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Since we know we can extract a playable cards with colour + number clues, it follows that number clues that mark the chop card are interpreted as:
Since we know we can extract a playable cards with colour + number clues, it follows that number clues that mark the chop card are interpreted as:
# Unique save if the chop card can be unique
# critical save if the chop card can be critical
# Double discard save if the player either side of the receiver has a non-unique card of the same number
# Double discard save if the player either side of the receiver has a non-critical card of the same number
# Otherwise a left-focused play clue.
# Otherwise a left-focused play clue.


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# negative clues (e.g. "not red"),
# negative clues (e.g. "not red"),
# recently discarded cards,
# recently discarded cards,
# unique cards,
# critical cards,
# tokens needed for saves or other plays
# tokens needed for saves or other plays


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|body=
|body=
Sometimes we need more information before we can know if a clue is a chop-focused save or a left-focused play clue.
Sometimes we need more information before we can know if a clue is a chop-focused save or a left-focused play clue.
Double discard avoidance saves are one of the most difficult clues to interpret because it's one of the very few times we can save non-unique cards without expecting a play response.
Double discard avoidance saves are one of the most difficult clues to interpret because it's one of the very few times we can save non-critical cards without expecting a play response.


Nothing much is going on and there have not been any good ways to splash, give trash clues or otherwise delay one of the players.
Nothing much is going on and there have not been any good ways to splash, give trash clues or otherwise delay one of the players.
Some players forbid a player from discarding if a [https://en.doc.boardgamearena.com/Gamehelphanabi#Definitions double discard] is possible
Some players forbid a player from discarding if a [[Tips_hanabi|double discard]] is possible
}}
}}


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=== Back to basics ===
=== Back to basics ===


* In a {{player|5}} player game with {{hand|4}} each and avalanche, there are up to 30 possible moves per player (excluding flamboyants).
In a {{player|5}} player game with {{cardholder|{{hCard}}{{hCard}}{{hCard}}{{hCard}}}}, each player can play one of the '''4''' {{hCard}} + discard one of the '''4''' {{hCard}} + clue one of the '''5''' numbers to any of the other '''×4''' players + clue one of the '''5''' colours to any of the other '''×4''' players = '''48''' possible moves per player.
:e.g. if each hand has one avalanche {{hm}} card.
That's a lot to think about. But amazingly our human brains can filter out the vast majority of those moves as not logical given a bit of agreement on clue, play and discard interpretations (conventions).
* In one round of play that means up to 150 possible unique positions!
* That's a lot to think about. But amazingly our human brains can filter out the vast majority of those moves as not logical given a bit of agreement on clue, play and discard interpretations (conventions).
<!--
, we agree as a team that we must:
Communicate to each other primarily via clues (as well as plays and discards)
Who: all
Where:
When:
Why: To win with the highest possible score
# What: not discard the last copy of any card.
#* How: mark the last copy


Two types of clues
=== Hand management ===


*To separate
Hand management is important in high level play to keep as many non-trash cards in the game for as long as possible.
*We always mark unique cards before they are discarded


*Most of the time we understand that the clue giver should be the player directly before the clue receiver.
==== When to discard ====
*This is because this seat has the newest information in view
 
*Relative seats of clue giver & receiver
*When we allow any player to clue any hand, it allows for a lot more freedom to clue.
*Cluing more than 1 seat away can happen for a '''[[Tips_hanabi#Skip|number of reasons]]'''.
 
*when to discard - when player right of you has nice cards like 2s
*Delaying certain players with nice non-unique cards
 
*Mark as many first copies of cards as possible to reduce the chance of getting '''bottom-decked'''.
*Bluffs are the easiest way to mark useful 1-away from playable cards.
*Where possible,
-->
=== Hand management ===


* Hand management is important in high level play to keep as many non-trash cards in the game for as long as possible.
* The player before you has a valuable card on their chop that cannot be clued - so drawing new cards gives more opportunity for them to clue instead of discard their valuable chop.
* The next player has a playable finesse position, but they have a save, fix or other important clue to give - so that the card remains in finesse position to be bluffed later.


==== When to skip players  ====
==== When to skip players  ====
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}}
}}


===== When to not save unique cards {{s:O}} =====
===== When to not save critical cards {{s:O}} =====


* No matter how many tokens you have, whether it is {{hclue|1}} or {{hclue|7}}, you do not always have to spend a token to save a card.
* No matter how many tokens you have, whether it is {{hclue|1}} or {{hclue|7}}, you do not always have to spend a token to save a card.
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* Each player must consider the likelihood of a certain move and assess if the risk-reward of all the possible moves.
* Each player must consider the likelihood of a certain move and assess if the risk-reward of all the possible moves.


[[#Back_to_basics We know that there are a lot of possible moves, and even more game states]].
We know that there are a lot of possible moves, and even more game states.


Examples of clear good/bad
Examples of clear good/bad
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* Reverse finesses are often not great if the finessed card could instead be bluffed, however, it can be useful to mark a chop card as a reverse to ensure it is not discarded.
* Reverse finesses are often not great if the finessed card could instead be bluffed, however, it can be useful to mark a chop card as a reverse to ensure it is not discarded.
*: e.g. Alice sees Bob has {{hw|2}} on chop and Donald just drew {{hw|1}}. Normally the best moves would be for Alice and Bob to discard so that Cathy can bluff Donald's {{hw|1}}, but {{hw|2}} is more valuable than any bluff target Alice can see, so she chooses to reverse with colour.
{{cardholder|{{hk}}{{hk}}{{hk}}{{hw|2}} |Bob 🡲}} {{cardholder|{{hk}}{{hk}}{{hk}}{{hk}} |Cathy 🡲}} {{cardholder|{{hw|1}}{{hk}}{{hk}}{{hk}} |Donald 🡲}} Usually Alice and Bob should discard so that Cathy can bluff Donald's {{hw|1}}, but Bob's {{hw|2}} is more valuable than any bluff target Alice can see, so she chooses to reverse with colour.


But what if reversing with colour would mark trash?
But what if reversing with colour would mark trash?
* If we can finesse with number, why can't we also reverse finesse with number?
* If we can finesse with number, why can't we also reverse finesse with number?
* A reverse with number is usually harder to read than a reverse with colour, but they can be a lot more efficient than colour + multiple correction clues (to prevent future bombs).
* A reverse with number is usually harder to read than a reverse with colour, but they are more efficient than colour + multiple correction clues (to prevent future bombs).


[https://boardgamearena.com/player?id=85786974 Travis Hall] gives a basic explanation of number reverses:
[https://boardgamearena.com/player?id=85786974 Travis Hall] gives a basic explanation of number reverses:
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* Multicolour reverses with a single colour can work, the most common situation being where the clue giver and receiver can both see a playable card of the colour clued either marked or in the finesse position in someone else's hand.
* Multicolour reverses with a single colour can work, the most common situation being where the clue giver and receiver can both see a playable card of the colour clued either marked or in the finesse position in someone else's hand.
* Such a reverse may also trigger a [[Gamehelphanabi#Definitions|hesitation]] play.
* Such a reverse may also trigger a [[Tips_hanabi|hesitation]] play.


=== When to GD ===
=== When to Gentleman's Discard (GD) ===


# Plays extra cards for free from one ''or more'' hands. <!--See [[#Patch_GD|Patch GD]].-->
# Plays extra cards for free from one ''or more'' hands.
# Protect cards
# Protect cards
# Token is needed
# Token is needed
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no prompt
no prompt


no save = non-unique
no save = non-critical
 
{{hPlay
|note1={{text|Alice to Bob: these 2 cards are white.|#f4f4f4|x=5|y=5}}
|note2=Bob plays {{hw|1|c=}}.
|note3={{text|Cathy to Alice: these 2 cards are white.|#f4f4f4|x=5|y=5}}
|note4=Alice plays {{hw|2|c=}}.
|note5=Bob discards.
|note6=Cathy discards.


<div style="columns:14rem auto;column-gap:2rem;white-space:nowrap;">
{{pill|What is the best move for Alice?|#088}}
: {{hr}} {{hy|5}} {{hg|5}} {{hb|5}} {{hw}} {{hclue|2}}
: {{cardholder|{{HBack}}{{HBack}}{{HBack}}{{HBack}} |Alice 🡲}} {{cardholder|{{hw|1}}{{hr|2}}{{hk}}{{hw|3}} |Bob 🡲}}
# Alice to Bob: these 2 cards are white.
# Bob plays {{hw|1}}.
# Cathy to Alice: these 2 cards are white.
#:{{cardholder|{{HBack|2|{{w}}|c=}}{{HBack}}{{HBack}}{{HBack|4|{{w}}|c=}} |Alice 🡲}} {{cardholder|{{hk}}{{hr|2}}{{hk}}{{hw|3|c=}} |Bob 🡲}}
# Alice plays {{hw|2}}.
# Bob discards his chop.
# Cathy discards.
#:{{cardholder|{{HBack}}{{HBack}}{{HBack}}{{HBack|4|{{w}}|c=}} |Alice 🡲}} {{cardholder|{{hw|4}}{{hk}}{{hr|2}}{{hw|3|c=}} |Bob 🡲}}
</div>


{{infoBoxes3 |titleAlign=left |background=#088
A) clue {{hw|3|c=|n=}} B) clue {{hw|4|c=}} C) clue {{hw|4|n=}} C) play {{HBack|4|{{w}}|c=}} D) discard {{HBack|4|{{w}}|c=}} E) discard chop {{HBack}}
|title1=What is the best move for Alice?
|body1=A) clue {{hw|3|n=}} B) clue {{hw|4|n=}} C) play {{HBack|4|{{w}}|c=}} D) discard {{HBack|4|{{w}}|c=}} E) discard chop {{HBack}}
}}


{{infoBox |minWidth=max-content |state=collapsed |titleAlign=left |background=green
{{infoBox |state=collapsed |titleAlign=left |background=green
|title=Solution
|title=Solution
|body={{pill|D) discard {{HBack|4|{{w}}|c=}} }}
|body={{pill|D) discard {{HBack|4|{{w}}|c=}} }}


# Alice's chop card was not marked before her '''free move''' to clue Bob, so she knows her oldest white card cannot be unique ({{hw|5}}).
# Alice's chop card was not marked before her '''free move''' to clue Bob, so she knows her oldest white card cannot be critical ({{hw|5}}).
# According to good touch, Alice can assume her white card is also not a 3 and could be a 4.
# According to good touch, Alice can assume her white card is also not a 3 and could be a 4.
# Alice sees Bob has a valuable {{hr|2}} on chop, marked {{hw|3}} and unmarked {{hw|4}} in his finesse position.
# Alice sees Bob has a valuable {{hr|2}} on chop, marked {{hw|3}} and unmarked {{hw|4}} in his finesse position.
In order to delay the future discard of {{hr|2}}, the best move for Alice is to discard her non-unique white card to trigger Bob to play {{hw|3|c=}}{{hw|4}}.
In order to delay the future discard of {{hr|2}}, the best move for Alice is to discard her non-critical white card to trigger Bob to play {{hw|3|c=}} and {{hw|4}}.
}}
|{{hGame
|{{hTable}}
|
|clues=2
|b={{hw|1|c=}}{{hk}}{{hk}}{{hw|3|c=}}
|c={{hk}}{{hk}}{{hr|2}}{{hk}}
|dHide=
|eHide=
}}
|{{hGame
|{{hTable|||||1}}
|
|clues=2
|b={{hk}}{{hk}}{{hk}}{{hw|3|c=}}
|c={{hk}}{{hk}}{{hr|2}}{{hk}}
|dHide=
|eHide=
}}
|{{hGame
|{{hTable|||||1}}
|
|clues=1
|a={{HBack}}{{HBack|2|{{w}}|c=}}{{HBack}}{{HBack|4|{{w}}|c=}}
|b={{hk}}{{hk}}{{hk}}{{hw|3|c=}}
|c={{hk}}{{hk}}{{hr|2}}{{hk}}
|dHide=
|eHide=
}}
|{{hGame
|{{hTable|||||2}}
|
|clues=1
|a={{HBack}}{{HBack}}{{HBack}}{{HBack|4|{{w}}|c=}}
|b={{hk}}{{hk}}{{hk}}{{hw|3|c=}}
|c={{hk}}{{hk}}{{hr|2}}{{hk}}
|dHide=
|eHide=
}}
|{{hGame
|{{hTable|||||2}}
|
|clues=2
|a={{HBack}}{{HBack}}{{HBack}}{{HBack|4|{{w}}|c=}}
|b={{hk}}{{hk}}{{hk}}{{hw|3|c=}}
|c={{hk}}{{hk}}{{hr|2}}{{hk}}
|dHide=
|eHide=
}}
|{{hGame
|{{hTable|||||2}}
|
|clues=3
|a={{HBack}}{{HBack}}{{HBack}}{{HBack|4|{{w}}|c=}}
|b={{hk}}{{hk}}{{hk}}{{hw|3|c=}}
|c={{hw|4}}{{hk}}{{hk}}{{hr|2}}
|dHide=
|eHide=
}}
}}
}}


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{{infoBoxes3 |state=collapsed |titleAlign=left |background=#088
{{infoBoxes3 |state=collapsed |titleAlign=left |background=#088
|title1=Example 1: basic tracking
|title1=Example 1: basic tracking
|body1={{hr}} {{hy}} {{hg}} {{hb}} {{hw}} {{hk}}
|body1={{hTable|k=}}
{{cardholder|{{hk}}{{hk}}{{hk}}{{hr|1|n=}} |Bob 🡲}}
{{cardholder|{{hk}}{{hk}}{{hk}}{{hr|1|n=}} |Bob 🡲}}
{{cardholder|{{hk|1}}{{hk}}{{hk}}{{hk}} |Cathy 🡲}}
{{cardholder|{{hk|1}}{{hk}}{{hk}}{{hk}} |Cathy 🡲}}
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* Alice to Bob: these two cards are 1s.
* Alice to Bob: these two cards are 1s.


{{hr}} {{hy|1}} {{hg|2}} {{hb|1}} {{hw}} {{hk|3}}
{{hTable||1|2|1||k=3}}
{{cardholder|{{hk}}{{hw|1|n=}}{{hr|1|n=}}{{hk}} |Bob 🡲}}
{{cardholder|{{hk}}{{hw|1|n=}}{{hr|1|n=}}{{hk}} |Bob 🡲}}
{{cardholder|{{hk|1}}{{hk}}{{hk}}{{hk}} |Cathy 🡲}}
{{cardholder|{{hk|1}}{{hk}}{{hk}}{{hk}} |Cathy 🡲}}
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When all players understand that a rightmost 1 play means they see {{hk|1}}, Alice can even mark trash cards:
When all players understand that a rightmost 1 play means they see {{hk|1}}, Alice can even mark trash cards:


{{hr}} {{hy|1}} {{hg|1}} {{hb|1}} {{hw|1}} {{hk|2}}
{{hTable||1|1|1|1|k=2}}
{{cardholder|{{hb|1|n=}}{{hg|1|n=}}{{hr|1|n=}}{{hk}} |Bob 🡲}}
{{cardholder|{{hb|1|n=}}{{hg|1|n=}}{{hr|1|n=}}{{hk}} |Bob 🡲}}
{{cardholder|{{hk|1}}{{hk}}{{hk}}{{hk}} |Cathy 🡲}}
{{cardholder|{{hk|1}}{{hk}}{{hk}}{{hk}} |Cathy 🡲}}
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|body3=We can extend this technique to optimise tracking:
|body3=We can extend this technique to optimise tracking:


{{hr}} {{hy}} {{hg}} {{hb}} {{hw}} {{hk}}
{{hTable|k=}}
 
{{cardholder|{{hk}}{{hk}}{{hk}}{{hr|1|n=}} |Bob 🡲}}
{{cardholder|{{hk}}{{hk}}{{hk}}{{hr|1|n=}} |Bob 🡲}}
{{cardholder|{{hk}}{{hk}}{{hk}}{{hk}} |Cathy 🡲}}
{{cardholder|{{hk}}{{hk}}{{hk}}{{hk}} |Cathy 🡲}}
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* Bob clues 1s to Donald.
* Bob clues 1s to Donald.


{{hr}} {{hy}} {{hg}} {{hb}} {{hw}} {{hk}}
{{hTable|k=}}
{{cardholder|{{hk}}{{hk}}{{hr|1|n=}}{{hg|1|n=}} |Cathy 🡲}}
{{cardholder|{{hk}}{{hk}}{{hr|1|n=}}{{hg|1|n=}} |Cathy 🡲}}
{{cardholder|{{hk}}{{hk}}{{hy|1|n=}}{{hb|1|n=}} |Donald 🡲}}
{{cardholder|{{hk}}{{hk}}{{hy|1|n=}}{{hb|1|n=}} |Donald 🡲}}
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* Donald also does not see {{hk|1}} so he plays his leftmost {{hy|1|n=}}.
* Donald also does not see {{hk|1}} so he plays his leftmost {{hy|1|n=}}.


{{hr|1}} {{hy|1}} {{hg}} {{hb}} {{hw}} {{hk}}
{{hTable|1|1||||k=}}
{{cardholder|{{hk}}{{hk}}{{hk}}{{hg|1|n=}} |Cathy 🡲}}
{{cardholder|{{hk}}{{hk}}{{hk}}{{hg|1|n=}} |Cathy 🡲}}
{{cardholder|{{hk}}{{hk}}{{hk}}{{hb|1|n=}} |Donald 🡲}}
{{cardholder|{{hk}}{{hk}}{{hk}}{{hb|1|n=}} |Donald 🡲}}
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The point is that so long as an important card is not in danger of being discarded, the situation should always resolve itself without any more clues given.
The point is that so long as an important card is not in danger of being discarded, the situation should always resolve itself without any more clues given.


== <div style="background:linear-gradient(45deg,#aff,#cfd,#fff0 40rem);padding:.25rem .5rem;border-top-left-radius:.5rem;">Endgame</div> ==
<div style="display:flex;justify-content:space-between;">{{text|[[User:Sammy_McSam/Hanabi|< Page 1]]|s=2}}{{text|[[User:Sammy_McSam/Hanabi_page_3|Page 3 >]]|s=2}}</div>
 
When to discard, play, empty clue, clue duplicates and advanced techniques.
 
=== Trash moves ===
 
When a direct clue is blocked by trash cards, we can finesse the playable card with a single clue that marks one or more trash cards.
 
==== 1. Trash push ====
 
* Trash push is optimal because
* Where the trash cards '''include the chop card''', the clued card is the '''rightmost''' unmarked card (i.e. touching the chop trash card).
 
{{Hr|5}} {{Hy|5}} {{Hg|5}} {{Hb|5}} {{Hw|3}} {{Hm|5}}
{{cardholder|{{Hm|4}}{{Hw|4}}{{Hm|1|n=}}{{Hr|1|n=}} |Bob 🡲}}
 
==== 2. Trash pull ====
 
* Pull is always inferior to push, both in order of interpretation and in quality.
* Where the trash cards '''do not include the chop card''', the clued card is the '''leftmost''' unmarked card (i.e. finesse position).
 
{{Hr|5}} {{Hy|5}} {{Hg|5}} {{Hb|5}} {{Hw|3}} {{Hm|5}}
{{cardholder|{{Hm|4|{{b}}|c=}}{{Hw|4}}{{Hm|1|{{b}}|c=}}{{Hr|1}} |Bob 🡲}}
 
{{infoBox |minWidth=max-content |state=collapsed |background=rebeccapurple
|title=which card is clued to play?
|body={{Hr|5}} {{Hy|5}} {{Hg|5}} {{Hb|5}} {{Hw|3}} {{Hm|5}}
* Alice to Bob: these two previously unmarked cards are blue.
 
{{cardholder|{{HBack|4|{{b}}|c=}}{{HBack}}{{HBack}}{{HBack|1|{{b}}|c=}} |Bob 🡲}}
}}
{{infoBox |minWidth=max-content |state=collapsed |background=green
|title=answer
|body=slot 3 because push always takes priority over pull.
}}
 
=== The critical move ===
 
To work out the most efficient sequence of moves, you need to determine three things:
;Critical colour: the colour that takes the most turns to complete.
: ''(i.e. must start as soon as possible to maximise the score).''
;Critical card: the first card of the critical colour.
: Note: this can be a '''duplicate''' of a card already marked!
;Critical move: the move that makes the critical card play.
: Note: this can be a '''clue''', '''play''' or '''discard'''.
 
: {{hr|2}} {{hy|5}} {{hg|5}} {{hb|5}} {{hw|2}}
 
{{cardholder|{{HBack}}{{HBack}}{{HBack}}{{HBack|3|{{r}}|n=|c=}} |Alice 🡲}}
{{cardholder|{{hw|3}}{{hk}}{{hk}}{{hr|4|n=|c=}} |Bob 🡲}}
{{cardholder|{{hk}}{{hk}}{{hk}}{{hr|5|n=|c=}} |Cathy 🡲}}
{{cardholder|{{hk}}{{hk}}{{hw|4|n=|c=}}{{hw|5|n=|c=}} |Donald 🡲}}
 
{{infoBoxes3 |minWidth=max-content |state=collapsed |background=rebeccapurple
|title1=What is the critical colour?
|body1='''Grouped by colour:'''
:{{cardholder|b={{r}}|{{hr|3|p=A}}{{hr|4|p=B}}{{hr|5|p=C}}{{hk|p=D}} }}
:{{cardholder|b={{w}}|{{hw|p=A|d=#324|c=}}{{hw|3|p=B|d=#324}}{{hk|p=C|d=#324}}{{hw|4|p=D|d=#324}} }} {{cardholder|b={{w}}|{{hk|p=A|d=#324}}{{hk|p=B|d=#324}}{{hk|p=C|d=#324}}{{hw|5|p=D|d=#324}} }}
 
'''white''' (1 clue + 3 plays + 4 empty = 8 turns)
|title2=What is the critical card?
|body2={{hw|3}}
|title3=What is the critical move?
|body3='''Alice''' clues {{hw|3|c}}
}}
 
{{infoBox |minWidth=max-content |state=collapsed
|title=Why it matters
|body='''Serialised:'''
:{{pill|Play {{hr|3}}}} {{cardholder|{{hr|3|p=A}}{{hr|4|p=B}}{{hr|5|p=C}}{{hw|p=D|c=}} }} {{cardholder|{{hk|p=A}}{{hw|3|p=B}}{{hk|p=C}}{{hw|4|p=D}} }} {{cardholder|{{hk|p=A}}{{hk|p=B}}{{hk|p=C}}{{hw|5|p=D}} }}
:{{pill|Clue {{hw|3}}}} {{cardholder|{{hw|p=A|c=}}{{hw|3|p=B}}{{hk|p=C}}{{hw|4|p=D}} }} {{cardholder|{{hr|3|p=A}}{{hr|4|p=B}}{{hr|5|p=C}}{{hw|5|p=D}} }}
}}
 
 
: {{hr|2}} {{hy|5}} {{hg|5}} {{hb|5}} {{hw|2}} {{pill|A) Play {{hr|3}}}} {{pill|B) Clue {{hw|3}}}}
 
 
{{cardholder|{{HBack}}{{HBack}}{{HBack|4|{{r}}|n=|c=}}{{HBack|3|{{r}}|n=|c=}} |Alice 🡲}}
{{cardholder|{{hw|3}}{{hk}}{{hk}}{{hk}} |Bob 🡲}}
{{cardholder|{{hk}}{{hk}}{{hk}}{{hr|5|n=|c=}} |Cathy 🡲}}
{{cardholder|{{hk}}{{hk}}{{hk}}{{hw|5|n=|c=}} |Donald 🡲}}
 
 
{{infoBox |minWidth=max-content |state=collapsed |background=green
|title=solution
|body='''1. Group by colour:'''
:{{cardholder|b={{r}}|{{hr|3|p=A}}{{hk|p=B}}{{hk|p=C}}{{hr|4|p=D}} }} {{cardholder|b={{r}}|{{hk|p=A}}{{hk|p=B}}{{hr|5|p=C}}{{hk|p=D}} }}
:{{cardholder|b={{w}}|{{hw|p=A|d=#324|c=}}{{hw|3|p=B|d=#324}}{{hk|p=C|d=#324}}{{hk|p=D|d=#324}} }} {{cardholder|b={{w}}|{{hk|p=A|d=#324}}{{hw|4|p=B|d=#324}}{{hk|p=C|d=#324}}{{hw|5|p=D|d=#324}} }}
'''2. Serialise:'''
:{{cardholder|{{hr|3|p=A}}{{hk|p=B}}{{hk|p=C}}{{hr|4|p=D}} }} {{cardholder|{{hw|p=A|c=}}{{hw|3|p=B}}{{hr|5|p=C}}{{hk|p=D}} }} {{cardholder|{{hk|p=A}}{{hw|4|p=B}}{{hk|p=C}}{{hw|5|p=D}} }}
:{{cardholder|{{hw|p=A|c=}}{{hw|3|p=B}}{{hk|p=C}}{{hk|p=D}} }} {{cardholder|{{hr|3|p=A}}{{hw|4|p=B}}{{hk|p=C}}{{hr|4|p=D}} }} {{cardholder|{{hk|p=A}}{{hk|p=B}}{{hr|5|p=C}}{{hw|5|p=D}} }}
}}
 
# Identify the critical colour - usually the player with the most unique cards, or consecutive cards of the same colour.
# Work out how many clue tokens are needed to reach the critical player.
# If you only have one unique card, discarding although counter-intuitive, is often the best move to generate a token!
 
This was a simple example. Test yourself with some '''[https://en.doc.boardgamearena.com/index.php?title=User:Sammy_McSam/Hanabi/Examples more complex examples]'''!
 
=== When to discard? ===
 
The endgame should be the easiest part since we can just calculate all possibilities, yet it is really hard to master.
 
With 5 '''flamboyants''', generating a token from a '''discard instead of a play''' may be the only way to reach the start of the critical path.
 
: {{HDeck|2}} {{hr|4}} {{hy|5}} {{hg|5}} {{hb|5}} {{hw|3}} {{hclue|0}}
 
{{cardholder|{{HBack}}{{HBack}}{{HBack}}{{HBack|5|{{r}}|n=|c=}} |Alice 🡲}}
{{cardholder|{{hk}}{{hk}}{{hk}}{{hk}} |Bob 🡲}}
{{cardholder|{{hk}}{{hk}}{{hw|4|n=|c=}}{{hw|5|n=|c=}} |Cathy 🡲}}
 
{{infoBoxes3 |minWidth=max-content |state=collapsed |background=rebeccapurple
|title1=What is the critical colour?
|body1='''Grouped by colour:'''
:{{cardholder|b={{w}}|{{hk|p=A|d=#324}}{{hk|p=B|d=#324}}{{hw|4|p=C|d=#324}} }} {{cardholder|b={{w}}|{{hk|p=A|d=#324}}{{hk|p=B|d=#324}}{{hw|5|p=C|d=#324}} }}
 
'''white''' (2 plays + 2 empty = 4 turns)
|title2=What is the critical card?
|body2={{hw|4}}
|title3=Who is the critical player?
|body3='''Cathy'''
}}
 
* To reach Cathy with a least {{HDeck|1}} remaining, only one of Bob or Alice can draw a card.
* '''Alice''' cannot clue ({{hclue|0}}) and '''must generate a token''' for Bob so that he can give a stall clue to avoid drawing the last card.
* Without 5 flamboyants Alice would just play her {{card|5}} which generates {{hclue|1}}.
* With 5 flamboyants Alice can't know if playing her {{card|5}} will generate a token, so Alice '''discards''' and '''plays after''' Cathy's '''critical card''' ({{hw|4}}).
 
==== General case with 5 flamboyants ====
 
When Alice '''does not have''' a card of the '''critical colour''', then '''discarding is better than playing!'''
 
=== Getting bottom decked ===
 
...is arguably the most 'unfair' part of Hanabi {{s:/}}.
 
Here's a '''[https://boardgamearena.com/archive/replay/250710-0850/?table=700345728&player=85540714&comments=84994396&goto=69 candidate for the worst ever bottom-decked situation]''': all three {{hb|1}} in the last {{HDeck|5}} cards {{S:O}}
 
=== Order of plays ===
 
Where the order may seem arbitrary, prioritise from most out-of-order to consecutive plays e.g.:
# {{hw|5}} {{hw|4}} {{hw|3}}
# {{hw|4}} {{hw|3}} {{hw|5}}
# {{hw|3}} {{hw|4}} {{hw|5}}
 
=== Replace flamboyant {{HanabiFlamboyant|4}} ===
 
The decision of which card to replace (or to skip) can communicate information to the team.
Priority highest to lowest:
# lowest rank unique
# lowest rank non-unique
# duplicate of an unmarked card
# duplicate of a marked card
# trash of number corresponding to the slot position of a playable card
# {{Hk|5}}
# skip
 
When there is no gain in returning a card playable in the future - either the immediate flamboyant {{HanabiFlamboyant|5}} will play from discard pile or , the decision of which trash card to replace into the deck can be a clue in itself corresponding to the slot position of a player.
When playing with black powder and 4 or 5 players, replacing an available 5k trash card indicates no playable card is visible.
 
== <div style="background:linear-gradient(45deg,#aff,#cfd,#fff0 40rem);padding:.25rem .5rem;border-top-left-radius:.5rem;">5 Flamboyants</div> ==
 
Don't let the '''5''' fool you - there are actually '''six''' randomly selected actions:
# {{HanabiFlamboyant|0}} Gain {{hclue|1}}
# {{HanabiFlamboyant|1}} Gain {{hclue|1}} & remove a mistake
# {{HanabiFlamboyant|2}} {{hCard|3|n=}} Give number clue
# {{HanabiFlamboyant|3}} {{hCard|C={{r}}|c=}} Give a color clue
# {{HanabiFlamboyant|4}} Replace a card from the discard pile into the deck
# {{HanabiFlamboyant|5}} Play a card from the discard pile
 
A 7th stack bonus is always irrelevant (and on BGA always gain {{hclue|1}} clue token), since there is no 8th stack.
<!--
If you are not bottom-decked and don't lose any unique cards:
* 5 colors: only one of the discard flamboyants is guaranteed
* 6/7 colors: both discard flamboyants are guaranteed
 
If you are not bottom-decked and lose one unique card:
* 5 colors: no discard flamboyants are guaranteed
* 6 colors: one discard flamboyant is guaranteed
* 7 colors: both discard flamboyants are guaranteed
 
<div style=display:flex>
{|class=wikitable
|+(not exactly) guaranteed scores if you are not bottom-decked
!style=text-align:right|Colors
!colspan=4|5
!colspan=4|6
!colspan=4|7
|-
!style=text-align:right|Uniques lost
!0
!1
!2
!3
!0
!1
!2
!3
!0
!1
!2
!3
|-
!style=text-align:left|Perfect
|✅
|❌
|❌
|❌
|✅
|✅
|❌
|❌
|✅
|✅
|❌
|❌
|-
!style=text-align:left|Perfect -1
|✅
|✅
|❌
|❌
|✅
|✅
|❌
|❌
|✅
|✅
|✅
|❌
|-
!style=text-align:left|Perfect -2
|✅
|✅
|✅
|❌
|✅
|✅
|✅
|❌
|✅
|✅
|✅
|✅
|-
!style=text-align:left|Perfect -3
|✅
|✅
|✅
|✅
|✅
|✅
|✅
|✅
|✅
|✅
|✅
|✅
|}</div>
-->
 
 
<!--
== {{s:(}} ==
 
# {{player|2}} {{master}} join a {{player|5}} game and don't understand basic finesse {{s:O2}}
#
#
#
#
-->
 
== <div style="background:linear-gradient(45deg,#aff,#cfd,#fff0 40rem);padding:.25rem .5rem;border-top-left-radius:.5rem;">Available Tokens</div> ==
 
{{infoBox |maxWidth=650
|title=Average clue tokens per played card
|body=
Imagine the end of an <q>ideal</q> game without flamboyants:
<hr>
{{player|3|size=2}}{{hand|5|size=2}}{{hr|5}} {{hy|5}} {{hg|5}} {{hb|5}} {{hw|5}}<br>
 
{{card|50|size=1.5}} (deck) ➖ {{card|25|size=1.5}} (played) ➖ {{card|12|size=1.5}} ({{player|3|size=1.5}}× at least{{hand|4}}) 🟰 {{card|13|size=1.5}} discards
 
{{hclue|13}} (discards) ➕ {{hclue|8}} (start) ➕ {{hclue|5}} ({{hr|5}} {{hy|5}} {{hg|5}} {{hb|5}} {{hw|5}}) ➖ {{hclue|1}} (last '''5''') 🟰 {{hclue|25}}
 
{{hclue|25}} ➗ {{card|25|size=1.5}} 🟰 {{hclue|1}} / {{hCard}}
<hr>
{{player|5|size=2}}{{hand|4|size=2}}{{hr|5}} {{hy|5}} {{hg|5}} {{hb|5}} {{hw|5}} ⇨ {{hclue|22}} ➗ {{card|25|size=1.5}} 🟰 {{hclue|.88}} / {{hCard}}
<hr>
{{player|2|size=2}}{{hand|6|size=2}}{{hr|5}} {{hy|5}} {{hg|5}} {{hb|5}} {{hw|5}} {{hm|5}} {{hk|1}} ⇨ {{hclue|39}} ➗ {{card|35|size=1.5}} 🟰 {{hclue|1.1}} / {{hCard}}
}}

Latest revision as of 19:18, 5 October 2026

⚠ Work in progress

MediaWiki-note-icons.png​This is page 2 of Hanabi conventions

When is it chop focus?

Travis Hall » 16 December 2023, 01:12

When playing with high-level partners, I generally try to regard a number clue touching chop as chop-focussed unless there is a timeliness consideration.[…]when giving a finesse, we can’t wait for the discard of the chop. For example:

Played: white2,with a white 2clue, white3,with a white 3clue,black powder,with a black powder clue,black powder,with a black powder clue,black powder,with a black powder clue, B 🡲 multicolour5,with a multicolour 5clue,black powder,with a black powder clue,white4,with a white 4clue,black powder4,with a black powder 4clue, C 🡲

A clues 4 to C. Cluing white is blocked by multicolour5,with a multicolour 5clue,. Cluing 4 can’t wait, because B will probably discard and white3,with a white 3clue, will move out of finesse. C can note the finesse response and adjust their expectation to play the left 4.

And I try to consistently clue the same way.

I recognise that many masters will clue 2s non-chop-focussed in the early game. Frankly, I’m not a fan, as this forces me to guess who does this and who does not, but I will guess because my rate of error is lower that way. I understand the consideration that 2s are the most valuable cards, but I’m not sure the risks are worth it.

Whenever somebody touches my chop with a number clue and expects me to play from the left, and I misfire, my question is always “Well, if my cards were the opposite way around, how would you have clued them?” Of the few who will answer that question at all, the answer is usually, “I would clue <number>,” and they don’t understand that this makes it impossible for me to do anything other than guess.

Since we know we can extract a playable cards with colour + number clues, it follows that number clues that mark the chop card are interpreted as:

  1. critical save if the chop card can be critical
  2. Double discard save if the player either side of the receiver has a non-critical card of the same number
  3. Otherwise a left-focused play clue.

black powder1,with a black powder 1clue,

Black powder 1

1 clues that mark the chop card are interpreted as a black powder1,with a black powder 1clue, save (unless the receiver already has a known play).

  • If a player can see black powder1,with a black powder 1clue,, it is logical to play all cards marked 1 from oldest to newest.

The oldest is the most valuable 1 because otherwise it could have been discarded before cluing 1.

Playing a chop card marked 1 can be played because:

  1. black powder1,with a black powder 1clue, is visible (and the player who can't see it is promised black powder1,with a black powder 1clue,)
    • This player should then track the newest position that can be black powder1,with a black powder 1clue,.
      • if this card reaches chop, it should not be saved with a direct clue.
      • if his card does receive a direct clue, it becomes a finesse.
  2. a playable 1 was discarded
  3. a playable 1 was not bluffed


The everlasting exception: context

Context > convention and can cause an unconventional move!

Think carefully about:

  1. timing (why now?),
  2. negative clues (e.g. "not red"),
  3. recently discarded cards,
  4. critical cards,
  5. tokens needed for saves or other plays
Example 1: double discard avoidance
Sometimes we need more information before we can know if a clue is a chop-focused save or a left-focused play clue.

Double discard avoidance saves are one of the most difficult clues to interpret because it's one of the very few times we can save non-critical cards without expecting a play response.

Nothing much is going on and there have not been any good ways to splash, give trash clues or otherwise delay one of the players.

Some players forbid a player from discarding if a double discard is possible

Strategy

Back to basics

In a 5players player game with card,with a Hanabi card clue,card,with a Hanabi card clue,card,with a Hanabi card clue,card,with a Hanabi card clue,​, each player can play one of the 4 card,with a Hanabi card clue, + discard one of the 4 card,with a Hanabi card clue, + clue one of the 5 numbers to any of the other ×4 players + clue one of the 5 colours to any of the other ×4 players = 48 possible moves per player. That's a lot to think about. But amazingly our human brains can filter out the vast majority of those moves as not logical given a bit of agreement on clue, play and discard interpretations (conventions).

Hand management

Hand management is important in high level play to keep as many non-trash cards in the game for as long as possible.

When to discard

  • The player before you has a valuable card on their chop that cannot be clued - so drawing new cards gives more opportunity for them to clue instead of discard their valuable chop.
  • The next player has a playable finesse position, but they have a save, fix or other important clue to give - so that the card remains in finesse position to be bluffed later.

When to skip players

(and how to irritate them cheeky​)

  • Opening with no information on any of your cards.
  • The player(s) skipped have duplicate cards that need to be marked with a good touch play clue.
  • If you have been the target of a trash bluff and not yet discarded cards to the right of the trash cards.
  • Players in front of you have trash.
  • The player behind you has many plays.

Double Discard Avoidance (DDA)

  • Many players have incomplete or non-existent methods for managing DDA because it is difficult as it requires a lot of contextual awareness.
  • Players need to be aware of how many opportunities there are to mark double chop cards.
  • Anytime a chop card is marked with a number of the same rank visible in the next player's hand DDA should be considered.
    • Or even if the double chop players are not next to each other but the in-between players are busy.

8 clue tokens

Efficiency

Bluffs

  • Bluffs are powerful...
  • Easiest way to mark nice cards
Maximising bluff opportunities sunglasses​
  • Once we realise the power of bluffs, it follows that we want to maximise the number of bluffing opportunities available to players.
  • In any given situation, it is possible to work out Alice's optimal move given the information available to her.
  • The basic idea is simple: look for the bluff opportunity that is furthest ahead.
  • Everyone should be making moves that enable that bluff opportunity to be used, and then work backwards from that player for the next opportunity.

So from Alice's point of view, she will see if:

  1. Donald can bluff Emily
  2. Cathy can bluff Donald
  3. Bob can bluff Cathy
  4. Alice can bluff Bob
Example 1
​
  1. Donald can bluff Emily
  2. Cathy cannot bluff Donald
  3. Bob can bluff Cathy
  4. Alice cannot bluff Bob

Then it's quite easy:

  1. Alice discards
  2. Bob bluffs Cathy
  3. Cathy discards
  4. Donald bluffs Emily
Example 2
Now if Alice can also bluff:
  • Donald can bluff Emily
  • Cathy cannot bluff Donald
  • Bob can bluff Cathy
  • Alice can bluff Bob

    • Then it's still easy:

    1. Alice either double bluffs Bob & Cathy or discards
    2. Bob responds or bluffs Cathy
    3. Cathy discards
    4. Donald bluffs Emily
    Example 3
    Now if Cathy can also bluff:
  • Donald can bluff Emily
  • Cathy cannot bluff Donald
  • Bob can bluff Cathy
  • Alice can bluff Bob

    • Then it's significantly more complicated for the team to predict, but not much more complex for Alice:

    1. Alice should probably discard (unless there is a really good bluff target available to her
    2. Bob makes a similar decision
    3. Cathy responds, double bluffs or discards
    4. Donald responds or bluffs Emily
    When to not save critical cards surprised​
    • No matter how many tokens you have, whether it is 1 clue tokens or 7 clue tokens, you do not always have to spend a token to save a card.
      • Some players might find this statement controversial.
    • Each player must consider the likelihood of a certain move and assess if the risk-reward of all the possible moves.

    We know that there are a lot of possible moves, and even more game states.

    Examples of clear good/bad

    Questionable examples

    Context examples

    When to Trash bluff
    • When you first learn about trash bluffs, you need to practice it and that's fine.
    • Once you are comfortable with how it works, you need to consider if you should use a trash bluff.
    • Examples where it is clearly bad
    Played: white1,with a white 1clue, blue1,with a blue 1clue,black powder,with a black powder clue,black powder,with a black powder clue,black powder,with a black powder clue, Bob 🡲 white1,with a white 1clue,white1,with a white 1clue,blue2,with a blue 2clue,blue2,with a blue 2clue, Cathy 🡲
    • With black powder: 1 bluffs are black powder1,with a black powder 1clue, promise bluffs unless black powder1,with a black powder 1clue, is known to Alice and the receiver.

    Would you trash bluff 5k when all 5s are not visible?

    white3,with a white 3clue,

    Reverses with number

    • Reverse finesses are often not great if the finessed card could instead be bluffed, however, it can be useful to mark a chop card as a reverse to ensure it is not discarded.

    black powder,with a black powder clue,black powder,with a black powder clue,black powder,with a black powder clue,white2,with a white 2clue, Bob 🡲 black powder,with a black powder clue,black powder,with a black powder clue,black powder,with a black powder clue,black powder,with a black powder clue, Cathy 🡲 white1,with a white 1clue,black powder,with a black powder clue,black powder,with a black powder clue,black powder,with a black powder clue, Donald 🡲 Usually Alice and Bob should discard so that Cathy can bluff Donald's white1,with a white 1clue,, but Bob's white2,with a white 2clue, is more valuable than any bluff target Alice can see, so she chooses to reverse with colour.

    But what if reversing with colour would mark trash?

    • If we can finesse with number, why can't we also reverse finesse with number?
    • A reverse with number is usually harder to read than a reverse with colour, but they are more efficient than colour + multiple correction clues (to prevent future bombs).

    Travis Hall gives a basic explanation of number reverses:

    Similarly, we often avoid number reverses, because if there’s both an available reverse to any card of that number and an immediately playable card of that number, the clue receiver has to guess at the correct move, and this can easily go wrong. Even so, when circumstance narrows the possibilities enough, we can sometimes do a number reverse safely.

    multicolour3,with a multicolour 3clue,

    Multicolour reverses with colour

    Travis Hall explains it well:

    We usually avoid reverse finesses in multicolour, because although multi does connect with any colour, if we reverse multis then responses to our most common play clues - colour clues to a playable card - just stop, all of them, if a playable multi is in someone’s blind finesse position. That can be very difficult to work around.

    • Multicolour reverses with a single colour can work, the most common situation being where the clue giver and receiver can both see a playable card of the colour clued either marked or in the finesse position in someone else's hand.
    • Such a reverse may also trigger a hesitation play.

    When to Gentleman's Discard (GD)

    1. Plays extra cards for free from one or more hands.
    2. Protect cards
    3. Token is needed

    GD without one of these benefits is usually of negative value:

    • Limits the freedom to clue.
    • Misleads the receiver - the cards to the right of the copy is not trash.

    Context

    Using the last token 0 clue tokens

    Cause a valuable discard

    • Marked in a hand
    • Unmarked in a hand

    Following player has a locked hand

    • Cause a trash or duplicate discard e.g. black powder5,with a black powder 5clue, from 5 save.
    • Cause a play

    Negatives

    Write notes if necessary.

    1. Keep track of your own negatives.
    2. Keep track of all negatives.

    Play finesse position e.g. multicolour bluff where:

    • a colour-marked card has a negative colour

    Multicolour bluff target is clued with a single colour

    • if it can be clued red, but another colour is chosen = finesse
    • if it can't be clued red = prompt


    Cluing

    Marking fewer than possible cards e.g. marking a single 2 with colour instead of multiple 2s with number = duplicate 2 in your hand

    no prompt

    no save = non-critical

    cards in the deckredyellowgreenbluewhitemulticolorblack powder
    ​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens1 clue tokens2 clue tokens3 clue tokens4 clue tokens5 clue tokens6 clue tokens7 clue tokens8 clue tokens
    card back,with a clue,card back,with a clue,card back,with a clue,card back,with a clue,Alice 🡲white1,with a white 1clue,black powder,with a black powder clue,black powder,with a black powder clue,white3,with a white 3clue,Bob 🡲black powder,with a black powder clue,black powder,with a black powder clue,red2,with a red 2clue,black powder,with a black powder clue,Cathy 🡲
    Alice to Bob: these 2 cards are white.
    cards in the deckredyellowgreenbluewhite1multicolorblack powder
    ​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens1 clue tokens2 clue tokens3 clue tokens4 clue tokens5 clue tokens6 clue tokens7 clue tokens8 clue tokens
    card back,with a clue,card back,with a clue,card back,with a clue,card back,with a clue,Alice 🡲black powder,with a black powder clue,black powder,with a black powder clue,black powder,with a black powder clue,white3,with a white 3clue,Bob 🡲black powder,with a black powder clue,black powder,with a black powder clue,red2,with a red 2clue,black powder,with a black powder clue,Cathy 🡲
    Bob plays white1,with a white 1clue,.
    cards in the deckredyellowgreenbluewhite1multicolorblack powder
    ​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens1 clue tokens2 clue tokens3 clue tokens4 clue tokens5 clue tokens6 clue tokens7 clue tokens8 clue tokens
    card back,with a clue,card back2,with a 2clue,card back,with a clue,card back4,with a 4clue,Alice 🡲black powder,with a black powder clue,black powder,with a black powder clue,black powder,with a black powder clue,white3,with a white 3clue,Bob 🡲black powder,with a black powder clue,black powder,with a black powder clue,red2,with a red 2clue,black powder,with a black powder clue,Cathy 🡲
    Cathy to Alice: these 2 cards are white.
    cards in the deckredyellowgreenbluewhite2multicolorblack powder
    ​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens1 clue tokens2 clue tokens3 clue tokens4 clue tokens5 clue tokens6 clue tokens7 clue tokens8 clue tokens
    card back,with a clue,card back,with a clue,card back,with a clue,card back4,with a 4clue,Alice 🡲black powder,with a black powder clue,black powder,with a black powder clue,black powder,with a black powder clue,white3,with a white 3clue,Bob 🡲black powder,with a black powder clue,black powder,with a black powder clue,red2,with a red 2clue,black powder,with a black powder clue,Cathy 🡲
    Alice plays white2,with a white 2clue,.
    cards in the deckredyellowgreenbluewhite2multicolorblack powder
    ​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens1 clue tokens2 clue tokens3 clue tokens4 clue tokens5 clue tokens6 clue tokens7 clue tokens8 clue tokens
    card back,with a clue,card back,with a clue,card back,with a clue,card back4,with a 4clue,Alice 🡲black powder,with a black powder clue,black powder,with a black powder clue,black powder,with a black powder clue,white3,with a white 3clue,Bob 🡲black powder,with a black powder clue,black powder,with a black powder clue,red2,with a red 2clue,black powder,with a black powder clue,Cathy 🡲
    Bob discards.
    cards in the deckredyellowgreenbluewhite2multicolorblack powder
    ​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens​ clue tokens1 clue tokens2 clue tokens3 clue tokens4 clue tokens5 clue tokens6 clue tokens7 clue tokens8 clue tokens
    card back,with a clue,card back,with a clue,card back,with a clue,card back4,with a 4clue,Alice 🡲black powder,with a black powder clue,black powder,with a black powder clue,black powder,with a black powder clue,white3,with a white 3clue,Bob 🡲white4,with a white 4clue,black powder,with a black powder clue,black powder,with a black powder clue,red2,with a red 2clue,Cathy 🡲
    Cathy discards.

    What is the best move for Alice?

    A) clue white3,with a white 3clue, B) clue white4,with a white 4clue, C) clue white4,with a white 4clue, C) play card back4,with a 4clue, D) discard card back4,with a 4clue, E) discard chop card back,with a clue,

    Solution
    D) discard card back4,with a 4clue,
    1. Alice's chop card was not marked before her free move to clue Bob, so she knows her oldest white card cannot be critical (white5,with a white 5clue,).
    2. According to good touch, Alice can assume her white card is also not a 3 and could be a 4.
    3. Alice sees Bob has a valuable red2,with a red 2clue, on chop, marked white3,with a white 3clue, and unmarked white4,with a white 4clue, in his finesse position.
    In order to delay the future discard of red2,with a red 2clue,, the best move for Alice is to discard her non-critical white card to trigger Bob to play white3,with a white 3clue, and white4,with a white 4clue,.
    ⯇
    ⯈
    ⯇
    ⯈
    ↺
    ⯇
    ⯈
    ↺
    ⯇
    ⯈
    ↺
    ⯇
    ⯈
    ↺
    ⯇
    ↺

    black powder1,with a black powder 1clue,

    Black powder 1 tracking

    Example 1: basic tracking
    cards in the deckredyellowgreenbluewhitemulticolorblack powder

    black powder,with a black powder clue,black powder,with a black powder clue,black powder,with a black powder clue,red1,with a red 1clue, Bob 🡲 black powder1,with a black powder 1clue,black powder,with a black powder clue,black powder,with a black powder clue,black powder,with a black powder clue, Cathy 🡲

    • First clue of the game. Alice to Bob: this card is a 1.
    • Bob plays red1,with a red 1clue,.
    • Cathy knows that Bob would not be able to play if he cannot see black powder1,with a black powder 1clue,.
    • Cathy cannot see black powder1,with a black powder 1clue, so she must have black powder1,with a black powder 1clue, in her hand.

    Cathy knows that ordinarily her black powder1,with a black powder 1clue, will be saved once it reaches her chop. But what if black powder1,with a black powder 1clue, is in her slot 1?

    If Cathy tracks her leftmost unmarked card, once black powder1,with a black powder 1clue, reaches her chop, she already knows it and black powder1,with a black powder 1clue, does not need to be saved at all!
    Example 2: any rightmost 1 play
    We can extend this technique to any position at any time:
    • Alice to Bob: these two cards are 1s.

    cards in the deckredyellow1green2blue1whitemulticolorblack powder3 black powder,with a black powder clue,white1,with a white 1clue,red1,with a red 1clue,black powder,with a black powder clue, Bob 🡲 black powder1,with a black powder 1clue,black powder,with a black powder clue,black powder,with a black powder clue,black powder,with a black powder clue, Cathy 🡲

    • Bob plays red1,with a red 1clue,.
    • Cathy knows that ordinarily Bob will play the leftmost 1 first since play clues are left-focused. But since Bob played his rightmost 1, logically this communicates something extra: that Bob can see black powder1,with a black powder 1clue,. So Cathy knows she has black powder1,with a black powder 1clue, in her hand and notes that her leftmost can be black powder1,with a black powder 1clue,.

    When all players understand that a rightmost 1 play means they see black powder1,with a black powder 1clue,, Alice can even mark trash cards:

    cards in the deckredyellow1green1blue1white1multicolorblack powder2 blue1,with a blue 1clue,green1,with a green 1clue,red1,with a red 1clue,black powder,with a black powder clue, Bob 🡲

    black powder1,with a black powder 1clue,black powder,with a black powder clue,black powder,with a black powder clue,black powder,with a black powder clue, Cathy 🡲
    Example 3: negatives
    We can extend this technique to optimise tracking:

    cards in the deckredyellowgreenbluewhitemulticolorblack powder

    black powder,with a black powder clue,black powder,with a black powder clue,black powder,with a black powder clue,red1,with a red 1clue, Bob 🡲 black powder,with a black powder clue,black powder,with a black powder clue,black powder,with a black powder clue,black powder,with a black powder clue, Cathy 🡲 yellow1,with a yellow 1clue,yellow3,with a yellow 3clue,yellow5,with a yellow 5clue,black powder1,with a black powder 1clue, Donald 🡲

    • Alice to Bob: this card is a 1.
    • Bob plays red1,with a red 1clue,.
    • Cathy clues yellow to Donald.
    • Donald knows that Bob would not be able to play if he cannot see black powder1,with a black powder 1clue,.
    • After Cathy clues yellow, the leftmost possible position for his black powder1,with a black powder 1clue, has moved to his chop.

    Taking example 2 further, we can even play all slot 4 1s when black powder1,with a black powder 1clue, is still in the deck!

    • Alice clues 1s to Cathy.
    • Bob clues 1s to Donald.

    cards in the deckredyellowgreenbluewhitemulticolorblack powder black powder,with a black powder clue,black powder,with a black powder clue,red1,with a red 1clue,green1,with a green 1clue, Cathy 🡲 black powder,with a black powder clue,black powder,with a black powder clue,yellow1,with a yellow 1clue,blue1,with a blue 1clue, Donald 🡲

    • Cathy does not see black powder1,with a black powder 1clue, so she plays her leftmost red1,with a red 1clue,.
    • Donald also does not see black powder1,with a black powder 1clue, so he plays his leftmost yellow1,with a yellow 1clue,.

    cards in the deckred1yellow1greenbluewhitemulticolorblack powder black powder,with a black powder clue,black powder,with a black powder clue,black powder,with a black powder clue,green1,with a green 1clue, Cathy 🡲 black powder,with a black powder clue,black powder,with a black powder clue,black powder,with a black powder clue,blue1,with a blue 1clue, Donald 🡲

    Since both players have communicated that they do not see black powder1,with a black powder 1clue,, it is still in the deck and next turn everyone can play their remaining 1s.

    Applying this principal generally is tricky because it can become unclear what has triggered a blind-play

    slot 3 blind plays

    • When you track black powder1,with a black powder 1clue,, the position becomes known when the leftmost possible position reaches your slot 3 and your slot 4 is not saved.

    card back,with a clue,card back,with a clue,black powder1,with a black powder 1clue,card back,with a clue, You 🡲

    red2,with a red 2clue,

    uncertain 2s

    Since 2s (& black powder4,with a black powder 4clue,) are so valuable, if a player is allowed or encouraged to discard a 2 when it could have been prevented or even just delayed, it is logical that there is another copy of that card in the same hand or visible in someone else's.

    • So you can track it like black powder1,with a black powder 1clue, and also blind play it before it is marked as soon as it is playable.
    Question
    Consider this situation:
    • Alice clues Donald's blue5,with a blue 5clue,

    card back,with a clue,card back,with a clue,card back,with a clue,card back,with a clue, Bob 🡲 blue1,with a blue 1clue,black powder,with a black powder clue,black powder,with a black powder clue,black powder,with a black powder clue, Cathy 🡲 black powder,with a black powder clue,black powder,with a black powder clue,blue5,with a blue 5clue,red5,with a red 5clue, Donald 🡲

    • Bob sees blue1,with a blue 1clue, and correctly assumes he has blue2,with a blue 2clue,blue3,with a blue 3clue,blue4,with a blue 4clue, and mentally congratulates Alice on a great clue.
    • So Bob saves red5,with a red 5clue,:

    card back,with a clue,card back,with a clue,card back,with a clue,card back,with a clue, Bob 🡲 blue1,with a blue 1clue,black powder,with a black powder clue,black powder,with a black powder clue,black powder,with a black powder clue, Cathy 🡲 black powder,with a black powder clue,black powder,with a black powder clue,blue5,with a blue 5clue,red5,with a red 5clue, Donald 🡲

    • Cathy discards.
    • Donald discards.
    • Alice discards.
    • What should Bob do?
    A) discard chopB) clue blue1,with a blue 1clue,C) play slot 1D) discard slot 1E) type "??" in chat
    Answer
    C) play slot 1 as blue1,with a blue 1clue,

    Always remember to:

    1. assume your teammates are giving valid clues (whether it's a good clue is a whole other question!)
    2. stop and consider all possibilities
    3. not type any reaction to a move in chat because it will usually spoil the game for everyone because you:
      1. tell everyone you found the move strange
      2. distract everyone from thinking about the best moves
      3. may provoke a player who is insecure or prideful into an argument
    Discussion at the end of the game can benefit everyone: Bob and Cathy can explain why they didn't respond and the whole team can discuss if it was a good finesse.

    Passing back a finesse

    • Normally we know that if we finesse a card and more than one player has a copy of the same finessed card, the first player will not play it because they see it in another hand, and the last player who does not see a future response must play the card.
    • However sometimes we have a situation where it would be clearly a blunder to play.
    • In the last example, Cathy's choice to discard instead of play for blue1,with a blue 1clue, was the correct choice given she saw all the connecting cards in Bob's hand. Note that if Cathy had a critical card on chop, this finesse would be a blunder.

    What if there were only one connecting card behind blue1,with a blue 1clue,?

    • Alice clues Donald's blue4,with a blue 4clue,

    blue1,with a blue 1clue,blue3,with a blue 3clue,black powder,with a black powder clue,black powder,with a black powder clue, Bob 🡲 blue1,with a blue 1clue,black powder,with a black powder clue,black powder,with a black powder clue,black powder,with a black powder clue, Cathy 🡲 black powder,with a black powder clue,black powder,with a black powder clue,white4,with a white 4clue,red5,with a red 5clue, Donald 🡲

    • Bob sees blue1,with a blue 1clue, in Cathy's hand, so he saves red5,with a red 5clue,

    Or Cathy has both connecting cards as well?

    • Double pass back

    The point is that so long as an important card is not in danger of being discarded, the situation should always resolve itself without any more clues given.

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