User:Sammy McSam/Hanabi page 2 - Revision history

Sammy McSam: Template:hTable

2026-06-26T11:57:36Z

← Older revision		Revision as of 13:57, 26 June 2026
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	<div style="columns:14rem auto;column-gap:2rem;white-space:nowrap;">		<div style="columns:14rem auto;column-gap:2rem;white-space:nowrap;">
	: {{~~hr}} {{hy~~\|5~~}} {{hg~~\|5~~}} {{hb~~\|5~~}} {{hw~~}} {{hclue\|2}}		: {{hTable\|\|5\|5\|5}} {{hclue\|2}}
	: {{cardholder\|{{HBack}}{{HBack}}{{HBack}}{{HBack}} \|Alice 🡲}} {{cardholder\|{{hw\|1}}{{hr\|2}}{{hk}}{{hw\|3}} \|Bob 🡲}}		: {{cardholder\|{{HBack}}{{HBack}}{{HBack}}{{HBack}} \|Alice 🡲}} {{cardholder\|{{hw\|1}}{{hr\|2}}{{hk}}{{hw\|3}} \|Bob 🡲}}
	# Alice to Bob: these 2 cards are white.		# Alice to Bob: these 2 cards are white.
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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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	* Where the trash cards '''include the chop card''', the clued card is the '''rightmost''' unmarked card (i.e. touching the chop trash card).		* 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}}		{{hTable\|5\|5\|5\|5\|3\|m=5}}
	{{cardholder\|{{Hm\|4}}{{Hw\|4}}{{Hm\|1\|n=}}{{Hr\|1\|n=}} \|Bob 🡲}}		{{cardholder\|{{Hm\|4}}{{Hw\|4}}{{Hm\|1\|n=}}{{Hr\|1\|n=}} \|Bob 🡲}}

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	* Where the trash cards '''do not include the chop card''', the clued card is the '''leftmost''' unmarked card (i.e. finesse position).		* 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}}		{{hTable\|5\|5\|5\|5\|3\|m=5}}
	{{cardholder\|{{Hm\|4\|{{b}}\|c=}}{{Hw\|4}}{{Hm\|1\|{{b}}\|c=}}{{Hr\|1}} \|Bob 🡲}}		{{cardholder\|{{Hm\|4\|{{b}}\|c=}}{{Hw\|4}}{{Hm\|1\|{{b}}\|c=}}{{Hr\|1}} \|Bob 🡲}}

	{{infoBox \|minWidth=max-content \|state=collapsed \|background=rebeccapurple		{{infoBox \|minWidth=max-content \|state=collapsed \|background=rebeccapurple
	\|title=which card is clued to play?		\|title=which card is clued to play?
	\|body={{Hr\|5~~}} {{Hy~~\|5~~}} {{Hg~~\|5~~}} {{Hb~~\|5~~}} {{Hw~~\|3~~}} {{Hm~~\|5}}		\|body={{hTable\|5\|5\|5\|5\|3\|m=5}}
	* Alice to Bob: these two previously unmarked cards are blue.		* Alice to Bob: these two previously unmarked cards are blue.

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	: Note: this can be a '''clue''', '''play''' or '''discard'''.		: Note: this can be a '''clue''', '''play''' or '''discard'''.

	: {{hr\|2~~}} {{hy~~\|5~~}} {{hg~~\|5~~}} {{hb~~\|5~~}} {{hw~~\|2}}		: {{hTable\|2\|5\|5\|5\|2}}

	{{cardholder\|{{HBack}}{{HBack}}{{HBack}}{{HBack\|3\|{{r}}\|n=\|c=}} \|Alice 🡲}}		{{cardholder\|{{HBack}}{{HBack}}{{HBack}}{{HBack\|3\|{{r}}\|n=\|c=}} \|Alice 🡲}}
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	: {{hr\|2~~}} {{hy~~\|5~~}} {{hg~~\|5~~}} {{hb~~\|5~~}} {{hw~~\|2}} {{pill\|A) Play {{hr\|3}}}} {{pill\|B) Clue {{hw\|3}}}}		: {{hTable\|2\|5\|5\|5\|2}} {{pill\|A) Play {{hr\|3}}}} {{pill\|B) Clue {{hw\|3}}}}


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	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.		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}}		: {{hTable\|4\|5\|5\|5\|3\|d=2}} {{hclue\|0}}

	{{cardholder\|{{HBack}}{{HBack}}{{HBack}}{{HBack\|5\|{{r}}\|n=\|c=}} \|Alice 🡲}}		{{cardholder\|{{HBack}}{{HBack}}{{HBack}}{{HBack\|5\|{{r}}\|n=\|c=}} \|Alice 🡲}}
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	Imagine the end of an <q>ideal</q> game without flamboyants:		Imagine the end of an <q>ideal</q> game without flamboyants:
	<hr>		<hr>
	{{player\|3\|size=2}}{{hand\|5\|size=2}}{{hr\|5~~}} {{hy~~\|5~~}} {{hg~~\|5~~}} {{hb~~\|5~~}} {{hw~~\|5}}<br>		{{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		{{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
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	{{hclue\|25}} ➗ {{card\|25\|size=1.5}} 🟰 {{hclue\|1}} / {{hCard}}		{{hclue\|25}} ➗ {{card\|25\|size=1.5}} 🟰 {{hclue\|1}} / {{hCard}}
	<hr>		<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}}		{{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>		<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}}		{{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}}
	}}		}}

Sammy McSam: overflow from page 1

2026-06-24T14:33:43Z

overflow from page 1

Show changes

Sammy McSam: Template:Hclue update

2026-05-05T21:15:15Z

Template:Hclue update

← Older revision		Revision as of 23:15, 5 May 2026
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	* To reach Cathy with a least {{HDeck\|1}} remaining, only one of Bob or Alice can draw a card.		* To reach Cathy with a least {{HDeck\|1}} remaining, only one of Bob or Alice can draw a card.
	* '''Alice''' cannot clue ({{hclue\|0~~\|size=1.2~~}}) and '''must generate a token''' for Bob so that he can give a stall clue to avoid drawing the last 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}}.		* 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}}).		* 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}}).

Sammy McSam: Template:InfoBox update

2026-02-10T17:14:17Z

Template:InfoBox update

Sammy McSam at 16:11, 7 February 2026

2026-02-07T16:11:30Z

← Older revision		Revision as of 18:11, 7 February 2026
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			{{pill\|⚠ Work in progress\|#fa8\|#fc8\|s=1.2}}
	{{info\|This is page 2 of [[User:Sammy_McSam/Hanabi\|Hanabi conventions]]}}		{{info\|This is page 2 of [[User:Sammy_McSam/Hanabi\|Hanabi conventions]]}}

Sammy McSam: Context

2026-02-07T16:06:02Z

Context

Show changes

Sammy McSam: /* Endgame */ Trash moves

2026-01-20T20:18:14Z

Endgame: Trash moves

← Older revision		Revision as of 22:18, 20 January 2026
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	When to discard, play, empty clue, clue duplicates and advanced techniques.		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 \|color=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 \|color=green
			\|title=answer
			\|body=slot 3 because push always takes priority over pull.
			}}

	=== The critical move ===		=== The critical move ===

Sammy McSam: Template:Cardholder update

2025-08-01T15:31:10Z

Template:Cardholder update

Sammy McSam: Available Tokens

2025-07-27T00:38:20Z

Available Tokens

← Older revision		Revision as of 02:38, 27 July 2025
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	#		#
	-->		-->

			== <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}}
			}}

Sammy McSam: page 2 of Hanabi conventions

2025-07-27T00:23:56Z

page 2 of Hanabi conventions

New page

{{pill|{{text|w=100|🛈}} This is page 2 of [[User:Sammy_McSam/Hanabi|Hanabi conventions]]|#aff|#cfd|s=1.2}}

== <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.

=== 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 |color=rebeccapurple
|title1=What is the critical colour?
|body1='''Grouped by colour:'''
:{{cardholder|c={{r}}|{{hr|3|p=A}}{{hr|4|p=B}}{{hr|5|p=C}}{{hk|p=D}} }}
:{{cardholder|c={{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|c={{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 |color=green
|title=solution
|body='''1. Group by colour:'''
:{{cardholder|c={{r}}|{{hr|3|p=A}}{{hk|p=B}}{{hk|p=C}}{{hr|4|p=D}} }} {{cardholder|c={{r}}|{{hk|p=A}}{{hk|p=B}}{{hr|5|p=C}}{{hk|p=D}} }}
:{{cardholder|c={{w}}|{{hw|p=A|d=#324|c=}}{{hw|3|p=B|d=#324}}{{hk|p=C|d=#324}}{{hk|p=D|d=#324}} }} {{cardholder|c={{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 |color=rebeccapurple
|title1=What is the critical colour?
|body1='''Grouped by colour:'''
:{{cardholder|c={{w}}|{{hk|p=A|d=#324}}{{hk|p=B|d=#324}}{{hw|4|p=C|d=#324}} }} {{cardholder|c={{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|size=1.2}}) 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.

← Older revision		Revision as of 19:14, 10 February 2026
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	</div>		</div>

	{{infoBoxes3 \|titleAlign=left \|~~color~~=#088		{{infoBoxes3 \|titleAlign=left \|background=#088
	\|title1=What is the best move for Alice?		\|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}}		\|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 \|~~color~~=green		{{infoBox \|minWidth=max-content \|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=}} }}
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	=== Black powder 1 tracking ===		=== Black powder 1 tracking ===

	{{infoBoxes3 \|state=collapsed \|titleAlign=left \|~~color~~=#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={{hr}} {{hy}} {{hg}} {{hb}} {{hw}} {{hk}}
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	* So you can track it like {{hk\|1}} and also blind play it before it is marked as soon as it is playable.		* So you can track it like {{hk\|1}} and also blind play it before it is marked as soon as it is playable.

	{{InfoBoxes \|state=collapsed \|titleAlign=left \|~~color1~~=green \|~~color2~~=rebeccapurple		{{InfoBoxes \|state=collapsed \|titleAlign=left \|background1=green \|background2=rebeccapurple
	\|title1=Question		\|title1=Question
	\|body1=		\|body1=
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	{{cardholder\|{{Hm\|4\|{{b}}\|c=}}{{Hw\|4}}{{Hm\|1\|{{b}}\|c=}}{{Hr\|1}} \|Bob 🡲}}		{{cardholder\|{{Hm\|4\|{{b}}\|c=}}{{Hw\|4}}{{Hm\|1\|{{b}}\|c=}}{{Hr\|1}} \|Bob 🡲}}

	{{infoBox \|minWidth=max-content \|state=collapsed \|~~color~~=rebeccapurple		{{infoBox \|minWidth=max-content \|state=collapsed \|background=rebeccapurple
	\|title=which card is clued to play?		\|title=which card is clued to play?
	\|body={{Hr\|5}} {{Hy\|5}} {{Hg\|5}} {{Hb\|5}} {{Hw\|3}} {{Hm\|5}}		\|body={{Hr\|5}} {{Hy\|5}} {{Hg\|5}} {{Hb\|5}} {{Hw\|3}} {{Hm\|5}}
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	{{cardholder\|{{HBack\|4\|{{b}}\|c=}}{{HBack}}{{HBack}}{{HBack\|1\|{{b}}\|c=}} \|Bob 🡲}}		{{cardholder\|{{HBack\|4\|{{b}}\|c=}}{{HBack}}{{HBack}}{{HBack\|1\|{{b}}\|c=}} \|Bob 🡲}}
	}}		}}
	{{infoBox \|minWidth=max-content \|state=collapsed \|~~color~~=green		{{infoBox \|minWidth=max-content \|state=collapsed \|background=green
	\|title=answer		\|title=answer
	\|body=slot 3 because push always takes priority over pull.		\|body=slot 3 because push always takes priority over pull.
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	{{cardholder\|{{hk}}{{hk}}{{hw\|4\|n=\|c=}}{{hw\|5\|n=\|c=}} \|Donald 🡲}}		{{cardholder\|{{hk}}{{hk}}{{hw\|4\|n=\|c=}}{{hw\|5\|n=\|c=}} \|Donald 🡲}}

	{{infoBoxes3 \|minWidth=max-content \|state=collapsed \|~~color~~=rebeccapurple		{{infoBoxes3 \|minWidth=max-content \|state=collapsed \|background=rebeccapurple
	\|title1=What is the critical colour?		\|title1=What is the critical colour?
	\|body1='''Grouped by colour:'''		\|body1='''Grouped by colour:'''
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	{{infoBox \|minWidth=max-content \|state=collapsed \|~~color~~=green		{{infoBox \|minWidth=max-content \|state=collapsed \|background=green
	\|title=solution		\|title=solution
	\|body='''1. Group by colour:'''		\|body='''1. Group by colour:'''
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	{{cardholder\|{{hk}}{{hk}}{{hw\|4\|n=\|c=}}{{hw\|5\|n=\|c=}} \|Cathy 🡲}}		{{cardholder\|{{hk}}{{hk}}{{hw\|4\|n=\|c=}}{{hw\|5\|n=\|c=}} \|Cathy 🡲}}

	{{infoBoxes3 \|minWidth=max-content \|state=collapsed \|~~color~~=rebeccapurple		{{infoBoxes3 \|minWidth=max-content \|state=collapsed \|background=rebeccapurple
	\|title1=What is the critical colour?		\|title1=What is the critical colour?
	\|body1='''Grouped by colour:'''		\|body1='''Grouped by colour:'''

← Older revision		Revision as of 17:31, 1 August 2025
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	{{~~pill~~\|~~{{text\|w=100\|🛈}}~~ This is page 2 of [[User:Sammy_McSam/Hanabi\|Hanabi conventions]]~~\|#aff\|#cfd\|s=1.2~~}}		{{info\|This is page 2 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> ==		== <div style="background:linear-gradient(45deg,#aff,#cfd,#fff0 40rem);padding:.25rem .5rem;border-top-left-radius:.5rem;">Endgame</div> ==
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	\|title1=What is the critical colour?		\|title1=What is the critical colour?
	\|body1='''Grouped by colour:'''		\|body1='''Grouped by colour:'''
	:{{cardholder\|c={{r}}\|{{hr\|3\|p=A}}{{hr\|4\|p=B}}{{hr\|5\|p=C}}{{hk\|p=D}} }}		:{{cardholder\|b={{r}}\|{{hr\|3\|p=A}}{{hr\|4\|p=B}}{{hr\|5\|p=C}}{{hk\|p=D}} }}
	:{{cardholder\|c={{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\|c={{w}}\|{{hk\|p=A\|d=#324}}{{hk\|p=B\|d=#324}}{{hk\|p=C\|d=#324}}{{hw\|5\|p=D\|d=#324}} }}		:{{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)		'''white''' (1 clue + 3 plays + 4 empty = 8 turns)
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	\|title=solution		\|title=solution
	\|body='''1. Group by colour:'''		\|body='''1. Group by colour:'''
	:{{cardholder\|c={{r}}\|{{hr\|3\|p=A}}{{hk\|p=B}}{{hk\|p=C}}{{hr\|4\|p=D}} }} {{cardholder\|c={{r}}\|{{hk\|p=A}}{{hk\|p=B}}{{hr\|5\|p=C}}{{hk\|p=D}} }}		:{{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\|c={{w}}\|{{hw\|p=A\|d=#324\|c=}}{{hw\|3\|p=B\|d=#324}}{{hk\|p=C\|d=#324}}{{hk\|p=D\|d=#324}} }} {{cardholder\|c={{w}}\|{{hk\|p=A\|d=#324}}{{hw\|4\|p=B\|d=#324}}{{hk\|p=C\|d=#324}}{{hw\|5\|p=D\|d=#324}} }}		:{{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:'''		'''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\|{{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}} }}
Line 83:		Line 83:
	\|title1=What is the critical colour?		\|title1=What is the critical colour?
	\|body1='''Grouped by colour:'''		\|body1='''Grouped by colour:'''
	:{{cardholder\|c={{w}}\|{{hk\|p=A\|d=#324}}{{hk\|p=B\|d=#324}}{{hw\|4\|p=C\|d=#324}} }} {{cardholder\|c={{w}}\|{{hk\|p=A\|d=#324}}{{hk\|p=B\|d=#324}}{{hw\|5\|p=C\|d=#324}} }}		:{{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)		'''white''' (2 plays + 2 empty = 4 turns)