The Occupied Play Clue & The Occupied Finesse (OPC)
Often, players will have a choice between playing a card and giving a clue. By default, it makes more sense for players to play the card and let some other teammate give the clue. That's just good teamwork!
On the other hand, in a lot of situations, players who have a playable card will still need to give a clue. Since Hanabi has asymmetric information, it is common that only one player will have the necessary knowledge to perform a Finesse or Prompt (or some other time-sensitive clue). Thus, if a player with a playable card is the only one who can reasonably give a certain type of clue, then it makes sense for them to perform the clue now, and then play their playable card later.
Similarly, if there are two or more clues that need to be given, then it makes sense for Alice and Bob to team up and perform the two actions in sequence. (If Alice has a playable card, this isn't really relevant; the two things would need to be clued regardless of whether Alice had a playable card or not.)
This section does not apply to those situations. Rather, it only applies when a clue really could have been given by two or more players, but a player with a playable card "stole" the clue, leaving the next player with nothing to do but to discard.
If a player "steals" a clue in this way, we would say that the player was Occupied. When an Occupied player gives a clue, it has a special meaning:
If the clue would normally be interpreted as a Save Clue, then it transforms into an Occupied Play Clue.
If the clue would normally be interpreted as a Play Clue, then it transforms into an Occupied Finesse.
And so on. In general, an Occupied move does one "extra" thing than would it normally would do.
For example, in a 3-player game:
Red 2 and blue 1 are played on the stacks.
Alice has a globally-known playable red 3 in her hand and Bob has nothing to do.
Alice clues number 2 to Cathy, which touches a green 2 on her chop. This would normally be a 2-Save.
However, since Alice is Occupied and Bob could have given the exact same clue, and Bob has nothing to do on his turn but to discard, the 2 Save transforms into an Occupied Play Clue.
Next, Bob sees that Alice's clue was Occupied. Thus, Bob knows that Cathy will go on to play the card.
If Bob does nothing, Cathy will think that this is an Occupied Play Clue on the blue 2. Since she really has a green 2, it will misplay.
Thus, Alice must intend for an Occupied Finesse. Bob plays his Finesse Position. It is a green 1 and it successfully plays.
Sometimes, a player will have two playable cards in their hand of the same suit, but they will be "blocked", meaning that both a color clue and a number clue will not be able to focus the first playable card.
One technique to get around this is to give a clue that focuses the wrong card, and then have the next player give a Fix Clue. This is called an Out-of-Order Play Clue because the cards were originally out-of-order, but the original focus is still playable.
For example, in a 3-player game:
It is the first turn and nothing is played on the stacks.
Cathy hand is as follows, from left to right: red 4, red 1, red 2, red 3, blue 4
Alice clues red to Cathy, touching slot 1, slot 2, slot 3, and slot 4.
Bob sees that Alice has indicated to Cathy that she has the red 1 on slot 1. Cathy will go on to misplay the red 4 as the red 1.
Normally, Bob would think this is a Finesse and try to play the red 1 into the red 4. However, that doesn't make any sense, because Cathy has the red 1, and then Alice would be violating Good Touch Principle.
Instead, Bob knows that the team should be using Cathy's red 1. Thus, Bob knows that he needs to give a Fix Clue to Cathy, because Alice intends for her and Bob to work together.
Bob clues number 4 to Cathy, touching the blue 4 and "filling in" the red 4.
Cathy is surprised because the card that she thought was red 1 is actually a red 4. Cathy knows that since the red 4 was the original focus of Alice's clue, then it must actually be playable right now. Thus, Cathy must have the red 1, the red 2, and the red 3.
Cathy plays the red 1 from slot 2 (the left-most red card that could be the red 1). She will go on to play the red 2, the red 3, and the red 4.
Cathy (and everyone else on the team) knows that even though the blue 4 was the focus of Bob's clue, it is not actually playable right now, and was just "collateral damage" of Bob's required Fix Clue.
Sometimes, a Finesse is initiated by giving a color clue that focuses the wrong card.
When this happens, the Finesse will still work: a player will blind-play a connecting card. However, a Fix Clue must then be given to the player who received the clue, or they will go on to misplay.
Normally, after receiving a Fix Clue, a player would "stop" and not assume anything else about his hand. However, when an Out-of-Order clue is given, the player should always go on to play the original focus of the clue.
For example, in a 3-player game:
It is the first turn and nothing is played on the stacks.
Bob has a red 3 and a red 2 (on slots 1 and 2 respectively).
Cathy has a red 1 on slot 1 (in Finesse Position).
Alice clues Bob red (as an Out-of-Order Reverse Finesse). The focus of the clue is the red 3 on slot 1.
Bob sees the red 1 on Cathy's Finesse Position, so he has to respect that it could be Reverse Finesse. Bob discards.
Cathy blind-plays red 1.
Alice must now give a Fix Clue to Bob, or else red 3 will be misplayed as red 2.
Alice clues number 2 to Bob.
Bob plays red 2.
Bob knows that his other red card must be red 3, since it was originally clued as playable and it caused a Reverse Finesse.
The 5 Color Ejection takes precedence over the Out-of-Order Finesse as long as the two-or-more-blind-plays rule is satisfied.
For example, in a 3-player game, this would be a 5 Color Ejection:
It is the first turn of the game and nothing is played on the stacks.
Alice clues red to Cathy, touching a red 5 on slot 1, a red 1 on slot 2, and a red 2 on slot 3.
Bob knows that this could be an Out-of-Order Finesse. Specifically, if Bob gives a follow-up number 5 Fix Clue to Cathy, then Cathy would play the red 1, Cathy would play the red 2, and Bob would blind-play the red 3, Bob would blind-play the red 4, into Cathy's red 5.
However, this line would require Bob to blind-play 2 cards, so Bob knows that he should prefer a 5 Color Ejection instead.
For example, in a 3-player game, this would be an Out-of-Order Finesse:
It is the first turn of the game and nothing is played on the stacks.
Alice clues red to Cathy, touching a red 5 on slot 1, a red 1 on slot 2, a red 2 on slot 3, and a red 4 on slot 4.
Bob knows that this could be an Out-of-Order Finesse. Specifically, if Bob gives a follow-up number 5 Fix Clue to Cathy, then Cathy would play the red 1, Cathy would play the red 2, Bob would blind-play the red 3, Cathy would play the red 4, and then Cathy would play the red 5.
Since this line only requires that Bob blind-plays 1 card, he knows that it cannot be a 5 Color Ejection, so Bob performs the Fix Clue to allow for the Out-of-Order Finesse.
Normally, if Alice gives a clue to Cathy touching the next playable card, but the focus is wrong, Bob would treat it as an Out-of-Order Play Clue. He would then give a Out-of-Order Fix Clue (instead of blind-playing a card).
Thus, if Alice gives a clue to Cathy, and Bob does blind-play a card, then by default, Cathy can mark all the cards that were touched with a note of not being the next playable card.
For example, in a 3-player game:
Red 2 is played on the stacks.
Alice clues red to Cathy, touching two cards on slot 1 and slot 2.
Bob blind-plays an unrelated card.
Cathy marks her slot 1 card as the red 4. (Cathy knows that Alice performed a Bluff and slot 1 was the focus of the clue.)
Cathy also marks her slot 2 card as the red 5. (Cathy knows that if it was a red 3, then Bob would be forced to give a Fix Clue.)
The Suboptimal Prompt & The Suboptimal Finesse & The Suboptimal Bluff
If the other copy of a card is in the trash, then the remaining copy is critical and needs to be saved. Critical cards of this nature can be saved with either a color clue or a number clue.
If both types of clues will only introduce one new card, then it is said that that there is a Free Choice between the two clue types.
In this situation, the clue type will be chosen that "fills in" other ancillary cards in the hand or gives important negative information.
If a clue type is chosen that is clearly worse than the other one, then the clue giver must be trying to communicate something extra.
The means that this innocent-looking Save Clue is really a Play Clue, and all of the in-between cards are called for.
Note that for a Suboptimal Save Finesse to work, the clue has to be really bad, not just technically suboptimal in some slight way.
Care has to be taken so that a Bluff does not look like a Finesse.
For example, in a 4-player game:
Red 2 and blue 2 are played on the stacks.
Alice clues Cathy number 4, which touches a red 4.
Bob blind-plays a blue 3 from his Finesse Position.
Since 3 connects to 4, Cathy knows she has the blue 4, and goes on to misplay red 4 as blue 4.
Thus, Alice should not have given this clue.
However, what if someone else on the team already has the connecting card? In this situation, the clue can be given without fear: from Good Touch Principle, the clue recipient will know that it is a Bluff instead of a Finesse.
For example, in a 4-player game:
Red 2 and blue 2 are played on the stacks.
Alice clues Cathy number 4, which touches a red 4.
Bob blind-plays a blue 3 from his Finesse Position.
Cathy's first thought is that since 3 connects to 4, she must have the blue 4. However, Cathy sees that Donald already has a clued blue 4 it in his hand. (The blue 4 just has a blue clue on it and the true identity of the card is not yet known to Donald.)
Cathy knows that she must not have the blue 4, because then Alice's clue would have violated Good Touch Principle. Cathy can reason that her 4 is instead some otherone-away-from-playable 4. The only other valid Bluff target is the red 4 (because the only one-away-from-playable 4 is red 4). So, Cathy marks her number 4 card as a red 4, and discards.
Donald is surprised by Alice's clue. From Donald's perspective, Cathy should have misplayed the red 4 as the blue 4, since 3 connects to 4.
Since Cathy did not misplay, Donald can reason that he must have the blue 4. Donald marks the previously unknown blue card in his hand as blue 4.
Sometimes, a card that is two-away-from-playable is re-clued in order to initiate a Finesse or a Bluff. Most times, the clue will "fill in" or give extra information to the existing card.
Other times, the clue will give no information (e.g. re-cluing number 3 to an already known 3). In this situation, if it was merely a Bluff, it would be pretty low value.
Thus, by convention, a "no information" clue on a two-away-from-playable card must "get" at least 2 new cards (as opposed to a single Bluff that only gets 1 new card).
For example, in a 3-player game:
Nothing is played on the stacks.
Alice clues 3's to Cathy, which touches one 3, the red 3.
Bob blind-plays blue 1. At this point, everyone knows that Alice has performed a 3 Bluff, and from Cathy's perspective, her 3 can be any 3 at all.
Cathy discards.
Alice clues 3's to Cathy, which re-touches the red 3 (and gives no additional information to it).
Bob blind-plays red 1. If this was a 3 Bluff, then no-one would be promised the red 2. However, since no new information was given, it must be a No-Information Double Finesse. Bob sees that Cathy does not have the red 2, so he must have the red 2, and can blind-play it on his next turn.
The "no-information" principle can also be used to perform a No-Information Layered Finesse on the next player. (The next player will know that it is a Layered Finesse instead of a Bluff because some other more-useful clue could have been given to initiate the Bluff.)
Usually, a "no-information" clue conveys a Double Finesse. But you can also use it to perform a Double Bluff (or a Double Half Bluff). For example, in a 3-player game:
Nothing is played on the stacks.
Alice clues 3's to Cathy, which touches one 3, the red 3.
Bob blind-plays blue 1. At this point, everyone knows that Alice has performed a 3 Bluff, and from Cathy's perspective, her 3 can be any 3 at all.
Cathy discards.
Alice clues 3's to Cathy, which re-touches the red 3 (and gives no additional information to it).
Bob blind-plays green 1. If this was a 3 Bluff, then no-one would be promised the green 2. However, since no new information was given, it must be a No-Information Double Finesse.
Cathy sees that Bob does not have the green 2, so she must have the green 2, so she blind-plays her Finesse Position card, and it is yellow 1 instead of green 2.
Since two cards were blind-played (that did not connect to anything), everyone now knows that the No-Information clue was a Double Bluff instead of a Double Finesse. From Cathy's perspective, her 3 can (still) be any 3 at all.