
The card that travels is Band of Misfits.

Resolution:

Procession has +1 card token.  Graverobber has -$2 cost token.  There are no $6 action cards in the kingdom.  BoM starts on top of your deck (0).
Procession draws BoM into your hand (1).  Choose BoM and play it (2) as Treasure Map.  It trashes itself (3).  For the second play, choose Graverobber and bring BoM back, returning it to the top of your deck (4).

[GendoIkari]

X is Procession.
The card that travels is Band of Misfits.

Resolution:

Procession has +1 card token.  Graverobber has -$2 cost token.  There are no $6 action cards in the kingdom.  BoM starts on top of your deck (0).
Procession draws BoM into your hand (1).  Choose BoM and play it (2) as Treasure Map.  It trashes itself (3).  For the second play, choose Graverobber and bring BoM back, returning it to the top of your deck (4).

You also need the +1 action token on Procession, so that you don't reduce your number of actions with this.

[Simon (DK)]

X is Procession.
The card that travels is Band of Misfits.

Resolution:

Procession has +1 card token.  Graverobber has -$2 cost token.  There are no $6 action cards in the kingdom.  BoM starts on top of your deck (0).
Procession draws BoM into your hand (1).  Choose BoM and play it (2) as Treasure Map.  It trashes itself (3).  For the second play, choose Graverobber and bring BoM back, returning it to the top of your deck (4).

You also need the +1 action token on Procession, so that you don't reduce your number of actions with this.

I'm not so sure about that because of the sentence "it is as if Action X had been an Action card that said "do nothing""

[GendoIkari]

X is Procession.
The card that travels is Band of Misfits.

Resolution:

Procession has +1 card token.  Graverobber has -$2 cost token.  There are no $6 action cards in the kingdom.  BoM starts on top of your deck (0).
Procession draws BoM into your hand (1).  Choose BoM and play it (2) as Treasure Map.  It trashes itself (3).  For the second play, choose Graverobber and bring BoM back, returning it to the top of your deck (4).

You also need the +1 action token on Procession, so that you don't reduce your number of actions with this.

I'm not so sure about that because of the sentence "it is as if Action X had been an Action card that said "do nothing""

Yeah, the OP is unclear on that point I think. It does say that, but it also says you won't have less actions than you did before.

[AJD]

X is Procession.
The card that travels is Band of Misfits.

Resolution:

Procession has +1 card token.  Graverobber has -$2 cost token.  There are no $6 action cards in the kingdom.  BoM starts on top of your deck (0).
Procession draws BoM into your hand (1).  Choose BoM and play it (2) as Treasure Map.  It trashes itself (3).  For the second play, choose Graverobber and bring BoM back, returning it to the top of your deck (4).

Not exactly the solution I had in mind (but close). Nice job!

My solution was King's Court a Band of Misfits as Treasure Map, Graverobber, and Ruined Library.

[AJD]

X is Procession.
The card that travels is Band of Misfits.

Resolution:

Procession has +1 card token.  Graverobber has -$2 cost token.  There are no $6 action cards in the kingdom.  BoM starts on top of your deck (0).
Procession draws BoM into your hand (1).  Choose BoM and play it (2) as Treasure Map.  It trashes itself (3).  For the second play, choose Graverobber and bring BoM back, returning it to the top of your deck (4).

You also need the +1 action token on Procession, so that you don't reduce your number of actions with this.

I'm not so sure about that because of the sentence "it is as if Action X had been an Action card that said "do nothing""

Yeah, the OP is unclear on that point I think. It does say that, but it also says you won't have less actions than you did before.

Won't have less actions than you did when Card X hit your play area. You've already used up your action on playing Card X by that point.

[eHalcyon]

X is Procession.
The card that travels is Band of Misfits.

Resolution:

Procession has +1 card token.  Graverobber has -$2 cost token.  There are no $6 action cards in the kingdom.  BoM starts on top of your deck (0).
Procession draws BoM into your hand (1).  Choose BoM and play it (2) as Treasure Map.  It trashes itself (3).  For the second play, choose Graverobber and bring BoM back, returning it to the top of your deck (4).

Not exactly the solution I had in mind (but close). Nice job!

My solution was King's Court a Band of Misfits as Treasure Map, Graverobber, and Ruined Library.

And I just realized that my use of Procession might as well be Throne Room haha.  I wasn't completely sure where I was going with my solution at the start and thought that it might make a difference.

[majiponi]

I'm not sure.
The first resolution of BoM ends when you choose Treasure Map to trash it.
The gamestate is different when you resolve Procession.
What is card X?

[eHalcyon]

I'm not sure.
The first resolution of BoM ends when you choose Treasure Map to trash it.
The gamestate is different when you resolve Procession.
What is card X?

I'm not sure what your question is.  Both my solution and AJD's solution explain it fully.  Since you mention BoM and Procession, you're probably asking about my solution.  I stated explicitly that card X is Procession, though it could just as well be Throne Room.  When you finish resolving it, the game state is exactly the same as it was when you first started resolving it.

[majiponi]

I'm not sure what your question is.  Both my solution and AJD's solution explain it fully.  Since you mention BoM and Procession, you're probably asking about my solution.  I stated explicitly that card X is Procession, though it could just as well be Throne Room.  When you finish resolving it, the game state is exactly the same as it was when you first started resolving it.

Oh, I didn't notice "All cards are in the same places they were when I put Action X in my play area,..."
I thought the state should be same to when I started to resolve - BEFORE putting X in my play.