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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 white 2clue, 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, B 🡲 multicolour5m,with a multicolour 5clue,black powder,with a black powder clue,white4w,with a white 4clue,black powder4,with a black powder 4clue, C 🡲

A clues 4 to C. Cluing white is blocked by multicolour5m,with a multicolour 5clue,. Cluing 4 can’t wait, because B will probably discard and white3w,with a white 3clue, 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 powder 1clue,

Black powder 1

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

• If a player can see black powder1,with a black powder 1clue,, 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 powder 1clue, is visible (and the player who can't see it is promised black powder1,with a black powder 1clue,)
   • This player should then track the newest position that can be black powder1,with a black powder 1clue,.
     • 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

Strategy

Back to basics

• In a 👤5players player game with ✋4cards in hand each and avalanche, there are up to 30 possible moves per player (excluding flamboyants).

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

• 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 clue, play and discard interpretations (conventions).

Hand management

• Hand management is important in high level play to keep as many non-trash cards in the game for as long as possible.

When to skip players

(and how to irritate them ​)

• Opening with no information on any of your cards.
• The player(s) skipped have duplicate cards that need to be marked with a good touch play clue.
• If you have been the target of a trash bluff and not yet discarded cards to the right of the trash cards.
• Players in front of you have trash.
• The player behind you has many plays.

Double Discard Avoidance (DDA)

• Many players have incomplete or non-existent methods for managing DDA because it is difficult as it requires a lot of contextual awareness.
• Players need to be aware of how many opportunities there are to mark double chop cards.
• Anytime a chop card is marked with a number of the same rank visible in the next player's hand DDA should be considered.
  • Or even if the double chop players are not next to each other but the in-between players are busy.

8 clue tokens

Efficiency

Bluffs

• Bluffs are powerful...
• Easiest way to mark nice cards

Maximising 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:

Donald can bluff Emily

Cathy cannot bluff Donald

Bob can bluff Cathy

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 1 clue tokens or 7 clue 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.

#Back_to_basics We know that there are a lot of possible moves, and even more game states.

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 white 1clue, 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, Bob 🡲 white1w,with a white 1clue,white1w,with a white 1clue,blue2b,with a blue 2clue,blue2b,with a blue 2clue, Cathy 🡲

• With black powder: 1 bluffs are black powder1,with a black powder 1clue, promise bluffs unless black powder1,with a black powder 1clue, is known to Alice and the receiver.

Would you trash bluff 5k when all 5s are not visible?

white3w,with a white 3clue,

Reverses with number

• 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 white 2clue, on chop and Donald just drew white1w,with a white 1clue,. Normally the best moves would be for Alice and Bob to discard so that Cathy can bluff Donald's white1w,with a white 1clue,, but white2w,with a white 2clue, 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.

multicolour3m,with a multicolour 3clue,

Multicolour reverses with colour

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 may also trigger a hesitation play.

When to GD

1. Plays extra cards for free from one or more hands.
2. Protect cards
3. Token is needed

GD without one of these benefits is usually of negative value:

• Limits the freedom to clue.
• Misleads the receiver - the cards to the right of the copy is not trash.

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

cards in the deckredryellow5ygreen5gblue5bwhitewmulticolormblack powder 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

cards in the deckredryellowygreengbluebwhitewmulticolormblack powder

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.

cards in the deckredryellow1ygreen2gblue1bwhitewmulticolormblack powder3 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:

cards in the deckredryellow1ygreen1gblue1bwhite1wmulticolormblack powder2 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:

cards in the deckredryellowygreengbluebwhitewmulticolormblack powder

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.

cards in the deckredryellowygreengbluebwhitewmulticolormblack powder 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,.

cards in the deckred1ryellow1ygreengbluebwhitewmulticolormblack powder 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.

---

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).

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 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 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 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 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,