Sammy McSam: Created page with "{{pill|⚠ Work in progress|#fa8|#fc8|s=1.2}} {{info|This is page 3 of Hanabi conventions}} ==
Endgame
== 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..."

2026-10-05T17:18:32Z

Created page with "{{pill|⚠ Work in progress|#fa8|#fc8|s=1.2}} {{info|This is page 3 of Hanabi conventions}} == <div style="background:linear-gradient(45deg,#aff,#cfd,#fff0 40rem);padding:.25rem .5rem;border-top-left-radius:.5rem;">Endgame</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..."

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{{pill|⚠ Work in progress|#fa8|#fc8|s=1.2}}
{{info|This is page 3 of [[User:Sammy_McSam/Hanabi|Hanabi conventions]]}}

== <div style="background:linear-gradient(45deg,#aff,#cfd,#fff0 40rem);padding:.25rem .5rem;border-top-left-radius:.5rem;">Endgame</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).

{{hTable|5|5|5|5|3|m=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).

{{hTable|5|5|5|5|3|m=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={{hTable|5|5|5|5|3|m=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'''.

: {{hTable|2|5|5|5|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}} }}
}}

: {{hTable|2|5|5|5|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 critical 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 critical 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.

: {{hTable|4|5|5|5|3|d=2}} {{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 critical
# lowest rank non-critical
# 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 colour 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.




== <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}}{{hTable|5|5|5|5|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}}{{hTable|5|5|5|5|5}} ⇨ {{hclue|22}} ➗ {{card|25|size=1.5}} 🟰 {{hclue|.88}} / {{hCard}}
<hr>
{{player|2|size=2}}{{hand|6|size=2}}{{hTable|5|5|5|5|5|m=5|k=1}} ⇨ {{hclue|39}} ➗ {{card|35|size=1.5}} 🟰 {{hclue|1.1}} / {{hCard}}
}}

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