Normally, when a trash card is clued, it signifies a Trash Chop Move or a Trash Push. However, for both of these strategies to work, it is assumed that the recipient of the clue will know that the card that was touched is useless.
What if the recipient of the clue does not know that the card that the clued card is trash? Then, they will go on to misplay that card, mistaking it for a "normal" Play Clue.
If players misrepresent the identity of a trash card in this way, it is a signal for the next person to blind-play their Finesse Position card. This is extremely similar to how a Finesse or a Bluff works (e.g. a clued card has been misrepresented as being immediately playable).
Trash Bluffs are a good tool to get a card played that is sitting behind other annoying cards.
For example, in a 3-player game:
All of the 1's are played on the stacks except for the red 1.
Cathy has no clued cards in her hand.
Alice clues Cathy number 1, which only touches her newest (slot 1) card. This card is a blue 1, but Cathy will assume that it is a red 1.
Bob blind-plays his Finesse Position card, and it is a playable blue 2.
Cathy now knows that her 1 must not be red 1, or else Bob would not have blind-played anything. The 1 must be some other trash card.
Just like normal Bluffs, Trash Bluffs can only be done while in Bluff Seat.
Normal Bluffs take precedence over Trash Bluffs. This means that players can only use cards to Trash Bluff with if they will be proved to be trash by a blind-play.
For example, if not all of the 1's have been played on the stacks, then you can use a number 1 clue to initiate a Trash Bluff, because a blind-play will prove that the clued 1 is not a good 1.
For example, if the red stack is played up to the red 3, then you cannot use a red clue to initiate a Trash Bluff, because a blind-play will make the clued card look like the red 5.
For example, if the red stack is played up to the red 4, then you can use a red clue to initiate a Trash Bluff, because a blind-play will prove that the clued card is not a red 5.
In the case where multiple cards are clued as part of a Trash Bluff, all of the touched cards are considered to be trash.
In a Finesse, we say that the clue "connects" to the blind-play. For example, a blue clue on a blue 2 would connect to a blind-play of blue 1. Or, a number 2 clue on a blue 2 would connect to a blind-play of blue 1.
In a Bluff, we say that the clue does not "connect" to the blind-play. For example, a blue clue on a blue 2 does not connect to a blind-play of a red 1. Or, a number 2 clue on a blue 2 does not connect to the blind-play of a red 2.
In the Trash Bluff example above, a number 1 clue on a blue 1 is used to Trash Bluff a blue 2. Similar to a Bluff, we would say this number 1 clue does not connect to the blind-play of a blue 2.
What if a Trash Bluff using a number 1 clue instead got a red 1 to blind-play? In this context, the red 1 would actually "connect" to the number 1 clue. Another way of saying this is that by cluing a trash 1 with a number 1 clue, the clue giver is saying that they see a matching 1 that is good.
Thus, it is possible to perform a Trash Bluff outside of Bluff Seat if the "connecting" card is on someone's Finesse Position. When this is done, it promises that someone has that specific card, so we call it a Trash Finesse rather than a Trash Bluff.
For example, in a 4-player game:
All the 1's are played on the stacks except for red 1.
Alice clues number 1 to Donald, which touches a blue 1. To Donald, this will look like it is a red 1.
At first glance, Bob might think this is a Trash Bluff, causing him to blind-play his Finesse Position card as either red 1 or some other currently-playable card.
However, Bob also sees that Cathy has a red 1 on her Finesse Position. Thus, Alice's clue was a Trash Finesse instead of a Trash Bluff, since it promises a playable 1.
Thus, Bob discards.
Cathy blind-plays her Finesse Position card and it is red 1.
Donald discards his known-trash 1.
In the case where multiple cards are clued as part of a Trash Finesse, all of the touched cards are considered to be trash. (This is same thing that happens in a Trash Bluff.)
Double Trash Finesses are explicitly disallowed. Thus, it is possible to perform a Trash Finesse in a situation like this:
All the 1's are played on the stacks except for red 1 and blue 1.
Alice clues number 1 to Donald, which touches two green 1's on slot 1 and 2. To Donald, this will look like it is both the red 1 and the blue 1.
Like in the previous example, Bob sees that Cathy has a red 1 on her Finesse Position.
At first glance, Bob might think that Alice is promising both red 1 and blue 1, which would mean that he would need to blind-play the blue 1.
However, a Trash Finesse only promises at least one matching card, and since he sees that Cathy has a matching card, then that is good enough. Thus, Bob discards.
Cathy blind-plays her Finesse Position card and it is red 1.
Donald knows that the focus of the clue (slot 1) is certainly trash, since that caused Cathy to blind-play.
Furthermore, Donald knows that his slot 2 card is also trash, because all the cards touched in a Trash Bluff or Trash Finesse are guaranteed to be trash.
It is also possible to perform a Trash Finesse in reverse. This is much harder to see than a forward Trash Finesse. Even so, players should generally entertain the possibility of this occurring.
When a clue looks like it could be a Reverse Trash Finesse, the player who receives the clue is forced into immediately discarding the card. If it was indeed a Reverse Trash Finesse, it will be a trash card and it will immediately demonstrate what is going on. Alternatively, if the clue was a normal Play Clue on a playable card, then the discard will be a Gentleman's Discard. By discarding, it covers both cases.
For example, in 3-player game:
The red 1 is played on the stacks. All of the 2's are played on the other stacks.
Alice clues number 2 to Bob, touching his slot 1 card as a Play Clue.
From Bob's perspective, this is probably just a Play Clue on the red 2 (which happens to be the final 2 that needs to be played).
However, Bob sees that Cathy also has a red 2 on her Finesse Position. That means that this could be a Reverse Trash Finesse.
If it is a Reverse Trash Finesse, then his 2 is a trash 2 (e.g. green 2). By immediately discarding it, it will prove to Cathy that she has a red 2.
Alternatively, if Bob does indeed have the red 2, then he can discard it to perform a Gentleman's Discard on Cathy.
Either way, discarding will cover both cases. Bob discards the 2 and it is revealed to be a green 2.
Cathy comes next. Cathy was highly surprised when Alice gave Bob a number 2 clue on the green 2. From Cathy's perspective of Bob's perspective, the green 2 clue would immediately misplay as red 2. However, when Bob discards the green 2 instead of playing it, Alice's plan becomes clear. Cathy had the red 2 all along. Cathy blind-plays her Finesse Position card as red 2.
Note that Reverse Trash Finesses should not always be entertained and depend on context. Specifically, towards the end of the game, Reverse Trash Finesses are "turned off". This is because towards the end of the game, the team needs Tempo, and Reverse Trash Finesses are slow and require even more discarding.
In the H-Group, we like to find the "best" move for every turn in the post-game review. This is fun and helps everybody improve. But this can be taken too far.
Sometimes, players will give clues that are very complicated. Maybe the clue looks like it could be two different moves. Or, maybe the clue relies on non-obvious contextual factors.
Often, these kinds of complicated clues end up in misplays and lost games. And in the post-game review, the people who gave the clues get defensive: "if everyone just played perfectly, then my clue would have worked!"
It's natural for people to feel this way, because normally, if Alice performs a Finesse, and Bob is not paying attention and misses it, then we would say that Bob is at fault. But things are a little different when Alice gives a really complicated clue that Bob should technically be able to figure out, but doesn't. In this case, Bob shares a little of the blame, but it is mostly Alice that is at fault.
Part of being good at Hanabi is recognizing when you should not try to do the most-optimal clue for the turn, because it would be confusing for your teammates. Clue clarity is really important and you should prioritize it! In the post-game review, you can always say: "On turn X, I considered this more-efficient clue, but it did not seem very clear. So I did this other more-clear clue instead."
Don't give confusing clues. If you do decide to give a confusing clue, and it doesn't work out, then you are at fault. This principle is more important than nearly all other principles.