User:Sammy McSam/Hanabi page 2

⚠ Work in progress

​This is page 2 of Hanabi conventions

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-unique

redr,with a red clue, yellow5y,with a yellow 5clue, green5g,with a green 5clue, blue5b,with a blue 5clue, whitew,with a white clue, 2 clue tokens

card back,with a clue,card back,with a clue,card back,with a clue,card back,with a clue, Alice 🡲 white1w,with a white 1clue,red2r,with a red 2clue,black powder,with a black powder clue,white3w,with a white 3clue, Bob 🡲

1. Alice to Bob: these 2 cards are white.
2. Bob plays white1w,with a white 1clue,.
3. Cathy to Alice: these 2 cards are white.

   card back2,with a 2clue,card back,with a clue,card back,with a clue,card back4,with a 4clue, Alice 🡲 black powder,with a black powder clue,red2r,with a red 2clue,black powder,with a black powder clue,white3w,with a white 3clue, Bob 🡲

4. Alice plays white2w,with a white 2clue,.
5. Bob discards his chop.
6. Cathy discards.

   card back,with a clue,card back,with a clue,card back,with a clue,card back4,with a 4clue, Alice 🡲 white4w,with a white 4clue,black powder,with a black powder clue,red2r,with a red 2clue,white3w,with a white 3clue, Bob 🡲

What is the best move for Alice?

A) clue white3w,with a white 3clue, B) clue white4w,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,

Title2

Body2

Title3

Body3

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 unique (white5w,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 red2r,with a red 2clue, on chop, marked white3w,with a white 3clue, and unmarked white4w,with a white 4clue, in his finesse position.

In order to delay the future discard of red2r,with a red 2clue,, the best move for Alice is to discard her non-unique white card to trigger Bob to play white3w,with a white 3clue,white4w,with a white 4clue,.

black powder1,with a black powder 1clue,

Black powder 1 tracking

Example 1: basic tracking

redr,with a red clue, yellowy,with a yellow clue, greeng,with a green clue, blueb,with a blue clue, whitew,with a white clue, 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,red1r,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 red1r,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.

redr,with a red clue, yellow1y,with a yellow 1clue, green2g,with a green 2clue, blue1b,with a blue 1clue, whitew,with a white clue, black powder3,with a black powder 3clue, black powder,with a black powder clue,white1w,with a white 1clue,red1r,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 red1r,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:

redr,with a red clue, yellow1y,with a yellow 1clue, green1g,with a green 1clue, blue1b,with a blue 1clue, white1w,with a white 1clue, black powder2,with a black powder 2clue, blue1b,with a blue 1clue,green1g,with a green 1clue,red1r,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:

redr,with a red clue, yellowy,with a yellow clue, greeng,with a green clue, blueb,with a blue clue, whitew,with a white clue, 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,red1r,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 🡲 yellow1y,with a yellow 1clue,yellow3y,with a yellow 3clue,yellow5y,with a yellow 5clue,black powder1,with a black powder 1clue, Donald 🡲

• Alice to Bob: this card is a 1.
• Bob plays red1r,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.

redr,with a red clue, yellowy,with a yellow clue, greeng,with a green clue, blueb,with a blue clue, whitew,with a white clue, black powder,with a black powder clue, black powder,with a black powder clue,black powder,with a black powder clue,red1r,with a red 1clue,green1g,with a green 1clue, Cathy 🡲 black powder,with a black powder clue,black powder,with a black powder clue,yellow1y,with a yellow 1clue,blue1b,with a blue 1clue, Donald 🡲

• Cathy does not see black powder1,with a black powder 1clue, so she plays her leftmost red1r,with a red 1clue,.
• Donald also does not see black powder1,with a black powder 1clue, so he plays his leftmost yellow1y,with a yellow 1clue,.

red1r,with a red 1clue, yellow1y,with a yellow 1clue, greeng,with a green clue, blueb,with a blue clue, whitew,with a white clue, 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,green1g,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,blue1b,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.

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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 🡲

red2r,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 blue5b,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 🡲 blue1b,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,blue5b,with a blue 5clue,red5r,with a red 5clue, Donald 🡲

• Bob sees blue1b,with a blue 1clue, and correctly assumes he has blue2b,with a blue 2clue,blue3b,with a blue 3clue,blue4b,with a blue 4clue, and mentally congratulates Alice on a great clue.
• So Bob saves red5r,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 🡲 blue1b,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,blue5b,with a blue 5clue,red5r,with a red 5clue, Donald 🡲

• Cathy discards.
• Donald discards.
• Alice discards.
• What should Bob do?

A) discard chopB) clue blue1b,with a blue 1clue,C) play slot 1D) discard slot 1E) type "??" in chat

Answer

C) play slot 1 as blue1b,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 blue1b,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 blue1b,with a blue 1clue,?

• Alice clues Donald's blue4b,with a blue 4clue,

blue1b,with a blue 1clue,blue3b,with a blue 3clue,black powder,with a black powder clue,black powder,with a black powder clue, Bob 🡲 blue1b,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,white4w,with a white 4clue,red5r,with a red 5clue, Donald 🡲

• Bob sees blue1b,with a blue 1clue, in Cathy's hand, so he saves red5r,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.

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).

red5r,with a red 5clue, yellow5y,with a yellow 5clue, green5g,with a green 5clue, blue5b,with a blue 5clue, white3w,with a white 3clue, multicolour5m,with a multicolour 5clue, 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).

red5r,with a red 5clue, yellow5y,with a yellow 5clue, green5g,with a green 5clue, blue5b,with a blue 5clue, white3w,with a white 3clue, multicolour5m,with a multicolour 5clue, 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?

red5r,with a red 5clue, yellow5y,with a yellow 5clue, green5g,with a green 5clue, blue5b,with a blue 5clue, white3w,with a white 3clue, multicolour5m,with a multicolour 5clue,

• 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.

red2r,with a red 2clue, yellow5y,with a yellow 5clue, green5g,with a green 5clue, blue5b,with a blue 5clue, white2w,with a white 2clue,

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, ​

red2r,with a red 2clue, yellow5y,with a yellow 5clue, green5g,with a green 5clue, blue5b,with a blue 5clue, white2w,with a white 2clue, 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 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.

2cards in the deck red4r,with a red 4clue, yellow5y,with a yellow 5clue, green5g,with a green 5clue, blue5b,with a blue 5clue, white3w,with a white 3clue, 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 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 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 color 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 handred5r,with a red 5clue, yellow5y,with a yellow 5clue, green5g,with a green 5clue, blue5b,with a blue 5clue, white5w,with a white 5clue,

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 handred5r,with a red 5clue, yellow5y,with a yellow 5clue, green5g,with a green 5clue, blue5b,with a blue 5clue, white5w,with a white 5clue, ⇨ 22 clue tokens ➗ 25 🟰 .88 clue tokens / card,with a Hanabi card clue,

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👤2players✋6cards in handred5r,with a red 5clue, yellow5y,with a yellow 5clue, green5g,with a green 5clue, blue5b,with a blue 5clue, white5w,with a white 5clue, multicolour5m,with a multicolour 5clue, black powder1,with a black powder 1clue, ⇨ 39 clue tokens ➗ 35 🟰 1.1 clue tokens / card,with a Hanabi card clue,