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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}} }}
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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={{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)
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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}}
}}

Latest revision as of 16:31, 1 August 2025

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

Endgame

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.
red2,with a red2clue, yellow5,with a yellow5clue, green5,with a green5clue, blue5,with a blue5clue, white2,with a white2clue,

card back,with a clue,card back,with a clue,card back,with a clue,card back3,with a 3clue, Alice 🡲 white3,with a white3clue,black powder,with a black powderclue,black powder,with a black powderclue,red4,with a red4clue, Bob 🡲 black powder,with a black powderclue,black powder,with a black powderclue,black powder,with a black powderclue,red5,with a red5clue, Cathy 🡲 black powder,with a black powderclue,black powder,with a black powderclue,white4,with a white4clue,white5,with a white5clue, Donald 🡲

What is the critical colour?
Grouped by colour:
red3,with a red3clue,red4,with a red4clue,red5,with a red5clue,black powder,with a black powderclue, ​
white,with a whiteclue,white3,with a white3clue,black powder,with a black powderclue,white4,with a white4clue, ​ black powder,with a black powderclue,black powder,with a black powderclue,black powder,with a black powderclue,white5,with a white5clue, ​
white (1 clue + 3 plays + 4 empty = 8 turns)
What is the critical card?
white3,with a white3clue,
What is the critical move?
Alice clues white3,with a white3clue,
Why it matters
Serialised:
Play red3,with a red3clue, red3,with a red3clue,red4,with a red4clue,red5,with a red5clue,white,with a whiteclue, ​ black powder,with a black powderclue,white3,with a white3clue,black powder,with a black powderclue,white4,with a white4clue, ​ black powder,with a black powderclue,black powder,with a black powderclue,black powder,with a black powderclue,white5,with a white5clue, ​
Clue white3,with a white3clue, white,with a whiteclue,white3,with a white3clue,black powder,with a black powderclue,white4,with a white4clue, ​ red3,with a red3clue,red4,with a red4clue,red5,with a red5clue,white5,with a white5clue, ​


red2,with a red2clue, yellow5,with a yellow5clue, green5,with a green5clue, blue5,with a blue5clue, white2,with a white2clue, A) Play red3,with a red3clue, B) Clue white3,with a white3clue,


card back,with a clue,card back,with a clue,card back4,with a 4clue,card back3,with a 3clue, Alice 🡲 white3,with a white3clue,black powder,with a black powderclue,black powder,with a black powderclue,black powder,with a black powderclue, Bob 🡲 black powder,with a black powderclue,black powder,with a black powderclue,black powder,with a black powderclue,red5,with a red5clue, Cathy 🡲 black powder,with a black powderclue,black powder,with a black powderclue,black powder,with a black powderclue,white5,with a white5clue, Donald 🡲


solution
1. Group by colour:
red3,with a red3clue,black powder,with a black powderclue,black powder,with a black powderclue,red4,with a red4clue, ​ black powder,with a black powderclue,black powder,with a black powderclue,red5,with a red5clue,black powder,with a black powderclue, ​
white,with a whiteclue,white3,with a white3clue,black powder,with a black powderclue,black powder,with a black powderclue, ​ black powder,with a black powderclue,white4,with a white4clue,black powder,with a black powderclue,white5,with a white5clue, ​

2. Serialise:

red3,with a red3clue,black powder,with a black powderclue,black powder,with a black powderclue,red4,with a red4clue, ​ white,with a whiteclue,white3,with a white3clue,red5,with a red5clue,black powder,with a black powderclue, ​ black powder,with a black powderclue,white4,with a white4clue,black powder,with a black powderclue,white5,with a white5clue, ​
white,with a whiteclue,white3,with a white3clue,black powder,with a black powderclue,black powder,with a black powderclue, ​ red3,with a red3clue,white4,with a white4clue,black powder,with a black powderclue,red4,with a red4clue, ​ black powder,with a black powderclue,black powder,with a black powderclue,red5,with a red5clue,white5,with a white5clue, ​
  1. Identify the critical colour - usually the player with the most unique cards, or consecutive cards of the same colour.
  2. Work out how many clue tokens are needed to reach the critical player.
  3. 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 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.

cards in the deck2,with a cards in the deck2clue, red4,with a red4clue, yellow5,with a yellow5clue, green5,with a green5clue, blue5,with a blue5clue, white3,with a white3clue, 0clue tokens

card back,with a clue,card back,with a clue,card back,with a clue,card back5,with a 5clue, Alice 🡲 black powder,with a black powderclue,black powder,with a black powderclue,black powder,with a black powderclue,black powder,with a black powderclue, Bob 🡲 black powder,with a black powderclue,black powder,with a black powderclue,white4,with a white4clue,white5,with a white5clue, Cathy 🡲

What is the critical colour?
Grouped by colour:
black powder,with a black powderclue,black powder,with a black powderclue,white4,with a white4clue, ​ black powder,with a black powderclue,black powder,with a black powderclue,white5,with a white5clue, ​
white (2 plays + 2 empty = 4 turns)
What is the critical card?
white4,with a white4clue,
Who is the critical player?
Cathy
  • To reach Cathy with a least cards in the deck1,with a cards in the deck1clue, remaining, only one of Bob or Alice can draw a card.
  • Alice cannot clue (0clue tokens) 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 5 which generates 1clue tokens.
  • With 5 flamboyants Alice can't know if playing her 5 will generate a token, so Alice discards and plays after Cathy's critical card (white4,with a white4clue,).

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 confused​.

Here's a candidate for the worst ever bottom-decked situation: all three blue1,with a blue1clue, in the last cards in the deck5,with a cards in the deck5clue, cards surprised​

Order of plays

Where the order may seem arbitrary, prioritise from most out-of-order to consecutive plays e.g.:

  1. white5,with a white5clue, white4,with a white4clue, white3,with a white3clue,
  2. white4,with a white4clue, white3,with a white3clue, white5,with a white5clue,
  3. white3,with a white3clue, white4,with a white4clue, white5,with a white5clue,

Replace flamboyant Flamboyant​

The decision of which card to replace (or to skip) can communicate information to the team. Priority highest to lowest:

  1. lowest rank unique
  2. lowest rank non-unique
  3. duplicate of an unmarked card
  4. duplicate of a marked card
  5. trash of number corresponding to the slot position of a playable card
  6. black powder5,with a black powder5clue,
  7. skip

When there is no gain in returning a card playable in the future - either the immediate flamboyant Flamboyant​ 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.

5 Flamboyants

Don't let the 5 fool you - there are actually six randomly selected actions:

  1. Flamboyant​ Gain 1clue tokens
  2. Flamboyant​ Gain 1clue tokens & remove a mistake
  3. Flamboyant​ card3,with a 3clue, Give number clue
  4. Flamboyant​ card,with a clue, Give a color clue
  5. Flamboyant​ Replace a card from the discard pile into the deck
  6. Flamboyant​ Play a card from the discard pile

A 7th stack bonus is always irrelevant (and on BGA always gain 1clue tokens clue token), since there is no 8th stack.


Available Tokens

Average clue tokens per played card
Imagine the end of an ideal game without flamboyants:

3players5cards in handred5,with a red5clue, yellow5,with a yellow5clue, green5,with a green5clue, blue5,with a blue5clue, white5,with a white5clue,

50 (deck) ➖ 25 (played) ➖ 12 (3players× at least4cards in hand) 🟰 13 discards

13clue tokens (discards) ➕ 8clue tokens (start) ➕ 5clue tokens (red5,with a red5clue, yellow5,with a yellow5clue, green5,with a green5clue, blue5,with a blue5clue, white5,with a white5clue,) ➖ 1clue tokens (last 5) 🟰 25clue tokens

25clue tokens ➗ 25 🟰 1clue tokens / card,with a clue,

5players4cards in handred5,with a red5clue, yellow5,with a yellow5clue, green5,with a green5clue, blue5,with a blue5clue, white5,with a white5clue, ⇨ 22clue tokens ➗ 25 🟰 .88clue tokens / card,with a clue,

2players6cards in handred5,with a red5clue, yellow5,with a yellow5clue, green5,with a green5clue, blue5,with a blue5clue, white5,with a white5clue, multicolour5,with a multicolour5clue, black powder1,with a black powder1clue, ⇨ 39clue tokens ➗ 35 🟰 1.1clue tokens / card,with a clue,
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