Reactor is a conventional framework oriented around giving, receiving, and taking safe actions. Players expect to receive safe actions from clues if they are the next player without one. When players receive information, the primary type of information they expect to recieve is actionable information. While every system has to provide actions to a degree, Reactor implementations take that idea to a limit. Reactor is built with the belief that in most gamestates, immediately actionable information is significantly better than inactionable information.
Reactor began as an attempt to tackle the Winter 2022 Holiday Mix Hanabi competition. Referential Sieve originally motivated Reactor: one perspective is that Reactor 1.0 transforms Referential Sieve to further appeal to players who love giving playful positionals.
Why play Reactor?
All basic conventions from Referential Sieve are required to play Reactor 1.0. A complete list of them can be found here: https://hanabi.wiki/en/conventions/ref-sieve-intro
No other Referential Sieve conventions should be used besides a select number of imported conventions detailed below (mostly under the Intermediate/Advanced Conventions section).
The reacter is the first player starting from Bob with no pending (signaled or good touched) plays.
A player is said to be loaded if a player has a pending (signaled or good touched) plays. Having known trash does not make a player loaded.
If everyone else is loaded, there is no designated reactor and Alice's clues to either player become stable clues - unless Alice gives a bad stable clue to Cathy, to which Bob must react immediately. Details on this type of reactive clue is provided in the Bad Stable Clues and Response Inversion section.
Known trash in a player's hand do not count for the purposes of determining the reacter. Most of the time in a typical game, Bob will be the reacter - so unless specified, we will use Bob and reacter, as well as Cathy and receiver, interchangeably in the sections below.
Clues from Alice to the reacter are one of the following types of Referential Sieve style stable clues described in https://hanabi.wiki/en/conventions/ref-sieve-intro:
Usually Alice gives such a clue when she is worried about their chop and wants to give them some alternative safe action.
Unlike in referential sieve, any unloaded rank clue which touches the reacter's rightmost previously-unclued card is a lock clue. They should not discard unless they receive another instruction while locked. This is desirable because if we really wanted Bob to discard something, we would often have ways of signaling that with a reactive clue instead.
The exception is for Clue Starved variants, where rank clues work the same way as in referential sieve even if a rank clue touches the rightmost card. For example, a rank clue touching slots 2 and 5 in Clue Starved calls for slot 3 to discard.
A rank clue to Bob's rightmost previously-unclued card from a locked player or a player at 8 clues is still a lock clue.
In a three player game, each reactive clue provides one safe action to both the reacter and the receiver.
To give a reactive clue, add together the slots of the two actions you're signaling, and give a clue to the receiver focusing that slot number (modulo 5). The focus is defined in the same way as referential play clues, except that the whole hand is treated as unclued: the focus is the leftmost (not necessarily newly) touched card, except that slot 1 has the lowest precedence. This means slot 1 can only be the focus if it is the only card touched.
For example, consider the following hands:
Bob: g4 r1 g1 g4 g5
Cathy: y2 p3 b1 y1 y4
To get Bob to play red 1 from slot 2 and Cathy to play blue 1 from slot 3, Alice would clue rank 4 to Cathy which focuses Cathy's slot 5, since the sum of the targeted slots (2 and 3) is 5.
Alice can also get Bob to play green 1 from slot 3 and Cathy to play blue 1 from slot 3. The sum of the slots (3 and 3) is 6, which itself is not a valid slot but wraps back around to slot 1. Thus Alice needs to find a clue which focus Cathy's slot 1 - a rank 2 clue to Cathy would work!
Alice can also get Bob to discard his duped green 4 on slot 1 while getting Cathy to play her blue 1 from slot 3. The sum of these slots is 4, so now Alice needs a color clue that focuses slot 4. Yellow to Cathy would do the trick, because even though yellow touches the yellow 2 on slot 1, that slot has the lowest precedence so the focus of the clue would be the next leftmost card touched, which is slot 4.
Unfortunately, it is not possible for Alice to get any two cards in Bob and Cathy's hands - like green 1 from slot 3 and yellow 1 from slot 4 for example. Alice and Bob must agree about what action in Cathy's hand a reactive clue is getting. This is accomplished using the concept of targeting priority. It consists of 4 priority levels (from highest priority to lowest priority).
(Cathy's playable) Bob targets the leftmost playable card that does not already have a play signal on it and is not 100% globally known to be playable by empathy. This is known as the leftmost non-obvious play principle.
(Bob-Cathy finesse) Bob tries to play into a one-away-from playable in Cathy's hand as a finesse. The order of slots that Bob tries is 1 -> 5 -> 4 -> 3 -> 2, similar to referential sieve finesse positions, and Bob plays the first of these slots that can possibly work.
Note that this priority level cannot apply to color clues.
(Cathy's trash) Bob targets the leftmost clued trash or dupe in Cathy's hand and discards accordingly. If there are no clued trash or dupes, then Bob targets the leftmost unclued trash or dupe in Cathy's hand. Globally known trash has the lowest priority among trash cards below unclued trash.
(Cathy's sacrifice) Bob targets the furthest from playable (through globally known cards) and non-critical card in Cathy's hand as a sacrifice discard. If there are ties target the card with the highest rank, followed by the leftmost card.
For example, consider the following hands, where cards in bold are globally known. Red 1 and green 1 have been played on the stacks.
Bob: b1 r2 g3 y3 y4
Cathy: p5 r4 b3 y5 g4
Cathy is currently locked and the team is in a difficult position while being low on clues, so we need to unlock Cathy by telling her to discard something. To determine the card to sacrifice, first determining how far away from playable each non-critical card is.
Since blue 3 and green 4 are both 2 away from playable, tiebreak rules picks the higher ranking card (green 4) to sacrifice. Therefore, Alice can clue Cathy purple (focusing slot 1) to get b1 to play from slot 1 and g4 to discard from slot 5.
The status of cards ("clued"/"obviously playable") is determined before the reactive clue touches the receiver's cards. For example, if the leftmost unclued trash card is revealed through the clue, or if the leftmost non-obviously playable card is revealed after the clue is given, the target does not change.
When Bob has no pending plays (so that Cathy is the reacter) and Alice gives Cathy a clue, Cathy should expect to interpret it as a Referential Sieve stable clue. However, if Bob sees that the clue is a bad referential sieve clue, it is always a reactive clue where Bob is the reacter - regardless of how many pending plays each player has! Bob should react to the clue before Cathy has the chance to respond to the RS interpretation.
Specifically, the following apply:
These conventions apply equally to players who are either locked or have 8 clue tokens on their turn.
If Alice is locked, clue that Alice gives to the receiver are usually respected as a true Referential Sieve stable clue. However, if the reacter sees any of the following the clue turns into a reactive clue.
In particular, a slot 1 discard is not a reaction in response to a clue given to Cathy by a locked player if Bob has no other safe actions. Thus locked Alice must remember that any reactive clue which depends on a slot 1 discard from Bob to work can fail and be interpreted as a simple stable clue.
Alice is allowed to lock Bob by cluing rank to his rightmost unclued card even if Alice herself is locked, if the team expects one of the players to be unlocked in the near future.
Sometimes a locked player has no good stable referential play or discard clues available to give. In that case, the following types of clues are permitted as stalls:
If Cathy's hand has a clued but non-obviously playable card, and another unclued copy of the same playable card to the left of the clued copy, then the unclued copy is ignored when computing the target.
If Alice or Bob has a globally known playable card, additional copies of that playable card in Cathy's hand are treated as follows:
Same hand non-playable dupes are always considered trash and have targeting priority over actual trash if they are further to the left for reactive clues.
When a safe action is given to a player (with a card that is called to discard) then the player must erase the discard signal on that card. After performing the safe action, the player is expected to discard his chop if he does not have known trash. The only exception is when the safe action is given through a reactive clue. In this case, the discard signal is still on.
By default, we assume that touched cards in "normal" suits are good. A normal suit is one of the standard suits red, yellow, green, blue, purple, and teal. There are suits where Good Touch Principle does not apply - this is covered in Variants Where Good Touch Principle Do Not Apply under the Variant Specific section.
If a card in a normal suit can only be playable or trash by empathy and targeting priority inferences, it is considered a queued play for the purposes of determining the reacter. It can be fixed by a fill-in clue, a reactive clue telling it to discard, or another reactive or RS clue providing empathy of it being trash (these retain their reactive / RS interpretations).
While we follow good touch principle, we typically do not overly worry about bad touching. Often, reactive clues that appear to bad touch do not due to the receiver making inferences about her hand given the targeting priority chosen.
For example, consider the following hands. Yellow 1, green 1, and blue 1 have been played on the stacks.
Bob: g4 g5 g1 g2 g3
Cathy: b1 y1 y2 y3 y4
Alice gives a 1 clue to Cathy, touching both the blue 1 and the yellow 1 on slots 1 and 2 and thus focusing slot 2. From Bob's perspective, the leftmost non-obvious play in Cathy's hand is the yellow 2 on slot 3. For this reactive clue to work, Bob must play the slot which when added to slot 3 produces the focused slot of 2, or 2 - 3 = 7 - 3 = 4 (mod 5).
Bob blind plays the green 2 from slot 4. Cathy now works out which slot she must play, which is 2 - 4 = 7 - 4 = 3 (mod 5). Cathy blind plays yellow 2 from slot 3. However, Cathy also knows from the targeting priority that the yellow 2 was the leftmost non-obviously playable card in her hand! This means that none of the clued 1s could have been playable, as otherwise Bob would have reacted by playing a different slot. Even though Cathy has two clued 1s which look like they would be playable from empathy, everyone should mark known trash on the two clued 1s because of targeting priority.
The endgame threshold is reached when at least one of the following criteria is met:
Clues in the endgame follow the same conventions as in the Locked and 8 Clue Players section.
When a stable rank clue is given with a rank all of whose members are known trash, it is a Referential Play Clue on the card to the left of the leftmost clued trash card (wrapping around if necessary).
The exception is for Brown, Muddy Rainbow, and Null variants, where trash clues with rank must be respected as Direct Discard Clues unless one of the trash cards is on chop or all cards of the special suit has been accounted for. It simply indicates to discard the touched cards.
Alice can give a reactive clue to trick Bob into playing the connecting card into Cathy's hand when he is really not, as long as Cathy knows that the card that she is supposed to play into Bob's reaction is definitely unplayable after the clue is given. Example:
Red 1 has been played on the stacks. No cards in Bob or Cathy's hands have been clued.
Bob: p1 p2 g1 y1 b1
Cathy: g3 b3 r3 p3 y3
Alice clues 3 to Cathy touching all five 3s, which focuses slot 2. Since the only 1 away 3 is red 3, Bob plays yellow 1 from slot 4 (4 + 3 = 7 = 2 mod 5). Cathy knows that all of her cards are unplayable after the 3 clue, however she can mark the 3 on slot 3 as exactly red 3 because it needs to have been one-away from playable in order for the bluff to have worked.
Hard elimination occurs in one of the following scenarios:
When a card is singled out with a hard elimination note, that card is considered globally known for the purposes of determining the target of reactive clues.
In hard variants, we do not have hard elimination for valuable non-playable 2s. Hard variants are defined as variants having an efficiency of greater than 1.42.
Any other valuable card that is either explicitly told to discard or implicitly discarded through PTD may have soft elimination notes. Most notably, non-playable 3s and 4s can only have soft elimination notes. When a card is singled out with a soft elimination note, that card is not globally known for the purposes of determining the target of reactive clues. The reason for this is because we want to minimize contextual dependency and to allow more room for error / more flexible line construction where sometimes we have to force the discard of a non-critical valuable card.
In practice, most "soft elimination" notes are hard in the sense that the player who has them will almost certainly play them on its own when it becomes playable.
When Bob has hard elimination notes for a playable card and Alice clues a finesse to Cathy, Bob should prioritize the finesse involving the card with hard elimination notes over other finesses (in the typical 15432 order). If there are multiple such cards (very rare), play the first possible slot in the 15432 finesse ordering which corresponds to a valid elimination finesse.
The intentional discard of a playable card goes to the rightmost possible slot of the player possessing the other copy of the card. This is allowed to be stacked behind other playable cards, akin to how prompts and layered finesses work in H-Group conventions.
The term Gentleman's Discard is used for situations where none of the clued cards in the target player's hand match the discarded playable card. For example:
Alice has a known playable blue 1 and Bob's hand is completely unclued:
Bob: r5 b5 y5 b1 g1
Alice is allowed to toss her blue 1, since the blue 1 goes to the rightmost slot in Bob's hand who will play it and continue "digging" to the left until he finds the promised card.
If there are matching clued cards, it is a Sarcastic Discard instead and the target player is promised that all matching cards leading up to the discarded card are playable from the right. For example:
Red 2 and Blue 2 are played on the stacks and nothing else. Alice has a known playable blue 3 and Bob's hand has three 3s clued (highlighted in bold):
Bob: g2 y3 b3 r3 g5
Once Alice tosses her blue 3, Bob is allowed to immediately start playing his clued 3s (which match the discarded blue 3) from right to left until the blue 3 is found.
In either scenario, if Alice discards a card that passes through unplayable cards, a fix clue must be given before the target player has an opportunity to start playing the discarded card. Example:
Suppose Red 2 and Blue 2 have been played, as before, and Alice discards a known playable blue 3. Cathy's hand has three 3s clued (highlighted in bold):
Cathy: g2 b3 r3 y3 g5
Bob must give a yellow fix clue (a blue clue is also possible but worse in this particular situation since it stops the red 3 from playing for free) to Cathy before she has the opportunity to bomb the yellow 3.
If it is not an emergency situation and Alice discards a clued non-playable card, it is called a Baton Discard and does not promise position (it does not even have to be among matching clued cards), and can be anywhere in the hand of the player with that card that will be sieved in after that player has exhausted their safe actions. This card will also have hard elimination notes.
When a player gives a clue that takes the team down to 0 or 0.5 clues, every player must mark ZCSP on their leftmost unclued card that has not been explicitly sieved in by a previous safe action.
If Alice has a card marked ZCSP and the player before Alice had 0 or 0.5 clues on their turn, Alice's next discard must be the card marked ZCSP. Otherwise, Alice may discard her normal chop.
If a player discards a card while they still have a pending play in a zero clue state, it is called a scream discard and calls for the first player without a safe action to reset their chop from the ZCSP card to the normal chop.
Whenever the player before Alice takes an action at 1 or more clues on their turn, Alice should erase the previous ZCSP note and discard chop normally or replace it with a new one if the new action causes the team to be at 0 or 0.5 clues.
This convention generally does not apply in the endgame.
When a card is called to play in Alice's hand but the identity of that card is unknown, then Alice is expected to play all of the cards (known or unknown) that were previously called to play which could lead into the new unknown playable card before playing that card.
However, if Alice has multiple globally known playable cards, the expected order of play of these cards follows the below priority table:
If Alice has multiple globally known playables and does not respect this priority table from the perspective of another player, it triggers one or more priority plays on the first such player, who is said to have been "prioritized". The prioritized player is promised that they hold the card which Alice's card leads into, and are also promised that they may repeatedly play the rightmost possible card, starting from clued cards and continuing into the unclued cards, until they find the promised card.
For example, Alice has a globally known red 2 and a green 3 in her hand, both of which are playable. Alice has no other playable cards in her hand. Blue 3 and yellow 3 are also played on the stacks. Cathy has two cards clued in her hand - a yellow 4 clued as 4 on slot 5, an unclued blue 4 on slot 4, and an unclued green 4 on slot 3. Cathy knows that red 2 should play before green 3 since it has a lower rank, so Cathy knows she has been prioritized for green 4. Cathy will first play the yellow 4 from slot 5 since that card could match, and then blind play the remaining cards starting from the right until she finds green 4.
Fix clues can be given to a player who will bomb a card from a priority play at some point. This is referred to as a load clue.
The exception is if the prioritized player is Bob and Bob has no clued cards that could match the card being prioritized. In this case, Bob is expected to blind play his rightmost unclued card and nothing else. This is referred to as a priority bluff.
Cards that are called to play from priority do not load for the purposes of considering reactive targets.
When pace is +1 or lower, all color reactive clues which would normally be one discard + one play become double play reactive clues instead.
Our reactive clue values change to be based on the value of the clue given rather than what cards it touches. Pinkish variants impact the reactive rank clues, while rainbowy variants impact the reactive color clues.
For example, if Alice clued 4 to Cathy in a pinkish variant, it means the sum of the targeted slots is 4 regardless of which slots the rank 4 clue touched in Cathy's hand. Similarly, if Alice clues the third leftmost color in a rainbowy variant, it means the sum of the targeted slots is 3 regardless of which slots were touched.
Pinkish and rainbowy variant rules apply to any variant with special ones or special fives with a pink or rainbow property, respectively. Both apply if an omni suit, omni special ones, or omni special 5s are present.
Additionally, the following are considered to be pinkish variants:
and the following are considered to be rainbowy variants:
In some rainbowy variants, it may be beneficial to have color clues call for two plays or two discards, and rank clues call for one play + one discard.
Examples of common variants where this may be helpful:
Swaps do not apply if there are three or fewer distinct color clues available.
The following conventions apply to variants with a rainbowy suit.
This convention applies to variants with 6 different color clues available.
In a pinkish special-ones/fives variant where a rank 1/5 clue is not possible, the 6th color has the same meaning as a rank value of 1/5 (respectively).
Otherwise, the 6th color has the same meaning as the 1st color (with a value of 1).
If there are 1 to 3 different color clues available, reactive color clues are assigned starting at the value 3 rather than 1. For example:
If there are 4 different color clues available, reactive color clues are assigned the values 1,5,3,4 for the first, second, third, fourth colors respectively. The reason for this is that a color value of 2 is often to get a slot 1 play + slot 1 discard which is less likely to be useful since the player called to discard slot 1 can just passively discard it instead.
This convention applies to variants containing a Brown suit, Muddy Rainbow suit, or Null suit.
Trash clues with rank must be respected as Direct Discard Clues unless one of the trash cards is on chop or all cards of the special suit has been accounted for. It simply indicates to discard the touched cards.
This convention applies to variants containing a non-dark special suit. A special suit is defined as any suit which is not one of red, yellow, green, blue, purple, or teal.
Cards in these suits whose empathy is revealed to be either playable or trash are not expected to automatically play and are also never considered to be obvious plays for the purposes of reactive clues, due to the high chance of bad touching and potential difficulties in fixing these cards.
This also applies to special-ones with the respective properties.
This convention is disabled in Clue Starved and Brown. In that variant, a brown clue to Bob is always a referential play clue.
If Bob has no safe actions, a brown clue that touches Bob's rightmost unclued card is a lock clue.
As mentioned previously, rank clues that touch Bob's rightmost unclued card is to be treated as a normal referential discard clue rather than a lock.
Zero clue safety promise is especially important in these variants - all players should write zcsp on everyone's leftmost unclued card that was not called to play and not cm'ed by context whenever a clue brings the team down to 0 or 0.5 clues.
If Bob has no safe actions, a red clue to Bob's rightmost unclued card is permitted as a lock clue, provided that the rightmost unclued card will not be known to be a non-muddy-rainbow card to Bob.
Red locks can be fake - if the rightmost unclued card was later revealed to be red, Bob should not retroactively interpret the lock as a stable color push.
Null playable cards have targeting priority over other playable cards. For example:
Nothing is played on the stacks. Alice sees the following hands:
Bob: b1 r1 p1 y5 g5
Cathy: g1 y1 u1 p4 b5
Alice gives a rank 4 clue to Cathy. By null playable priority targeting, Bob targets the null 1 over the other playable cards to the left, and thus plays his blue 1 (slot 4 - 3 = 1).
This convention does not apply to null finesses.
Null trash, also called waste, has the highest targeting priority over other trash of the same quality (i.e. cluedness).
The reasoning is that null cards inhibit our ability to give effective clues the most, and thus we want them out of players' hands as soon as possible.
Trash null 1s are also considered to be null trash.
Any stable clue to Bob which does not touch any new cards or fill in any positive information is considered to be a lock on Bob. In addition, Bob marks their rightmost unclued card as a null card and treats it as permanently clued, so the next rank clue to Bob touching the card one to the left also becomes a lock.
If Alice intentionally bombs a known trash card or blind bombs chop, it is a lock on Bob's entire hand. Bob also marks their rightmost unclued card as null and permanently clued, as before.
Rank - color swaps apply to this variant with the deficient color clue convention applied (i.e. "Odd" has a discard value of 3 and Even" has a discard value of 4).
(Experimental) Instead of normal referential rank discard clues, a stable "Odd" clue means to cm one card and a stable "Even" clue means to cm two cards. All cards touched by rank stable clues are unclued (should be marked with an x), except those which have either been cm'd or touched with a color clue. In addition, permanent cms are on, which means that if a card was previously cm'd, the next cm clue skips over that cm'd card.
In pinkish variants, according to Referential Sieve conventions a stable 1 clue in the starting hand promises that all of the 1s are playable from right to left. The focus of the stable 1 clue is the rightmost touched card and is always promised to be a playable 1. The remaining clued 1s are called Passive 1s to refer to the fact that they will play on their own if there are still 1s remaining to play and they are not fixed.
However, any Passive 1s are ignored completely by reactive clues. That is, if Cathy has Passive 1s in her hand:
If Bob has only Passive 1s in his hand, he is still considered to have a loaded play for the purposes of determining who the reacter is. However, if Alice gives Cathy a reactive clue, any Passive 1s that Bob plays out of order or any discard of a Passive 1 by Bob are considered to be a reaction by Cathy.
PS: There is a competing convention (for omnis) where only the rightmost 1 is playing and the other 1s are not passively playing.
These conventions apply to variants containing a Pink suit, Light Pink suit, or Omni suit.
A lock clue (rank clue to Bob's rightmost unclued card) which does not immediately reveal a safe action to Bob promises the rank of the rightmost unclued card.
In a pinkish-ones variant, rank to rightmost unclued may not promise the true rank as it is permissible to lock a player with a 1 on their rightmost unclued card.
In a pinkish-fives variant, a 2 clue must be given to lock a player who has a 5 on their rightmost unclued card.
When possible, a referential discard stable clue should promise the true rank of the clued card next to the card being told to discard. For example, Alice should clue 2 rather than 5 to tell Bob to discard his duped green 3:
Bob: i5 i2 g3 g3 r3
However, it is permissible to disobey pink promise in the following example as rank 3 won't get g3 to discard. Alice should clue 4 or 5 to i3 depending on the situation.
Bob: i3 g3 g3 r3 r2
The START card has a higher targeting priority than all other playable cards in the same hand. For example, consider the following starting hands.
Bob: g4 g5 g1 gS g2
Cathy: y1 b5 bS b4 b3
Alice gives a 3 clue to Cathy as a reactive play clue focusing slot 5. Since bS has a higher targeting priority than y1 and b5, Bob should blind play slot 5 - 3 = 2 into this clue.
If a sacrifice discard needs to be made, the 2 and 4 of an unplayed stack are both considered to be 1 away, and the 3 is considered to be 2 away from playable.
In a 4 player game, there are up to two reacters.
Thus, there are three types of clues:
Since there are 4 cards in each player's hand, the sum of the slots is computed modulo 4:
The most common source of lost games in 4-player games are:
As a result, the following are the cornerstone conventions for 4-player games. Whenever a conventional conflict exists, these conventions ALWAYS have priority. Please read and re-read the following conventions and fully understand the examples before attempting a 4 player game.
As usual, the first reacter is the first person going clockwise from Bob who is not loaded with a play. Reactive clues to the person immediately after the first reacter in clockwise order are simple reactive clues.
If Bob is not loaded and unlocked Alice clues Donald while Cathy is loaded with a play, Cathy's reaction is always skipped over and the clue becomes a simple reactive clue on Bob + Donald.
If Bob is loaded, we shift each of Bob, Cathy, Donald cyclically and apply the same principle. Thus, a clue from Alice to Bob when Bob and Donald are both loaded is a simple reactive clue on Cathy + Bob.
If only Cathy is loaded, a clue from Alice to Cathy is a simple reactive on Bob + Cathy.
If Bob and Cathy are both loaded, a clue from Alice to Cathy is a simple reactive clue on Donald + Cathy.
If Alice gives a bad stable clue, it becomes a reactive clue which ignores the loadedness of all players except for Cathy, in accordance with the Loaded Cathy Skip principle.
Rarely, Bob must also react if Bob is loaded and Alice gives a bad simple reactive clue to Cathy and Donald. Example:
Nothing has been played on the stacks. Bob has a red 1 on slot 1 which was previously called to play.
Bob: [r1] y3 p1 y4
Cathy: p5 b1 p2 p3
Donald: y1 r5 g5 y5
Alice gives a red clue to donald focusing slot 2. If Bob plays slot 1 as red 1, then Cathy will either discard purple 5 from slot 1 (if Bob plays something other than y1), or play purple 5 from slot 1 (if Bob plays y1) since she will interpret the slot 2 focused clue as a simple reactive between Cathy and Donald. Since either scenario is bad, Bob knows this that this is instead a double reactive clue and thus plays purple 1 from slot 3 (since 3 + 2 + 1 = 6 = 2 (mod 4)). Cathy and Donald know that since Bob did something unexpected (something other than playing the red 1) that the clue by Alice was a double reactive clue.
Note that this can only occur if Bob knows definitively that the simple reactive clue will lead to a bomb or the discard of a critical card. Otherwise, Bob has to respect a simple reactive clue between Cathy and Donald.
A double reactive clue occurs in one of the two following scenarios:
Suppose, without loss of generality, that Bob is the first reacter, Cathy is the second reacter and Donald is the receiver.
The parity of the number of plays called for by rank and color clues do not change compared to 3 players. When Alice clues Donald:
The focused slot will be the sum of the slots of three actions by Bob, Cathy, and Donald (modulo 4). When Alice gives a reactive clue to Donald, Bob will have to determine which actionable slots to "anchor to" and subtract from the total sum of slots to determine his action. This process is referred to as reactive reduction. The reduction priority table is as follows - Bob finds the first reduction that applies when calculating a double reactive action.
One notable exception is that whenever Bob plays a card which connects to a card Donald's hand, Cathy's Connecting Principle (described in a below section) applies and may change Cathy's action to be different from what Bob originally intended for Cathy to do. It is Alice's job to make sure that both interpretations work before giving the clue.
Example 1:
Bob: b1 r1 p1 g1
Cathy: g2 y1 g2 g3
Donald: y1 g4 g1 b5
Donald has a playable on slot 1, so that slot is "locked in". Since y1 is being called to play, Bob will always target the leftmost g2 trash in Cathy's hand, so that card is also locked in. Alice has a choice of cluing 1, 4, or 5 to get b1 (slot 1), g1 (slot 4), or r1 (slot 2) respectively.
Example 2:
Bob: b1 b2 b3 b4
Cathy: g2 y1 g2 g3
Donald: y2 g4 g5 b5
Alice sees a finesse from Cathy to Donald is possible if Cathy + Donald's targeted slots sum to 3. A blue clue to Donald (focusing slot 4) would get three plays - b1 from Bob, y1 from Cathy, and y2 from Donald.
Example 3:
Bob: b1 b2 b3 b4
Cathy: g2 y1 g2 g3
Donald: y4 y4 g4 r3
No finesse is possible from Cathy to Donald, but Donald does have two duped y4s. The target for Donald would be the y4 on slot 1, so a good clue here would be 3 to Donald (focusing slot 4), getting b1 + y1 played and the left y4 discarded.
Example 4:
Bob: b1 r1 p1 g1
Cathy: g2 y1 g2 g3
Donald: b2 y4 g4 r3
Donald has no trash and no playables and a finesse from Cathy to Donald isn't available. However, Cathy has a playable y1 on slot 2 so that will be the target. Alice can then clue red to Donald focusing slot 4 which will get 3 plays - Bob subtracts the slot 2 target in Cathy's hand to get a slot sum of 2 for himself and Donald, and playing b1 from slot 1 is a possible finesse into the slot 1 b2 in Donald's hand.
This section applies to when Donald has no immediately playable cards.
Suppose Alice gives a triple play clue to Donald. If Bob's play connected with a card in Donald's hand (making it now playable), Cathy must choose that target rather than finding the first of her finesse positions which would have originally made one of Donald's cards playable.
Example:
Nothing has been played on the stacks.
Bob: b1 p1 b5 p5
Cathy: g5 g1 r1 r5
Donald: g3 b2 r3 p2
Alice gives a Green clue to Donald focusing the g3 on slot 1. Bob sees that there does not exist a finesse from Cathy to Donald, and thus must play into Donald himself. He subtracts the g1 (slot 2) target from Cathy's hand to get a sum of slots of 3. A slot 1 play of b1 could play into Donald's b2 in slot 2, so Bob blind plays slot 1.
Now Cathy has to decide if the finesse was between her and Donald or between Bob and Donald. By Cathy's Connecting Principle she sees that b1 connected with b2, so that must have been the intended reaction. Cathy thus plays g1 from slot 2 = -2 = 1 - 1 - 2 (mod 4).
Note that it up to Alice to make sure that Cathy's Connecting Principle is respected before giving a clue that could look like a Bob-Donald Finesse! As a general rule of thumb, triple play clues involving finesses in 4p are complicated and if a simple 3p reactive clue is effective then that is often preferred for clarity reasons.
Here's an example of an illegal finesse from Alice. Again, nothing has been played on the stacks:
Bob: b1 p1 r1 g1
Cathy: y1 g5 b5 r5
Donald: b2 y2 r3 p5
Alice clues Purple to Donald focusing slot 4. Bob sees that Cathy's y1 (slot 1) plays into Donald's y2 (slot 2), so Bob plays b1 from slot 1. However, Cathy applies Cathy's Connecting Principle to deduce that the finesse was between Bob and Donald (slot 1 + slot 1), so bombs g5 herself from slot 2.
In general, to avoid violating Cathy's Connecting Principle, Alice must ensure that one of the following holds:
Example of the last point:
Bob: b1 p1 r1 g1
Cathy: y1 r1 b5 r5
Donald: b2 y2 r3 p5
Alice clues Purple to Donald. This is the same setup as before except the green 5 has been replaced by a red 1. Bob plays blue 1 expecting Cathy to play y1 into y2, but Cathy plays r1 instead because Cathy's Connecting Principle tells her that the original finesse is between Bob and Donald. The conflict in the previous example is that the Bob assumes Cathy-Donald finesses have priority according to the targeting priority table while Cathy follows the Cathy's Connecting Principle and the two point to different slots in Cathy's hand. However, if both of the slots turn out to be playable, then Alice can proceed with the clue as usual.
Suppose Alice gives a reactive clue and Bob sees multiple possible finesses between Cathy and Donald. How should Bob react? We call this situation an ambiguous finesse and the correct reaction from Bob is to target the finesse between Cathy and Donald that would result in Cathy playing the first possible slot in the finesse ordering 1->4->3->2. Example:
Bob: y1 p1 g1 p5
Cathy: b5 g5 r1 b1
Donald: b2 y5 r2 r5
Alice clues Yellow to Donald focusing slot 2. Bob sees that there are two possible finesses (r1->r2 or b1->b2). He chooses the one that results in Cathy playing the first possible finesse position, so in this case slot 4 which is b1 into b2. The sum of these slots is 1 and thus Bob plays yellow 1 from slot 1.
Note that it is up to Alice to make sure that the Cathy + Donald finesse does not fail because Cathy ends up playing a card even earlier in the finesse ordering. For example, if we swapped the r2 and r5 in Donald's hand in the above example, the finesse fails because after Bob plays yellow 1 from slot 1, Cathy will bomb b5 from slot 1 because that is the first of her slots which plays into a valid 1-away in Donald's hand (r2).
Bob: y1 p1 g1 p5
Cathy: b5 g5 r1 b1
Donald: b2 y5 r5 r2
In the rare case that Cathy has two dupes of playables that both play into the same 1-away in Donald's hand, Bob always targets the one that comes first in finesse position ordering, even if the one that comes later is clued.
In a 5 player game, there could be up to three reacters.
Tentatively the reduction table for 5-player is as follows:
Other reductions are not currently well-defined due to low sample size/agreement. In general, the following 4-player principles should apply, for future conventional development:
If Cathy has a card that was called to play but is subsequently duped and about to bomb, a reactive color clue to Cathy will target the card that is about to bomb with priority over any playables in Cathy's hand.
A rank clue from Alice to Bob that touches the rightmost previously-unclued card is a lock fix clue if Bob is loaded. The effect of a lock fix clue is that Bob's playable card is called to discard.
Does the unclued copy exception from the Important Exception section apply to finesses?
If there are two dupe cards into one hand and one is clued and the other one is not, and they are targeted by a reactive discard clue, prioritize the unclued dupe over the clued dupe.
The general rule, when there are other trash cards in hand, is to ignore the clued dupe when deciding on a discard target.
The reason of why this is advantageous is that the clued dupe retains the position of the card.
Cathy's playable is targeted if it is "not 100% globally known to be playable by empathy".
This convention is one more exception to be aware off. It differs from
the loaded convention which only insists on being playable or trash by empathy.
Is the value lost by retargeting playable cards worth the possibility of fixing bad touched ones?
Implicitly discarded through PTD on chop when Alice had at least one/two clues.
Maybe this should fall under a context read but we should avoid mixing "hard elim" and context.