Note: The contents of this page were taken from here with heavy editing.
Floris van Doorn created a convention framework called Hat-Guessing in June 2016. This is based on the paper How to Make the Perfect Fireworks Display: Two Strategies for Hanabi by Christopher Cox, Jessica De Silva, Phillip Deorsey, and Josh Tobin.
- In most Hanabi convention frameworks, you clue cards to tell the player to play that card (or discard that card). In Hat Guessing, clues have nothing to do with the cards that are "touched" by the clue.
- When a player gives a clue in Hat Guessing, they encode actions for all other members of the team within the clue using modular arithmetic.
- For example, on the first turn of a 4-player game:
- Alice goes first.
- Bob has blue 1 on slot 1, Cathy has red 1 on slot 1, and Donald has green 1 on slot 1.
- So, Alice wants all three of her teammates to play slot 1.
- From the clue interpretation table below, we see that "play slot 1" is assigned a value of 1.
- Alice adds up all of the actions: 1 + 1 + 1 = 3
- Thus, Alice needs to convey "3" to the team, so she clues red to Bob (which is color not on the newest card to the player one seat away).
- Bob comes next and has to figure out which move that Alice has planned for him.
- From the clue interpretation table below, Bob knows that Alice encoded a value of 3.
- Bob also can look ahead and see that Cathy will be assigned a value of 1 and Donald will be assigned a value of 1.
- Bob calculates: 3 (Alice's clue) - 1 (Cathy's future action) - 1 (Donald's future action) = 1 (play slot 1)
- Bob blind-plays slot 1.
- Cathy performs a similar analysis that Bob does, but it is a bit easier for her. Instead of having to figure out the actions of two future players (Cathy + Donald), she only has to figure out the action of 1 player (Donald) in order to make her calculation.
- Cathy calculates: 3 (Alice's clue) - 1 (Bob's past action) - 1 (Donald's future action) = 1 (play slot 1)
- Cathy plays slot 1.
- Donald has the easiest time of all. He does not have to figure out anyone's action. He just has to plug in the values for what the two previous players did in order to determine that he is supposed to play slot 1.
- Donald calculates: 3 (Alice's clue) - 1 (Bob's past action) - 1 (Cathy's past action) = 1 (play slot 1)
- Donald blind-plays slot 1.
| # mod 9 |
action |
person clued |
type of clue |
| 0 (9) |
give clue |
1 player away |
number on newest |
| 1 (10) |
play 1 |
1 player away |
color on newest |
| 2 (11) |
discard 5 |
1 player away |
number clue which is not 1 and doesn't touch newest |
| 3 (12) |
play 3 |
1 player away |
color clue not touching newest |
| 4 (13) |
play 4 |
2 players away |
number on newest |
| 5 (14) |
play 5 |
2 players away |
color on newest |
| 6 (15) |
discard 2 |
2 players away |
number clue which is not 1 and not on newest |
| 7 (16) |
discard 3 |
2 players away |
color clue not on newest |
| 8 (17) |
discard 4 |
any player |
number 1 clue not on newest |
| # mod 12 |
action |
person clued |
type of clue |
| 0 (12) |
give clue |
1 player away |
number on newest |
| 1 (13) |
play 1 |
1 player away |
color on newest |
| 2 (14) |
play 2 |
1 player away |
number not on newest |
| 3 (15) |
play 3 |
1 player away |
color not on newest |
| 4 (16) |
play 4 |
2 players away |
number on newest |
| 5 (17) |
discard 1 |
2 players away |
color on newest |
| 6 (18) |
discard 2 |
2 players away |
number not on newest card |
| 7 (19) |
discard 3 |
2 players away |
color not touching newest card |
| 8 (20) |
discard 4 |
3 players away |
number on newest |
| 9 (21) |
3rd rightmost is critical |
3 players away |
color on newest |
| 10 (22) |
2nd rightmost is critical |
3 players away |
number not on newest |
| 11 (23) |
rightmost is critical |
3 players away |
color not on newest |
| # mod 13 |
action |
person clued |
type of clue |
| 0 (13) |
give clue |
1 player away |
number on newest |
| 1 (14) |
play 1 |
1 player away |
color on newest |
| 2 (15) |
play 2 |
1 player away |
number not on newest |
| 3 (16) |
play 3 |
1 player away |
color not on newest |
| 4 (17) |
play 4 |
2 players away |
number on newest |
| 5 (18) |
discard 1 |
2 players away |
color on newest |
| 6 (19) |
discard 2 |
2 players away |
number not on newest |
| 7 (20) |
discard 3 |
2 players away |
color not on newest |
| 8 (21) |
discard 4 |
3 players away |
number on newest |
| 9 (22) |
slot 1 is critical |
3 players away |
color on newest |
| 10 (23) |
slot 2 is critical |
3 players away |
number not on newest |
| 11 (24) |
slot 3 is critical |
3 players away |
color not on newest |
| 12 (25) |
slot 4 is critical |
4 players away |
any clue |
- A positively identified (i.e. touched by a clue) card is defined as an Obvious play if it can be deduced as such purely through
- the positive and negative information on it
- the state of the play stacks
- the state of the discard stacks
- totally identified cards in hands
- Global Elimination Notes
- In a similar fashion, critical cards can be Obviously critical, and known-trash cards can be Obvious discards.
- A card is never Obvious if a player needs to use contextual knowledge to determine the identity.
- The fastest way to check if a card is an Obvious play, an Obvious critical, or an Obvious discard is to:
- use empathy mode
- ignoring the crosses that originate from not-totally-identified cards in hands
- check all resultant possible identities against the play stacks
- This concept is used as an error mitigation tradeoff. For example, it is easy for a player to miss a negative 5 on an unclued chop card, and the benefit of being able to skip cluing non-obviously known cards is quite small.
- A called card is any card that has been targeted by an instruction.
- In Hat Guessing, trash cards are called to be discarded.
- If a non-trash card is called to be discarded, this indicates the presence of the other copy in someone else's hand.
- When this happens, all players should make Elimination Notes on the relevant cards. (Elimination Notes are a concept borrowed from the H-Group Convention Framework.)
- This convention does not always apply if the discarder is the First Responder. See After Executing an Action.
- If the other copy is in the same hand as the one that triggered the Elimination Notes, then the Elimination Notes should be written to the right of the card. For example, in a 3-player game:
- It is the first turn of the game and nothing is played on the stacks.
- Alice gives a Hat-Guessing clue.
- Bob calculates that Alice told him to discard slot 3, so he discards slot 3, and it is a blue 3.
- Bob knows that the blue 3 is not a trash card - the team still needs it. Alice was not allowed to make him discard that.
- Thus, Bob writes Elimination Notes for blue 3 on slot 4 and slot 5 (the two slots to the right of where he originally discarded the blue 3).
- Duplicate copies of currently-called playable cards (from a previous clue) are considered to be trash.
- When giving a clue in Hat-Guessing, you give each other player an instruction.
- You have to give each player an instruction with the highest possible priority:
- Play instruction (regardless of whether the target is clued or not)
- Discard instruction or critical save instruction (see below)
- Clue instruction
- You cannot target a card that has already been given an instruction from a previous clue.
- You cannot target a card that is already an Obvious trash card, an Obvious discard, or an Obvious critical card.
- Sometimes, a player has more than one uncalled playable card in their hand.
- In this situation, you must give them a play instruction with the highest possible priority:
- Unique cards (e.g. 5s, critical cards, and cards of which the player holds all copies)
- Leftmost 1 where the player holds two copies
- Lowest rank
- Leftmost
- If a player does not have any uncalled playable cards, then you can give them a "discard" instruction or a "save this critical card for later" instruction.
- In this situation, you must give them an instruction with the highest possible priority:
- Discard of the rightmost of the leftmost copies of important dupes in a hand.
- (For example, in a hand of
b2 r2 r2 b2, they should be told to discard slot 2.)
- Discard of the rightmost trash, but only if the receiving player has no queued discard instructions or Obvious trash.
- Critical save the rightmost critical.
- Discard the rightmost trash.
- Whenever someone gives a clue, it always gives an instruction to every other player.
- Each player has a Play Queue.
- These are the cards that this player will play, in the given order.
- All play instructions are added at the end of their Play Queue.
- It is impossible to change the order of the queue, or to get a player to play a card in a non-standard order.
- When giving a clue, you first have to decide in which order the players are able to respond. This is called the Respond Order.
- The players with the longest Play Queue respond to this clue last.
- If tied, the player furthest away from you responds last.
- You have to decide the instructions in reverse Respond Order.
- This is relevant when two players have the same playable card in their hand: you should give this instruction to the last player in Respond Order, and give a different instruction to the first player in Respond Order.
- For example, in a 4-player game:
- It is the first turn of the game and nothing is played on the stacks.
- Alice sees that both Cathy and Donald both have a red 1 on slot 1.
- Since Donald is last in Respond Order, Donald will receive the instruction to play red 1.
- Cathy will not receive the instruction to play red 1. Instead, Cathy will get an instruction to play the leftmost 1 behind the red 1 (if any), or some other instruction.
- When interpreting the clue, Bob has to make sure to also assign the red 1 play instruction to Donald, and not to Cathy.
- If, instead, Cathy still has green 1 to play from a previous clue, and Donald has an empty Play Queue, then Cathy is last in Respond Order. Cathy will get the instruction to play red 1, and Donald will get a different instruction.
- The first player in Respond Order is called the First Responder, and the last player in Respond Order is called the Final Responder. Every other player is called an Intermediate Responder.
- Critical Instructions can be given in 4 and 5 player games. They are not present in 3 player games.
- In 4 player games, you count from the right to indicate which card is critical. You skip all called cards, and cards that are known to be not critical.
- For example: If Donald has a red 5 in slot 4 that was already called as critical, and you now want to tell him that slot 3 is also critical, you assign him 11 (rightmost critical).
- When giving a Discard Instruction, if one copy of a card has been given a play instruction from a previous clue, then you must count the other one as trash, even if the first copy is not yet played.
- You are not allowed to give a discard instruction to the second copy of a card if you gave a play instruction to the first copy in the same clue (except if the First Responder Exception applies).
- After assigning an instruction to everyone, add up the instruction numbers, and look in the table to see what kind of clue that you should give to convey the specified [Clue Value].
- If you are allowed to give multiple clues, then you should give the clue that would touch the most useful cards or give the most new information.
- Good Touch Principle does not apply. You are allowed to touch trash cards if that would give more information to other useful cards.
- If you cannot give a legal clue with the desired instruction number, you should assign a different action to the First Responder that does allow for a valid clue (this is unlikely to happen in No Variant).
- After giving a clue, the receiving player will obviously gain positive or negative information on the cards in their hand.
- This information might be enough to give them a new Obvious Play. If this is the case, the Obvious Play is added as a play instruction at the end of the Play Queue.
- If a player received a play instruction as part of the same clue that gave them the Obvious Play, then the play instruction is added to the Play Queue first.
- If multiple cards become Obvious Plays, they are added to the Play Queue from left to right.
- No Finesses can be performed in Hat Guessing. This follows from the fact that instructions are decided in reverse Respond Order.
- It is possible to give play instructions to cards that would play on top of cards in the Play Queue of some player.
- This is of course only possible if the intermediate card is played before the turn when the player receiving the instruction will try to play their card.
- The clue giver, and all players interpreting the clue, will know the exact Play Queues of all players, and can decide whether this is true.
- The First Responder is the first person to respond to a clue. This is usually the player immediately after the clue-giver. If that player has a non-empty Play Queue, then it might be a different player.
- As a special exception, a clue giver may give any play instruction or new discard instruction to the First Responder. This does not need to follow Instruction Priority. (The reason is because they can immediately demonstrate their action to the rest of the team.)
- The clue giver is still not allowed to give a discard instruction on a card that is already known trash (either by a previous discard instruction, or by positive/negative information).
- For example, in a 3-player No Variant game:
- It is the first turn of the game and nothing is played on the stacks.
- Bob's hand is, from newest to oldest,
r1 y1 g1 r3 r3.
- Alice knows that normally, the red 1 has play priority, since it is the leftmost 1.
- However, Alice also sees that Donald has the yellow 2 in his hand. It would be useful to get the yellow 1 to play before the red 1, so that the team can get the yellow 2 played sooner than later.
- Alice also knows that since Bob is her First Responder, she can break the play priority and just get Bob to play any card she wants. Alice will give a play instruction for Bob to play the yellow 1.
- Unlike play instructions and discard instructions, clue instructions and critical instructions given to the First Responder still have to follow Instruction Priority as per normal.
- If given a clue instruction or a critical instruction, the First Responder must give a clue, or discard a card they already knew was trash.
- If given a play instruction or a discard instruction, the First Responder must respond immediately. They are not allowed to defer this action or discard a different card first.
- In some cases, this means that the First Responder might need to "jump" ahead of previous discard instructions.
- For example, in a 4-player game:
- All the 1's are played on the stacks.
- Alice gives a clue that instructs Bob to play slot 1, Cathy to clue, and Donald to discard slot 4.
- Bob blind-plays slot 1. It is a red 2 and successfully plays.
- From Cathy's perspective, Donald's hand is, from newest to oldest,
r4 b4 r1 r1.
- Donald already knows that his slot 4 card is trash, and Cathy is not allowed to repeat this instruction. Cathy decides to tell Donald that his slot 3 card is trash.
- Cathy gives a clue that instructs Donald to discard slot 3, Alice to play slot 1, and Bob to play slot 1.
- Donald knows that the first clue told him to discard slot 4 and the second clue told him to discard slot 3. Normally, he would follow the instructions in order. But in this case, since he is Cathy's First Responder, it is his responsibility to immediately demonstrate Cathy's instruction for him to the entire team. Thus, Donald discards slot 3 (instead of slot 4).
- For example, in a 4-player game:
- The setup is the exact same as the previous example, except that Donald's hand is
r4 b4 y4 r1.
- In this hand, Cathy has no additional information to convey to Donald. He already knows about his one trash card, and the rest of the cards are not-yet-playable, but still useful to the team.
- If the team has no playable cards, Cathy could decide to instruct Donald to discard one of his 4s. Otherwise, Cathy needs to give a clue instruction to Donald.
- On Donald's turn, he knows that Cathy instructed him to give a clue. And since Donald is Cathy's First Responder, he must immediately react to whatever Cathy told him.
- Donald has to give a clue, or discard slot 4, which he knows is trash from a previous clue. All players know that in both cases, Cathy instructed Donald to give a clue, since Cathy is not allowed to give a discard instruction on cards that are already known to be trash.
- When it is your turn, you should first play any cards still in your Play Queue from previous clues.
- You must do this before interpreting new clues, since later play instructions could be calling cards that play on top of existing cards in your hand.
- This means that a player may not know exactly how big their Play Queue is. However, they will always know if their Play Queue is empty or not (and what the first instruction is).
- Every player with an empty Play Queue also knows the full Play Queue of every player.
- If your Play Queue is empty, you can interpret the next clue (the first clue that you have not interpreted before).
- This will only be accurate if every player before you in Respond Order has already performed their action. (In other words, you must wait until it is your turn in order to interpret a clue.)
- Oftentimes you can make a good guess of every instruction to the players before you. But make sure to pay attention if they deviate from the expected instructions!
- When interpreting a clue, make sure to go back to the turn when the clue was given, to correctly interpret the positions of all cards.
- To find out what instructions are contained within a clue, read the Clue Value from the table.
- Subtract the Instruction Value from all players that were before you in the Respond Order.
- You can determine these Instruction Values from the actions of the other players.
- If a player played a card from this clue, you know they received a Play Instruction on that card.
- Exception: if this card could not have been gotten with the clue (for example, if a Finesse was required), then they must have received a different instruction, and they deduced that their card was playable through public or private information.
- If the first responder discarded a card, they received a Discard Instruction on that card.
- In any other case (if any player gave a clue, or if an Intermediate Responder discards), you can deduce what instruction was given to them by applying the Instruction Priority on their hand (using the exact state of the board when the clue was given, before using the positive or negative information by that clue).
- Subtract the Instruction Value from all players that are after you in the Respond Order.
- You can deduce what instruction was given to them by applying the Instruction Priority on their hand.
- Make sure to assign their instructions in reverse Respond Order, just like the clue giver did.
- The remaining number is your Instruction Value.
- As mentioned previously, the First Responder is required to follow any play or discard instruction. Moreover, if the First Responder receives a clue or critical instruction, they are required to give a clue.
- Any Intermediate Responder is required to follow all play instructions given to them. The Final Responder should generally also do this, but has Final Freedom.
- When they receive any other instruction (discard, critical, clue), they should mark the card as called trash or called critical.
- In this case, they can use their judgment to decide what to do.
- They can discard a card (either from this instruction, or a previous instruction, or an Obvious trash card).
- They can give a clue (if they think that is useful enough).
- In rare cases, they can play a card.
- This is uncommon, since usually they would have received a play instruction on that card if they want to play it now.
- It is possible that this play instruction was illegal (for example, if it was a Finesse).
- In this case, they can play this card, and every player can reason that this player did not receive this play instruction.
- If you play a card, this might make some cards in any player's hand Obviously Playable. These cards are added to their respective Play Queues.
- If multiple cards are about to be added to a player's Play Queue, this is done from left to right.
- Usually this will not allow the other card to be added to the Play Queue, since the cards could be the same.
- If multiple players are about to add a card to their Play Queue, the player that is first in Respond Order does it first.
- This is the player with the shortest Play Queue. On a tie it is the player first in turn order.
- This can cause the card in the other player's hand to not be added, if the cards could be identical.
- If you discard a useful card, this sometimes triggers Global Elimination Notes.
- If you are the First Responder, this does not happen when you discard a 3 or 4.
- Sometimes it is necessary to let a useful card die in order to draw playable cards.
- If you discard a 2, the player that doesn't see the other copy of that 2 makes Global Elimination Notes.
- If you are not the First Responder, you make Global Elimination Notes when you discard any useful card.
- Sometimes you can discard a playable card. This will only happen if another copy of that card is already in someone's Play Queue.
- If a player is required to make Global Elimination Notes, everyone should also make these notes on that player's hand.
- In rare cases, the Final Responder to a clue can ignore a play instruction given to them. This is called having Final Freedom.
- They are not allowed to do this if they might have a Play Queue longer than 1.
- They should only do this if they know the exact identity of their playable card (from the context of the game), and if they can give a very useful clue.
- If the player in Final Freedom knows that they have called the other copy of their card, they can discard their copy to make it clear to the team what has happened.
- If a misplay occurs as the result of a clue, all further instructions from that clue are cancelled, without exception.
- If that leaves a player with no instructions to process, that player will give a clue, and they have to assign play instructions to cards that might have been called already before.
- A player without a new instruction is still allowed to play the card that they thought was targeted (at their discretion). This convention only means that when giving new clues, instructions have to be repeated.
- Sometimes it is valuable to revert to ordinary conventions.
- When there are only 5s left to play, a 5 clue not on the newest card is a non-hat clue, since an alternative hat clue exists.
- From then on, no clues should be interpreted as hat clues anymore.
- In many custom variants, it is hard to guarantee that a clue will not be "blocked".
- In these cases you will need to remove some rows from the tables.
See Jeff's document for tables that allow Finesses.
See Jeff's document.