This level introduces Bluffs, a way to tell a Fib to the next player to cause them to blind-play.
Bluffs can be very fun, since they allow for a lot more blind-plays than previously possible.
However, the fact that players are no longer always telling the truth to each other causes this level to be much more complicated and difficult to integrate than any of the previous levels.
Make sure that you are totally comfortable with the earlier levels before attempting to add Bluffs to the mix. (We recommend at least 100-200 games of experience.)
Finesses are quite efficient. So, when you see a playable card in someone's Finesse Position slot, you will often want to "get" the card with a Finesse (instead of cluing it directly). However, often times, the proper "connecting" card is not on the table.
In this situation, players can perform an alternate strategy by fibbing to the next player. By cluing an unrelated, one-away-from-playable card, the next player will think that it is a Finesse and that they have the connecting card. Then, they will blind-play their Finesse Position card. This is called a Bluff.
After the card is blind-played, the player who received the clue will realize that something strange has happened - the type of clue did not connect to the card that was blind-played. Thus, the clued card is not currently playable and must be a one-away-from-playable card.
For example, in a 3-player game:
All the 2's are played on the stacks.
Alice clues Cathy red, which touches a red 4 as a Play Clue.
Next, it is Bob's turn. Bob sees that, with this red clue, Cathy has just been signaled that she has the red 3.
From Bob's perspective, this looks like a Finesse - if Bob does not blind-play the red 3 right now, Cathy will go on to misplay the red 4 as the red 3.
Bob blind-plays his slot 1 card, expecting it to be a red 3. Instead, it is a blue 3, and it successfully plays on the stacks. Bob now knows that he was Bluffed by Alice.
Next, Cathy sees that Bob just blind-played a blue 3 immediately after this red clue, so she knows that she must have a one-away-from-playable red card - the red 4. Cathy holds on to the red 4 for later and discards.
Bluffing is only allowed if the very next player will blind-play on the very next turn.
We formalize this concept as Lie Principle:
If a card is represented to be something different than what it really is, and the state of misinformation resolves immediately (i.e. the very next turn), then it is called a Fib. Fibbing is okay.
If a card is represented to be something different than what it really is, and the state of misinformation does not resolve immediately, it is called a Lie. Lies are illegal. Players should never assume that they are Lied to.
Alice clues number 4 to Bob, which touches one new 4 as a Play Clue.
Bob does not see any playable cards in anyone else's hand.
The closest 4 to being playable is the red 4, so Bob knows that the 4 in his hand is probably a red 4.
Since Bob does not see any red 3's, Bob knows he must have the red 3, and he blind-plays his Finesse Position card. It is a blue 1 and successfully plays.
Bob now knows that he was Bluffed by Alice and that the 4 in his hand is exactly the red 4.
It is also permissible to Bluff "through" cards that are already clued. This can be better than a normal Bluff, because in addition to getting the blind-play, it also can give information to the player with the in-between card.
For example, in a 4-player game:
All the 1's are played on the stacks.
Bob has nothing clued in his hand.
Cathy has a red 3 clued in her hand with just a number 3. She does not know what suit it is.
Alice clues Donald red, which touches one red 4 as a Play Clue.
Bob knows that he must have the red 2. If he blind-plays the red 2 (as a Finesse), then Cathy will play the red 3 (as a Prompt), and Donald will play the red 4.
Bob plays his Finesse Position card as a red 2. Instead, it is a blue 2 and it successfully plays.
From Cathy's perspective, she knows that the red 4 is two-away-from-playable instead of one-away-from-playable. Bluffs on two-away-from-playable cards are normally illegal. Thus, Cathy's mystery 3 must be exactly red 3, making the red 4 one-away-from-playable after all.
Cathy discards.
From Donald's perspective, since red (the type of clue that was given) does not connect to blue (the card that was blind-played), this must be a Bluff. Normally, since the red 1 is currently played on the stacks, Donald would think that he has the red 3 (e.g. the one-away-from-playable red card).
However, Cathy already has a clued red 3 in her hand. If Donald also had a red 3, then Alice's clue would be violating Good Touch Principle. Thus, Donald must have the red 4 instead.
Sometimes, the player who has the in-between card might have more than one "matching" clued card. In this situation, the player is promised that they have the in-between card, but they are not promised the position - it can be any of the matching clued cards.
For example, in the previous situation, if Cathy had two different red cards clued in her hand, then either one could be the red 3 - she is not promised the position of the card.
Sometimes, a player will give a clue that looks like it could be either a Finesse or a Bluff. Between these two moves, which should have precedence?
For example, in a 4-player game:
All of the 1's are played on the stacks.
Cathy has a blue 2 on her Finesse Position.
Alice clues blue to Donald, touching a blue 3. This is a Play Clue.
Now, it is Bob's turn.
What to think depends on whether you are Bob or whether you are someone else on the team.
First, let's consider the case of Bob, the very next player. Bob should always assume a Finesse over a Bluff. From his perspective:
Bob knows that if this is a Finesse, then Cathy will blind-play the blue 2, and then Donald will know that he has the blue 3. If this is the case, Bob should not do anything special.
Bob also knows that if this is a Bluff, then Bob should blind-play his Finesse Position card immediately.
Bob knows that if there is any way that this could be a Finesse (the truth), he should assume that the truth is being told. Thus, Bob knows that it must be a Finesse on Cathy and should not blind-play anything.
This is called Bob's Truth Principle, because Bob always assumes the truth over a Fib.
This convention is easy to remember because at the time of the blind-play, Bob does not need to play any differently than he did at level 10. He simply assumes the truth is being told.
Previously, we considered the case of Bob before he blind-played a card.
Now, we can consider the case of Bob after he has blind-played a card, which also extends to Cathy and every other player on the team. How does everyone know whether Alice did a Finesse or a Bluff on Bob?
The way to find out is to look at whether the card that blind-played "connects" to the clue that was given. If the clue connects, then it is a Finesse. If the clue did not connect, then it is a Bluff.
This is called Cathy's Connecting Principle in order to highlight that everyone needs to assume different things than Bob did (before he blind-played anything).
If it is ambiguous whether or not the card connects, then everyone should assume a Bluff over a Finesse. Note that this is the opposite of the precedence in Bob's Truth Principle!
Alice clues Cathy number 4, touching a 4 as a Play Clue.
Bob blind-plays the blue 1.
This could be a Triple Finesse (on blue 1 + blue 2 + blue 3 into blue 4) or it could be a Bluff (on just blue 1 into red 4).
However, this must be a Bluff, because 1 does not connect to 4. So Cathy should think that she has the one-away-from-playable 4, the red 4.
The point of this example is to show that because a 2 happens to be played on the stacks, the red 4 is a one-away-from-playable card and therefore becomes a legal Bluff target.
Example 5: Rank Disconnect Where a Bluff Is Impossible --> Triple Finesse
This is a 4-player game.
Nothing is played on the stacks.
Alice clues Donald number 4, touching a 4 as a Play Clue.
Bob blind-plays the red 1.
Cathy discards.
Donald needs to evaluate whether or not Alice's clue is a Finesse or a Bluff. However, he knows that it cannot be a Bluff, because there are no one-away-from-playable 4's. So even though 1 does not connect to 4, this must be a Finesse, because Alice is not allowed to perform a Bluff with any card that she wants.
Donald does not see any other red cards in Bob's hand. So Donald should think that he has the red 4, because that would connect to the blind-play of a red 1. Subsequently, Donald must have red 2 on his Finesse Position and red 3 on his Second Finesse Position.
Example 6: Rank Connect Where a Finesse Is Impossible --> Bluff
Red 2 and blue 2 is played on the stacks.
Alice clues Cathy number 4, touching a 4 as a Play Clue.
Bob blind-plays the blue 3.
Normally, Cathy would think that this is a Finesse, because 3 connects to 4, meaning that Cathy's 4 is the blue 4.
However, Cathy notices that her 4 has a negative blue clue on it. Thus, it cannot be the blue 4.
This must instead be a Bluff. Cathy marks her 4 as the red 4 (since red 4 is the only other one-away-from-playable 4).
Example 7: Color Connect With Rainbow --> Finesse
This is a game with a rainbow suit. (The other examples in this section assume a "No Variant" game.)
Rainbow 1 is played on the stacks.
Alice clues Cathy red, touching a red card as a Play Clue.
Bob blind-plays a rainbow 2.
This must be a Finesse, because red connects to red (rainbow cards connect to every color). So Cathy should think that she has the rainbow 3.
Example 8: Color Connect With Rainbow Where a Finesse Is Impossible --> Bluff
This is a game with a rainbow suit. (The other examples in this section assume a "No Variant" game.)
Rainbow 1 and red 2 are played on the stacks.
Alice clues Cathy red, touching a red card as a Play Clue.
Bob blind-plays a rainbow 2.
Normally, Cathy would think that this is a Finesse, because red connects to red (rainbow cards connect to every color), meaning that Cathy's red card is the rainbow 3.
However, Cathy notices that her red card has a negative blue clue on it. Thus, it cannot be the rainbow 3.
This must instead be a Bluff. Cathy marks her red card as the red 4 (since the red 4 is the one-away-from-playable red card).
Part of Hanabi involves making sure that if you perform an action, someone else on the team won't discard anything important (e.g. Save Principle). Additionally, part of Hanabi involves accounting for all the possibilities (e.g. Schrödinger's Cat Principle).
Combined, these two principles usually result in players taking the most conservative possible approach, even if a certain action would have a very low risk of losing the game.
One exception to the above rules is when Bob is playing into either a Finesse or a Bluff. In this case, Bob knows that Alice is "guiding" him and he does not have to worry about Cathy's chop card. If Alice needs Bob to save Cathy's chop card, then Alice would wait until later to perform the Finesse or Bluff.
For example, in a 4-player game:
No cards are played on the stacks.
Alice clues red to Donald, touching a red 2 as a Play Clue.
Bob does not see any red 1's in anyone else's hand. Thus, Bob knows that Alice intends for him to blind-play a card.
From Bob's perspective, it can be either a Finesse (on exactly red 1) or a Bluff (on the 1 of any of the other suits).
Cathy has a critical 5 on chop.
Should Bob risk blind-playing or should he save the 5?
Normally, Bob would play it safe and save the 5. However, in this case, he knows that Guide Principle applies, and Alice is guiding him to play right now.
Bob blind-plays his Finesse Position. It is the red 1 and it successfully plays.
Cathy does not discard since Alice saw that Cathy had something to clue.
When a clue could have multiple interpretations, usually Schrödinger's Cat Principle is involved - players must wait a round and see what their teammates do in order to find out the true meaning of the clue. But what if a clue could have multiple interpretations and a player does not have to wait for information from anyone else?
For example:
Alice gives a weird clue to Cathy.
Bob does not see any "connecting" cards in anybody else's hands, so he can rule out a Prompt and he can rule out a Reverse Finesse.
In this situation, we would say that Bob is the reacting player. If a reacting player does not "react" to a clue in some demonstrable way, then someone else on the team will go on to misplay a card. So, the reacting player has to immediately decide what the clue means and perform the resulting action.
In some situations, there can be two reacting players in a row. For example, if Alice clues a two-away-from-playable card, then Bob must react and Cathy must react.
So how does a reacting player figure out what the clue means? They should use Occam's Razor - always assume the simplest possible interpretation.
Assume a direct Play Clue or a Delayed Play Clue (if it could be possible that no Prompts & no blind-plays are involved).
Assume a Prompt (if it could be possible that no blind-plays are involved).
Assume a Finesse (or a Prompt + Finesse) over a Bluff.
Assume the "move" that results in the least number of blind-plays.
In general, this means assuming a one-blind-play Bluff over a two-blind-play Finesse. But keep in mind that only certain cards are legal Bluff targets - you can't just do a Bluff with any card.
Assume the "move" that results in the least number of Prompts.
This means that if something could be either a one-blind-play Finesseor a one-blind-play Finesse with a Prompt involved, then the pure Finesse is simpler and you should assume that.
Before cluing a card directly, you should first consider if the card is on Finesse Position. If it is, and you clue it directly, you may be "stealing" someone's Finesse or Bluff.
Thus, in this situation, it may be better to discard and let the player in Bluff Seat get the card. If you do decide to clue the card directly, you should always feel a Pang of Guilt.
Sometimes, players only play one card into a Layered Finesse, and then stop (when they should instead be digging for the promised card).
Since Bluffs are only allowed from Bluff Seat, if the clue-giver is not in Bluff Seat then such a clue is always a Layered Finesse and not a Bluff.
However, Bluffs take precedence over Layered Finesses from Bluff Seat.
In other words, if Alice gives a clue which causes Bob to blind-play an unrelated card immediately, then Bob should assume a Bluff when possible.
In still other words, Layered Finesses are generally "turned off" from Bluff Seat.
Of course, this only applies if the clue actually satisfies the criteria for a potential Bluff.
In particular, if Alice gives a clue to Bob but Bob does not blind-play immediately, then according to the Lie Principle, the clue should always be interpreted as a Layered Finesse as it cannot possibly be a legal Bluff.
In particular, if Alice gives a clue to Bob which is not a legal Bluff target, the clue should always be interpreted as a Layered Finesse.
It is illegal to trick players into thinking that they are Prompted. Promptsmust be the truth.
For example, in a 4-player game:
Red 1 and blue 1 are played on the stacks.
Bob has a card in his hand with a number 2 clue on it. He does not know its true identity.
Alice clues red to Donald, touching a red 3 as a Play Clue.
Since red 1 is on the stacks, Bob knows that Alice is indicating to the team that someone has the red 2.
Bob looks around and sees that no-one else has the red 2.
Thus, Bob knows that this must be a Prompt, so his unknown 2 must be a red 2. Bob plays the unknown 2. It is instead a blue 2, and it successfully plays on the stacks.
Cathy is slightly surprised that Bob played the blue 2. However, this is not completely out of the ordinary, as Bob might have been able to figure it out somehow.
Cathy performs the same analysis that Bob does. Namely, Cathy knows that Alice is indicating that someone on the team has the red 2, and Cathy does not see the red 2 in anyone else's hand.
Thus, Cathy knows that Alice's clue to Donald must be a Finesse, so Cathy must have the red 2 on her Finesse Position. Cathy plays her Finesse Position card. It is instead the blue 5 and misplays.
This was Alice's fault, because Bluffs are only allowed if they can be revealed immediately from a blind-play.
Queued Finesses are encouraged, since they have few downsides.
However, players should never queue a Bluff on top of a player who is Finessed. This is because the blind-playing player will assume that a Layered Finesse is occurring and go on to play the card from the first Finesse. This means that the Bluff will not be resolved immediately, violating Lie Principle. This mistake is really bad because it causes severe Information Desynchronization.