User:Sammy McSam/Hanabi

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⚠ Work in progress ⚠ May contain logic

Extraction

It is possible to extract a card that is 'blocked' by an unplayable card using two clues.

• 1st clue marks the target with colour.
• 2nd clue marks the target with number.

Example 1: avalanche

redr,with a redclue, yellow1y,with a yellow1clue, greeng,with a greenclue, blueb,with a blueclue, whitew,with a whiteclue, multicolourm,with a multicolourclue,

white5w,with a white5clue,yellow4y,with a yellow4clue,red3r,with a red3clue,green5g,with a green5clue, Bob 🡲 white4w,with a white4clue,green4g,with a green4clue,multicolour2m,with a multicolour2clue,yellow2y,with a yellow2clue, Cathy 🡲

• Avalanche of colors option is on, so multicolour cards are marked by any colour clue.
• Cathy's yellow2y,with a yellow2clue, should play before it is discarded.
• The focus of a 2 clue on its own will be multicolour2m,with a multicolour2clue, and the focus of a yellow clue will also be multicolour2m,with a multicolour2clue,.

• Alice to Cathy: these 2 cards are yellow.

redr,with a redclue, yellow1y,with a yellow1clue, greeng,with a greenclue, blueb,with a blueclue, whitew,with a whiteclue, multicolourm,with a multicolourclue, white5w,with a white5clue,yellow4y,with a yellow4clue,red3r,with a red3clue,green5g,with a green5clue, Bob 🡲 white4w,with a white4clue,green4g,with a green4clue,multicolour2m,with a 12clue,yellow2y,with a yellow2clue, Cathy 🡲

• Bob to Cathy: these 2 cards are 2s - this fix clue changes the focus from the left 2 to the other 2.

redr,with a redclue, yellow1y,with a yellow1clue, greeng,with a greenclue, blueb,with a blueclue, whitew,with a whiteclue, multicolourm,with a multicolourclue, white5w,with a white5clue,yellow4y,with a yellow4clue,red3r,with a red3clue,green5g,with a green5clue, Bob 🡲 white4w,with a white4clue,green4g,with a green4clue,multicolour2m,with a 12clue,yellow2y,with a yellow2clue, Cathy 🡲

• Note: if a multicolour card is the intended target of a play clue, the clearest clue would be a colour that does not splash any other card.

Example 2: 5 colors

redr,with a redclue, yellowy,with a yellowclue, greeng,with a greenclue, blueb,with a blueclue, white1w,with a white1clue,

extract white2w,with a white2clue,:

1. Alice to Cathy: these 2 cards are white.
   • Focus is left.

   card back2,with a 2clue,card back3,with a 3clue,card back,with a clue,card back2,with a 2clue, Cathy 🡲 red2r,with a red2clue,white3w,with a white3clue,black powder,with a black powderclue,white2w,with a white2clue, Cathy 🡲

2. Bob to Cathy: these 2 cards are 2s.
   • Changes focus from left to right.

   card back2,with a 2clue,card back3,with a 3clue,card back,with a clue,card back2,with a 2clue, Cathy 🡲 red2r,with a red2clue,white3w,with a white3clue,black powder,with a black powderclue,white2w,with a white2clue, Cathy 🡲

Example 3: avalanche

redr,with a redclue, yellowy,with a yellowclue, greeng,with a greenclue, blueb,with a blueclue, white1w,with a white1clue, multicolourm,with a multicolourclue,

extract white2w,with a white2clue, with avalanche:

1. Alice to Cathy: these 3 cards are white.
   • Focus is left.

   card back2,with a 2clue,card back3,with a 3clue,card back,with a clue,card back2,with a 2clue, Cathy 🡲 multicolour2m,with a white2clue,white3w,with a white3clue,black powder,with a black powderclue,white2w,with a white2clue, Cathy 🡲

2. Bob to Cathy: these 2 cards are 2s.
   • Changes focus from left to right.

   card back2,with a 2clue,card back3,with a 3clue,card back,with a clue,card back2,with a 2clue, Cathy 🡲 multicolour2m,with a white2clue,white3w,with a white3clue,black powder,with a black powderclue,white2w,with a white2clue, Cathy 🡲

Since black powder can't be clued with colour, extraction is a little different:

• 1st clue marks the target with number.
• 2nd clue marks the card to the left of the target with colour.

Example 4: black powder

redr,with a redclue, yellowy,with a yellowclue, greeng,with a greenclue, blueb,with a blueclue, whitew,with a whiteclue, black powder3,with a black powder3clue,

extract black powder2,with a black powder2clue,:

1. Alice to Cathy: these 3 cards are 2s.
   • Focus is left.

   card back2,with a 2clue,card back2,with a 2clue,card back2,with a 2clue,card back,with a clue, Cathy 🡲 yellow2y,with a yellow2clue,red2r,with a red2clue,black powder2,with a black powder2clue,black powder,with a black powderclue, Cathy 🡲

2. Bob to Cathy: this card is red.
   • Changes focus from left to right.

   card back2,with a 2clue,card back2,with a 2clue,card back2,with a 2clue,card back,with a clue, Cathy 🡲 yellow2y,with a yellow2clue,red2r,with a red2clue,black powder2,with a black powder2clue,black powder,with a black powderclue, Cathy 🡲

Why extraction works

1. Alice gives a white colour clue to indicate to Bob that she is giving a play clue to Cathy.
2. Bob has one job: don't let Cathy bomb. He sees that one of Cathy's marked white cards is playable, so he understands that he just has to help Cathy play the correct card:

• If the leftmost white card is playable, Bob does not need to do anything.
• If the leftmost white card is not playable, Bob needs to help with a follow-up fix clue.

Why colour before number?

• In each colour, only one card can be playable (two with avalanche), whereas there can be many playable cards of a certain number. So Alice singles out one colour to help Bob know her intention is for him to help Cathy play the correct card.
• A colour clue can mark a chop card without looking like a save.

How do I know it's not a finesse?

The leftmost card may be 1-away-from-playable. But if Bob can see that one of the cards Alice marked with colour is playable, he will prefer to give a fix clue and not blind play his finesse position.

The everlasting exception: context

Context > convention and can cause an unconventional move!

Think carefully about:

1. timing (why now?),
2. negative clues (e.g. "not red"),
3. recently discarded cards,
4. unique cards,
5. tokens needed for saves or other plays

Examples

card back,with a clue,card back,with a clue,card back5,with a 5clue,card back5,with a 5clue,Bob 🡲 yellow4y,with a yellow4clue,black powder4,with a black powder4clue,black powder,with a black powderclue,black powder,with a black powderclue,Cathy 🡲

card back,with a clue,card back,with a clue,card back5,with a 5clue,card back5,with a 5clue,Bob 🡲 yellow4y,with a yellow4clue,black powder4,with a black powder4clue,black powder,with a black powderclue,black powder,with a black powderclue,Cathy 🡲

• Alice clues 4s to Cathy. How should Bob respond?

Answer

With no context, the interpretation falls to the fewest blind plays: i.e. prefer to play the marked card back5,with a 5clue, as yellow3y,with a yellow3clue, rather than slot 1 as black powder5,with a black powder5clue,.

What context could change this interpretation?

Some possible answers:

1. Bob has negative 3.
2. Bob had yellow2y,with a yellow2clue, which was marked with number 2 instead of a number 3 fix, and either:
   1. Bob did not discard what would have been a trash 3
   2. yellow4y,with a yellow4clue, was discarded when it could have easily been marked to prompt yellow3y,with a yellow3clue,

In this game the context was 2.1: On move 23 a fix clue was given with number 2 instead of 3, Bob can know that their card back5,with a 5clue, is not yellow3y,with a yellow3clue, (else the fix should be 3¹, not 2). This is why it is important for each player to pay attention to how their own cards are fixed (and what cards they discard afterwards).

¹Note that there are no trash 3s at this point. If there were at least one trash 3 (e.g. white3w,with a white3clue, were played or already marked somewhere), Bob should only make this conclusion after discarding his unmarked card, to check that a 3 fix was not given due to bad touch.

Example 1: chop-focus play

Discarded: red2r,with a red2clue,white2w,with a white2clue,

• Bob has discarded a playable white2w,with a white2clue,.
• Alice to Bob: this card is a 2.
• The conventional move is for Bob to save his 2 as either red2r,with a red2clue, or white2w,with a white2clue,.
• But the context contradicts this: Alice and Cathy would not allow him to discard white2w,with a white2clue, unless there is a 2nd copy visible.

1. Bob plays his

Example 2: Prompt extraction

redr,with a redclue, yellowy,with a yellowclue, greeng,with a greenclue, blueb,with a blueclue, white1w,with a white1clue, general case for directly clued finesse position?

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When is it chop focus?

Travis Hall » 16 December 2023, 01:12

When playing with high-level partners, I generally try to regard a number clue touching chop as chop-focussed unless there is a timeliness consideration.[…]when giving a finesse, we can’t wait for the discard of the chop. For example:

Played: white2w,with a white2clue, white3w,with a white3clue,black powder,with a black powderclue,black powder,with a black powderclue,black powder,with a black powderclue, B 🡲 multicolour5m,with a multicolour5clue,black powder,with a black powderclue,white4w,with a white4clue,black powder4,with a black powder4clue, C 🡲

A clues 4 to C. Cluing white is blocked by multicolour5m,with a multicolour5clue,. Cluing 4 can’t wait, because B will probably discard and white3w,with a white3clue, will move out of finesse. C can note the finesse response and adjust their expectation to play the left 4.

And I try to consistently clue the same way.

I recognise that many masters will clue 2s non-chop-focussed in the early game. Frankly, I’m not a fan, as this forces me to guess who does this and who does not, but I will guess because my rate of error is lower that way. I understand the consideration that 2s are the most valuable cards, but I’m not sure the risks are worth it.

Whenever somebody touches my chop with a number clue and expects me to play from the left, and I misfire, my question is always “Well, if my cards were the opposite way around, how would you have clued them?” Of the few who will answer that question at all, the answer is usually, “I would clue <number>,” and they don’t understand that this makes it impossible for me to do anything other than guess.

Since we know we can extract a playable cards with colour + number clues, it follows that number clues that mark the chop card are interpreted as:

1. Unique save if the chop card can be unique
2. Double discard save if the player either side of the receiver has a non-unique card of the same number
3. Otherwise a left-focused play clue.

black powder1,with a black powder1clue,

• 1 clues that mark the chop card are interpreted as a black powder1,with a black powder1clue, save (unless the receiver already has a known play).

• If a player can see black powder1,with a black powder1clue,, it is logical to play all cards marked 1 from oldest to newest.

The oldest is the most valuable 1 because otherwise it could have been discarded before cluing 1.

Playing a chop card marked 1 can be played because:

1. black powder1,with a black powder1clue, is visible (and the player who can't see it is promised black powder1,with a black powder1clue,)
   • This player should then track the newest position that can be black powder1,with a black powder1clue,.
     • if this card reaches chop, it should not be saved with a direct clue.
     • if his card does receive a direct clue, it becomes a finesse.
2. a playable 1 was discarded
3. a playable 1 was not bluffed

The everlasting exception: context

Context > convention and can cause an unconventional move!

Think carefully about:

1. timing (why now?),
2. negative clues (e.g. "not red"),
3. recently discarded cards,
4. unique cards,
5. tokens needed for saves or other plays

Example 1: double discard avoidance

Sometimes we need more information before we can know if a clue is a chop-focused save or a left-focused play clue.

Double discard avoidance saves are one of the most difficult clues to interpret because it's one of the very few times we can save non-unique cards without expecting a play response.

Nothing much is going on and there have not been any good ways to splash, give trash clues or otherwise delay one of the players.

Some players forbid a player from discarding if a double discard is possible

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Strategy

Back to basics

, we agree as a team that we must: Communicate to each other primarily via clues (as well as plays and discards) Who: all Where: When: Why: To win with the highest possible score

1. What: not discard the last copy of any card.
   • How: mark the last copy

Two types of clues

To separate We always mark unique cards before they are discarded

Most of the time we understand that the clue giver should be the player directly before the clue receiver. This is because this seat has the newest information in view

Relative seats of clue giver & receiver When we allow any player to clue any hand, it allows for a lot more freedom to clue. Cluing more than 1 seat away can happen for a number of reasons.

when to discard - when player right of you has nice cards like 2s Delaying certain players with nice non-unique cards

Mark as many first copies of cards as possible to reduce the chance of getting bottom-decked. Bluffs are the easiest way to mark useful 1-away from playable cards. Where possible,

Hand management

When to skip players

(and how to irritate them ​)

Efficiency 8clue tokens

Bluffs

Bluffs are powerful...

Maximizing bluff opportunities ​

Once we realise the power of bluffs, it follows that we want to maximise the number of bluffing opportunities available to players. In any given situation, it is possible to work out Alice's optimal move given the information available to her.

The basic idea is simple: look for the bluff opportunity that is furthest ahead. Everyone should be making moves that enable that bluff opportunity to be used, and then work backwards from that player for the next opportunity.

So from Alice's point of view, she will see if:

1. Donald can bluff Emily
2. Cathy can bluff Donald
3. Bob can bluff Cathy
4. Alice can bluff Bob

Example 1

​

1. Donald can bluff Emily
2. Cathy cannot bluff Donald
3. Bob can bluff Cathy
4. Alice cannot bluff Bob

Then it's quite easy:

1. Alice discards
2. Bob bluffs Cathy
3. Cathy discards
4. Donald bluffs Emily

Example 2

Now if Alice can also bluff:

1. Donald can bluff Emily
2. Cathy cannot bluff Donald
3. Bob can bluff Cathy
4. Alice can bluff Bob

Then it's still easy:

1. Alice either double bluffs Bob & Cathy or discards
2. Bob responds or bluffs Cathy
3. Cathy discards
4. Donald bluffs Emily

Example 3

Now if Cathy can also bluff:

Donald can bluff Emily

Cathy cannot bluff Donald

Bob can bluff Cathy

Alice can bluff Bob

Then it's significantly more complicated for the team to predict, but not much more complex for Alice:

1. Alice should probably discard (unless there is a really good bluff target available to her
2. Bob makes a similar decision
3. Cathy responds, double bluffs or discards
4. Donald responds or bluffs Emily

When to not save unique cards =

No matter how many tokens you have, whether it is 1clue tokens or 7clue tokens, you do not always have to spend a token to save a card. Some players might find this statement controversial. Each player must consider the likelihood of a certain move and assess if the risk-reward of all the possible moves.

Did you know that in a 👤5players player game with ✋4cards in hand each, avalanche, there are up to 30 possible moves per player (not counting flamboyant bonuses)?

e.g. if each hand has one avalanche multicolourm,with a multicolourclue, card.

And in one round of play that means up to 150 possible unique positions! That's a lot to think about. But amazingly our human brains can filter out the vast majority of those moves as not logical given a bit of agreement on conventions.

Examples of clear good/bad

Questionable examples

Context examples

When to Trash bluff

When you first learn about trash bluffs, you need to practice it and that's fine. Once you are comfortable with how it works, you need to consider if you should use a trash bluff.

Examples where it is clearly bad

Played: white1w,with a white1clue, blue1b,with a blue1clue,black powder,with a black powderclue,black powder,with a black powderclue,black powder,with a black powderclue, Bob 🡲 white1w,with a white1clue,white1w,with a white1clue,blue2b,with a blue2clue,blue2b,with a blue2clue, Cathy 🡲

Reverses with number white3w,with a white3clue,

Reverse finesses are often not great if the finessed card could instead be bluffed, however, it can be useful to mark a chop card as a reverse to ensure it is not discarded.

• e.g. Alice sees Bob has white2w,with a white2clue, on chop and Donald just drew white1w,with a white1clue,. Normally the best moves would be for Alice and Bob to discard so that Cathy can bluff Donald's white1w,with a white1clue,, but white2w,with a white2clue, is more valuable than any bluff target Alice can see, so she chooses to reverse with colour.

But what if reversing with colour would mark trash? If we can finesse with number, why can't we also reverse finesse with number? A reverse with number is usually harder to read than a reverse with colour, but they can be a lot more efficient than colour + multiple correction clues (to prevent future bombs).

Travis Hall gives a basic explanation of number reverses:

Similarly, we often avoid number reverses, because if there’s both an available reverse to any card of that number and an immediately playable card of that number, the clue receiver has to guess at the correct move, and this can easily go wrong. Even so, when circumstance narrows the possibilities enough, we can sometimes do a number reverse safely.

Multicolour reverses with colour multicolour3m,with a multicolour3clue,

Travis Hall explains it well:

We usually avoid reverse finesses in multicolour, because although multi does connect with any colour, if we reverse multis then responses to our most common play clues - colour clues to a playable card - just stop, all of them, if a playable multi is in someone’s blind finesse position. That can be very difficult to work around.

Multicolour reverses with a single colour can work, the most common situation being where the clue giver and receiver can both see a playable card of the colour clued either marked or in the finesse position in someone else's hand. Such a reverse will also trigger a hesitation play.

When to GD

• Token is needed
• Protect cards
• Free plays from one or more hands.

GD without benefit is a 'zero value' GD and limits the freedom to clue.

Context

Using the last token 0clue 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 powder5clue, from 5 save.
• Cause a play

Negatives white5w,with a white5clue,white4w,with a white4clue,

Write notes if necessary.

1. Keep track of your own negatives.
2. Keep rack 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 redclue, yellow5y,with a yellow5clue, green5g,with a green5clue, blue5b,with a blue5clue, whitew,with a whiteclue, 2clue 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 white1clue,red2r,with a red2clue,black powder,with a black powderclue,white3w,with a white3clue, Bob 🡲

1. Alice to Bob: these 2 cards are white.
2. Bob plays white1w,with a white1clue,.
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 powderclue,red2r,with a red2clue,black powder,with a black powderclue,white3w,with a white3clue, Bob 🡲

4. Alice plays white2w,with a white2clue,.
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 white4clue,black powder,with a black powderclue,red2r,with a red2clue,white3w,with a white3clue, Bob 🡲

What is the best move for Alice?

A) clue white3w,with a white3clue, B) clue white4w,with a white4clue, C) play card back4,with a 4clue, D) discard card back4,with a 4clue, E) discard chop card back,with a clue,

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 white5clue,).
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 red2clue, on chop, marked white3w,with a white3clue, and unmarked white4w,with a white4clue, in his finesse position.

In order to delay the future discard of red2r,with a red2clue,, the best move for Alice is to discard her non-unique white card to trigger Bob to play white3w,with a white3clue,white4w,with a white4clue,.

Trash bluffs

Stop trash bluffing 1s when 1k is not visible Would you trash bluff 5k when all 5s are not visible?

black powder1,with a black powder1clue, tracking

when you can know 1k certain

how you can play chop 1s when 1k is still in the deck

tricks to save on saving black powder1,with a black powder1clue, when 1k is known somewhere and other cards are all marked later when 1k is known somewhere and there are promised cards in the same hand

apply this principal generally is tricky because it can become unclear what has triggered a blind-play

slot 3 blind plays

certain 1k

uncertain 2

Consider this situation:

• Alice clues Donald's blue5b,with a blue5clue,

card back,with a clue,card back,with a clue,card back,with a clue,card back,with a clue, Bob 🡲 blue1b,with a blue1clue,black powder,with a black powderclue,black powder,with a black powderclue,black powder,with a black powderclue, Cathy 🡲 black powder,with a black powderclue,black powder,with a black powderclue,blue5b,with a blue5clue,red5r,with a red5clue, Donald 🡲

• Bob sees blue1b,with a blue1clue, and correctly assumes he has blue2b,with a blue2clue,blue3b,with a blue3clue,blue4b,with a blue4clue, and mentally congratulates Alice on a great clue.
• So Bob saves red5r,with a red5clue,:

card back,with a clue,card back,with a clue,card back,with a clue,card back,with a clue, Bob 🡲 blue1b,with a blue1clue,black powder,with a black powderclue,black powder,with a black powderclue,black powder,with a black powderclue, Cathy 🡲 black powder,with a black powderclue,black powder,with a black powderclue,blue5b,with a blue5clue,red5r,with a red5clue, Donald 🡲

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

A) discardB) clue blue1b,with a blue1clue,C) play slot 1D) discard slot 1E) type "??" in chat

Answer

C) play slot 1 as blue1b,with a blue1clue,

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 blue1clue, 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 blue1clue,?

• Alice clues Donald's blue4b,with a blue4clue,

blue1b,with a blue1clue,blue3b,with a blue3clue,black powder,with a black powderclue,black powder,with a black powderclue, Bob 🡲 blue1b,with a blue1clue,black powder,with a black powderclue,black powder,with a black powderclue,black powder,with a black powderclue, Cathy 🡲 black powder,with a black powderclue,black powder,with a black powderclue,white4w,with a white4clue,red5r,with a red5clue, Donald 🡲

• Bob sees blue1b,with a blue1clue, in Cathy's hand, so he saves red5r,with a red5clue,

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.

Interpretation

Name that move #1

Alice clues Cathy card back2,with a 2clue,

• Bob plays white1w,with a white1clue,
• white1w,with a white1clue, connects to card back2,with a 2clue,, so Cathy plays card back2,with a 2clue, as white2w,with a white2clue,.

Answer

Finesse obvs

Name that move #2

Alice clues Cathy red2r,with a red2clue,

• Bob plays white1w,with a white1clue,
• white1w,with a white1clue, connects to card back2,with a 2clue,, but there is another 1 layered behind it in a playable position.
• Cathy *does not play card back2,with a 2clue,, but discards or clues something unrelated.
• Alice does something unrelated.
• white1w,with a white1clue, does not connect to red2r,with a red2clue, and Cathy could have bombed red2r,with a red2clue, as white2w,with a white2clue, unless Bob really has red1r,with a red1clue,.
• Bob plays slot 2 as red1r,with a red1clue,. green2g,with a green2clue, successfully plays.
• Cathy now knows to wait for red1r,with a red1clue, to play before playing card back2,with a 2clue, as red2r,with a red2clue,.

Answer

Layered Finesse

Name that move #3

* Alice clues Cathy card back2,with a 2clue,

• Bob plays red2r,with a red2clue,
• red2r,with a red2clue, cannot connect to card back2,with a 2clue,, end of responses.

Answer

Bluff

Finesse + bluff

• Alice clues Cathy card back2,with a 2clue,
• Bob plays white1w,with a white1clue,
• white1w,with a white1clue, connects to card back2,with a 2clue,, so Cathy plays card back2,with a 2clue, as white2w,with a white2clue,

https://boardgamearena.com/table?table=693788252

example1 A clues D '2': B plays 1b: 1b *connects* to '2' -> D can play 2b C plays 1g: 1b *cannot connect* to '2' -> D cannot play 2b 2b - 2b = 0

example2 A clues D '3': B plays 1b: 1b *connects* to '3' -> D can play 2b + 3b C plays 1g: 1b *can connect* to '3' -> D cannot play 2b [2b + 3b] - 2b = 3b

example3 A clues D '4': B plays 1b: 1b *connects* to '4' -> D can play 2b + 3b + 4b C plays 1g: 1b *can connect* to '4' -> D cannot play 2b [2b + 3b + 4b] - 2b = 3b + 4b

in the game A clues D '4': B plays 2r: D will play 3r+4r C plays 3m: D will

• Tips page example
• More complex example

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.

red2r,with a red2clue, yellow5y,with a yellow5clue, green5g,with a green5clue, blue5b,with a blue5clue, white2w,with a white2clue,

card back,with a clue,card back,with a clue,card back,with a clue,card back3,with a 3clue, Alice 🡲 white3w,with a white3clue,black powder,with a black powderclue,black powder,with a black powderclue,red4r,with a red4clue, Bob 🡲 black powder,with a black powderclue,black powder,with a black powderclue,black powder,with a black powderclue,red5r,with a red5clue, Cathy 🡲 black powder,with a black powderclue,black powder,with a black powderclue,white4w,with a white4clue,white5w,with a white5clue, Donald 🡲

What is the critical colour?

Grouped by colour:

red3rA,with a red3clue,red4rB,with a red4clue,red5rC,with a red5clue,black powderD,with a black powderclue, ​

whitewA,with a whiteclue,white3wB,with a white3clue,black powderC,with a black powderclue,white4wD,with a white4clue, ​ black powderA,with a black powderclue,black powderB,with a black powderclue,black powderC,with a black powderclue,white5wD,with a white5clue, ​

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

What is the critical card?

white3w,with a white3clue,

What is the critical move?

Alice clues white3w,with a white3clue,

Why it matters

Serialised:

Play red3r,with a red3clue, red3rA,with a red3clue,red4rB,with a red4clue,red5rC,with a red5clue,whitewD,with a whiteclue, ​ black powderA,with a black powderclue,white3wB,with a white3clue,black powderC,with a black powderclue,white4wD,with a white4clue, ​ black powderA,with a black powderclue,black powderB,with a black powderclue,black powderC,with a black powderclue,white5wD,with a white5clue, ​

Clue white3w,with a white3clue, whitewA,with a whiteclue,white3wB,with a white3clue,black powderC,with a black powderclue,white4wD,with a white4clue, ​ red3rA,with a red3clue,red4rB,with a red4clue,red5rC,with a red5clue,white5wD,with a white5clue, ​

red2r,with a red2clue, yellow5y,with a yellow5clue, green5g,with a green5clue, blue5b,with a blue5clue, white2w,with a white2clue, A) Play red3r,with a red3clue, B) Clue white3w,with a white3clue,

card back,with a clue,card back,with a clue,card back4,with a 4clue,card back3,with a 3clue, Alice 🡲 white3w,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,red5r,with a red5clue, Cathy 🡲 black powder,with a black powderclue,black powder,with a black powderclue,black powder,with a black powderclue,white5w,with a white5clue, Donald 🡲

solution

1. Group by colour:

red3rA,with a red3clue,black powderB,with a black powderclue,black powderC,with a black powderclue,red4rD,with a red4clue, ​ black powderA,with a black powderclue,black powderB,with a black powderclue,red5rC,with a red5clue,black powderD,with a black powderclue, ​

whitewA,with a whiteclue,white3wB,with a white3clue,black powderC,with a black powderclue,black powderD,with a black powderclue, ​ black powderA,with a black powderclue,white4wB,with a white4clue,black powderC,with a black powderclue,white5wD,with a white5clue, ​

2. Serialise:

red3rA,with a red3clue,black powderB,with a black powderclue,black powderC,with a black powderclue,red4rD,with a red4clue, ​ whitewA,with a whiteclue,white3wB,with a white3clue,red5rC,with a red5clue,black powderD,with a black powderclue, ​ black powderA,with a black powderclue,white4wB,with a white4clue,black powderC,with a black powderclue,white5wD,with a white5clue, ​

whitewA,with a whiteclue,white3wB,with a white3clue,black powderC,with a black powderclue,black powderD,with a black powderclue, ​ red3rA,with a red3clue,white4wB,with a white4clue,black powderC,with a black powderclue,red4rD,with a red4clue, ​ black powderA,with a black powderclue,black powderB,with a black powderclue,red5rC,with a red5clue,white5wD,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, red4r,with a red4clue, yellow5y,with a yellow5clue, green5g,with a green5clue, blue5b,with a blue5clue, white3w,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,white4w,with a white4clue,white5w,with a white5clue, Cathy 🡲

What is the critical colour?

Grouped by colour:

black powderA,with a black powderclue,black powderB,with a black powderclue,white4wC,with a white4clue, ​ black powderA,with a black powderclue,black powderB,with a black powderclue,white5wC,with a white5clue, ​

white (2 plays + 2 empty = 4 turns)

What is the critical card?

white4w,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 a token.
• 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 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 ​.

Here's a candidate for the worst ever bottom-decked situation: all three blue1b,with a blue1clue, in the last cards in the deck5,with a cards in the deck5clue, cards ​

Order of plays

Where the order may seem arbitrary, prioritise from most out-of-order to consecutive plays 543, 435, 345

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

Where all non-unique future-playable cards are visible player has

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.

with more stringent bluffs we get layered, and it is the most enjoyable part of the game for many

5 Flamboyants

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

1. +1 clue token
2. +1 clue token & -1 mistake
3. give color clue
4. give number 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 +1 clue token), since there is no 8th stack.

2 players

When to discard a unique card

Without 5 flamboyants

• Unplayable
• Locked hand + 0clue tokens
• Locked hand + 1clue tokens + unique chop

Extra: Locked hand + 0clue tokens + playable unique chop = bomb unique card as a positional misplay

With 5 flamboyants

• There is more flexibility with losing unique cards when the pick and/or play flamboyants are still available.
• Flamboyants create more complexity in decision making.
• Let's focus on the cases where you can be certain of a maximum score:

red4r,with a red4clue,yellow5y,with a yellow5clue,green5g,with a green5clue,blue5b,with a blue5clue,whitew,with a whiteclue, Discarded: white2w,with a white2clue,white3w,with a white3clue,white4w,with a white4clue,

Pick and play flams are both available

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 red5clue, yellow5y,with a yellow5clue, green5g,with a green5clue, blue5b,with a blue5clue, white5w,with a white5clue,

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

13clue tokens (discards) ➕ 8clue tokens (start) ➕ 5clue tokens (red5r,with a red5clue, yellow5y,with a yellow5clue, green5g,with a green5clue, blue5b,with a blue5clue, white5w,with a white5clue,) ➖ 1clue tokens (last 5) 🟰 25clue tokens

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

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👤5players✋4cards in handred5r,with a red5clue, yellow5y,with a yellow5clue, green5g,with a green5clue, blue5b,with a blue5clue, white5w,with a white5clue, ⇨ 22clue tokens ➗ 25 🟰 .88clue tokens / card,with a clue,

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👤2players✋6cards in handred5r,with a red5clue, yellow5y,with a yellow5clue, green5g,with a green5clue, blue5b,with a blue5clue, white5w,with a white5clue, multicolour5m,with a multicolour5clue, black powder1,with a black powder1clue, ⇨ 39clue tokens ➗ 35 🟰 1.1clue tokens / card,with a clue,