User:Sammy McSam/Hanabi page 3

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​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 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).

cards in the deckred5ryellow5ygreen5gblue5bwhite3wmulticolor5mblack powder multicolour4m,with a multicolour 4clue,white4w,with a white 4clue,multicolour1m,with a multicolour 1clue,red1r,with a red 1clue, 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).

cards in the deckred5ryellow5ygreen5gblue5bwhite3wmulticolor5mblack powder multicolour4m,with a multicolour 4clue,white4w,with a white 4clue,multicolour1m,with a multicolour 1clue,red1r,with a red 1clue, Bob 🡲

which card is clued to play?

cards in the deckred5ryellow5ygreen5gblue5bwhite3wmulticolor5mblack powder

• Alice to Bob: these two previously unmarked cards are blue.

card back4,with a 4clue,card back,with a clue,card back,with a clue,card back1,with a 1clue, Bob 🡲

answer

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.

cards in the deckred2ryellow5ygreen5gblue5bwhite2wmulticolormblack powder

card back,with a clue,card back,with a clue,card back,with a clue,card back3,with a 3clue, Alice 🡲 white3w,with a white 3clue,black powder,with a black powder clue,black powder,with a black powder clue,red4r,with a red 4clue, Bob 🡲 black powder,with a black powder clue,black powder,with a black powder clue,black powder,with a black powder clue,red5r,with a red 5clue, Cathy 🡲 black powder,with a black powder clue,black powder,with a black powder clue,white4w,with a white 4clue,white5w,with a white 5clue, Donald 🡲

What is the critical colour?

Grouped by colour:

red3rA,with a red 3clue,red4rB,with a red 4clue,red5rC,with a red 5clue,black powderD,with a black powder clue, ​

whitewA,with a white clue,white3wB,with a white 3clue,black powderC,with a black powder clue,white4wD,with a white 4clue, ​ black powderA,with a black powder clue,black powderB,with a black powder clue,black powderC,with a black powder clue,white5wD,with a white 5clue, ​

white (1 clue + 3 plays + 4 empty = 8 turns)

What is the critical card?

white3w,with a white 3clue,

What is the critical move?

Alice clues white3w,with a white 3clue,

Why it matters

Serialised:

Play red3r,with a red 3clue, red3rA,with a red 3clue,red4rB,with a red 4clue,red5rC,with a red 5clue,whitewD,with a white clue, ​ black powderA,with a black powder clue,white3wB,with a white 3clue,black powderC,with a black powder clue,white4wD,with a white 4clue, ​ black powderA,with a black powder clue,black powderB,with a black powder clue,black powderC,with a black powder clue,white5wD,with a white 5clue, ​

Clue white3w,with a white 3clue, whitewA,with a white clue,white3wB,with a white 3clue,black powderC,with a black powder clue,white4wD,with a white 4clue, ​ red3rA,with a red 3clue,red4rB,with a red 4clue,red5rC,with a red 5clue,white5wD,with a white 5clue, ​

cards in the deckred2ryellow5ygreen5gblue5bwhite2wmulticolormblack powder A) Play red3r,with a red 3clue, B) Clue white3w,with a white 3clue,

card back,with a clue,card back,with a clue,card back4,with a 4clue,card back3,with a 3clue, Alice 🡲 white3w,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, Bob 🡲 black powder,with a black powder clue,black powder,with a black powder clue,black powder,with a black powder clue,red5r,with a red 5clue, Cathy 🡲 black powder,with a black powder clue,black powder,with a black powder clue,black powder,with a black powder clue,white5w,with a white 5clue, Donald 🡲

solution

1. Group by colour:

red3rA,with a red 3clue,black powderB,with a black powder clue,black powderC,with a black powder clue,red4rD,with a red 4clue, ​ black powderA,with a black powder clue,black powderB,with a black powder clue,red5rC,with a red 5clue,black powderD,with a black powder clue, ​

whitewA,with a white clue,white3wB,with a white 3clue,black powderC,with a black powder clue,black powderD,with a black powder clue, ​ black powderA,with a black powder clue,white4wB,with a white 4clue,black powderC,with a black powder clue,white5wD,with a white 5clue, ​

2. Serialise:

red3rA,with a red 3clue,black powderB,with a black powder clue,black powderC,with a black powder clue,red4rD,with a red 4clue, ​ whitewA,with a white clue,white3wB,with a white 3clue,red5rC,with a red 5clue,black powderD,with a black powder clue, ​ black powderA,with a black powder clue,white4wB,with a white 4clue,black powderC,with a black powder clue,white5wD,with a white 5clue, ​

whitewA,with a white clue,white3wB,with a white 3clue,black powderC,with a black powder clue,black powderD,with a black powder clue, ​ red3rA,with a red 3clue,white4wB,with a white 4clue,black powderC,with a black powder clue,red4rD,with a red 4clue, ​ black powderA,with a black powder clue,black powderB,with a black powder clue,red5rC,with a red 5clue,white5wD,with a white 5clue, ​

1. Identify the critical colour - usually the player with the most critical 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 critical 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.

2cards in the deckred4ryellow5ygreen5gblue5bwhite3wmulticolormblack powder 0 clue 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 powder clue,black powder,with a black powder clue,black powder,with a black powder clue,black powder,with a black powder clue, Bob 🡲 black powder,with a black powder clue,black powder,with a black powder clue,white4w,with a white 4clue,white5w,with a white 5clue, Cathy 🡲

What is the critical colour?

Grouped by colour:

black powderA,with a black powder clue,black powderB,with a black powder clue,white4wC,with a white 4clue, ​ black powderA,with a black powder clue,black powderB,with a black powder clue,white5wC,with a white 5clue, ​

white (2 plays + 2 empty = 4 turns)

What is the critical card?

white4w,with a white 4clue,

Who is the critical player?

Cathy

• To reach Cathy with a least 1cards in the deck remaining, only one of Bob or Alice can draw a card.
• Alice cannot clue (0 clue 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 1 clue 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 (white4w,with a white 4clue,).

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 ​.

Here's a candidate for the worst ever bottom-decked situation: all three blue1b,with a blue 1clue, in the last 5cards in the deck cards ​

Order of plays

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

1. white5w,with a white 5clue, white4w,with a white 4clue, white3w,with a white 3clue,
2. white4w,with a white 4clue, white3w,with a white 3clue, white5w,with a white 5clue,
3. white3w,with a white 3clue, white4w,with a white 4clue, white5w,with a white 5clue,

Replace flamboyant ​

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

1. lowest rank critical
2. lowest rank non-critical
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 powder 5clue,
7. skip

When there is no gain in returning a card playable in the future - either the immediate 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. ​ Gain 1 clue tokens
2. ​ Gain 1 clue tokens & remove a mistake
3. ​ card3,with a Hanabi card 3clue, Give number clue
4. ​ card,with a Hanabi card clue, Give a colour clue
5. ​ Replace a card from the discard pile into the deck
6. ​ Play a card from the discard pile

A 7th stack bonus is always irrelevant (and on BGA always gain 1 clue 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:

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👤3players✋5cards in handcards in the deckred5ryellow5ygreen5gblue5bwhite5wmulticolormblack powder

50 (deck) ➖ 25 (played) ➖ 12 (👤3players× at least✋4cards in hand) 🟰 13 discards

13 clue tokens (discards) ➕ 8 clue tokens (start) ➕ 5 clue tokens (red5r,with a red 5clue, yellow5y,with a yellow 5clue, green5g,with a green 5clue, blue5b,with a blue 5clue, white5w,with a white 5clue,) ➖ 1 clue tokens (last 5) 🟰 25 clue tokens

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

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👤5players✋4cards in handcards in the deckred5ryellow5ygreen5gblue5bwhite5wmulticolormblack powder ⇨ 22 clue tokens ➗ 25 🟰 .88 clue tokens / card,with a Hanabi card clue,

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👤2players✋6cards in handcards in the deckred5ryellow5ygreen5gblue5bwhite5wmulticolor5mblack powder1 ⇨ 39 clue tokens ➗ 35 🟰 1.1 clue tokens / card,with a Hanabi card clue,

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