Endgame
When to discard, play, empty clue, clue duplicates and advanced techniques.
The critical move
To work out the most efficient sequence of moves, you need to determine three things:
- Critical colour
- the colour that takes the most turns to complete.
- (i.e. must start as soon as possible to maximise the score).
- Critical card
- the first card of the critical colour.
- Note: this can be a duplicate of a card already marked!
- Critical move
- the move that makes the critical card play.
- Note: this can be a clue, play or discard.
- red2 yellow5 green5 blue5 white2
card backcard backcard backcard back3,with a 3clue, Alice 🡲 white3black powderblack powderred4,with a red4clue, Bob 🡲 black powderblack powderblack powderred5,with a red5clue, Cathy 🡲 black powderblack powderwhite4,with a white4clue,white5,with a white5clue, Donald 🡲
- red3red4red5black powder
- white,with a whiteclue,white3black powderwhite4 black powderblack powderblack powderwhite5
- Play red3 red3red4red5white,with a whiteclue, black powderwhite3black powderwhite4 black powderblack powderblack powderwhite5
- Clue white3 white,with a whiteclue,white3black powderwhite4 red3red4red5white5
- red2 yellow5 green5 blue5 white2 A) Play red3 B) Clue white3
card backcard backcard back4,with a 4clue,card back3,with a 3clue, Alice 🡲
white3black powderblack powderblack powder Bob 🡲
black powderblack powderblack powderred5,with a red5clue, Cathy 🡲
black powderblack powderblack powderwhite5,with a white5clue, Donald 🡲
- red3black powderblack powderred4 black powderblack powderred5black powder
- white,with a whiteclue,white3black powderblack powder black powderwhite4black powderwhite5
2. Serialise:
- red3black powderblack powderred4 white,with a whiteclue,white3red5black powder black powderwhite4black powderwhite5
- white,with a whiteclue,white3black powderblack powder red3white4black powderred4 black powderblack powderred5white5
- Identify the critical colour - usually the player with the most unique cards, or consecutive cards of the same colour.
- Work out how many clue tokens are needed to reach the critical player.
- 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 red4 yellow5 green5 blue5 white3 0clue tokens
card backcard backcard backcard back5,with a 5clue, Alice 🡲 black powderblack powderblack powderblack powder Bob 🡲 black powderblack powderwhite4,with a white4clue,white5,with a white5clue, Cathy 🡲
- black powderblack powderwhite4 black powderblack powderwhite5
- To reach Cathy with a least cards in the deck1 remaining, only one of Bob or Alice can draw a card.
- Alice cannot clue (0clue tokens) and must generate a token for Bob so that he can give a stall clue to avoid drawing the last card.
- Without 5 flamboyants Alice would just play her 5 which generates 1clue tokens.
- With 5 flamboyants Alice can't know if playing her 5 will generate a token, so Alice discards and plays after Cathy's critical card (white4).
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 blue1 in the last cards in the deck5 cards
Order of plays
Where the order may seem arbitrary, prioritise from most out-of-order to consecutive plays e.g.:
- white5 white4 white3
- white4 white3 white5
- white3 white4 white5
Replace flamboyant
The decision of which card to replace (or to skip) can communicate information to the team. Priority highest to lowest:
- lowest rank unique
- lowest rank non-unique
- duplicate of an unmarked card
- duplicate of a marked card
- trash of number corresponding to the slot position of a playable card
- black powder5
- 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:
- 1clue tokens Gain
- 1clue tokens & remove a mistake Gain
- card3,with a 3clue, Give number clue
- card,with a clue, Give a color clue
- Replace a card from the discard pile into the deck
- Play a card from the discard pile
A 7th stack bonus is always irrelevant (and on BGA always gain 1clue tokens clue token), since there is no 8th stack.
Available Tokens
idealgame without flamboyants:
3players5cards in handred5 yellow5 green5 blue5 white5
50 (deck) ➖ 25 (played) ➖ 12 (3players× at least4cards in hand) 🟰 13 discards
13clue tokens (discards) ➕ 8clue tokens (start) ➕ 5clue tokens (red5 yellow5 green5 blue5 white5) ➖ 1clue tokens (last 5) 🟰 25clue tokens
25clue tokens ➗ 25 🟰 1clue tokens / card
5players4cards in handred5 yellow5 green5 blue5 white5 ⇨ 22clue tokens ➗ 25 🟰 .88clue tokens / card
2players6cards in handred5 yellow5 green5 blue5 white5 multicolour5 black powder1 ⇨ 39clue tokens ➗ 35 🟰 1.1clue tokens / card