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Hanabi» Forums » General

Subject: Hanabi endgame puzzle rss

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It's florrat's turn. The uncolored 4 has been saved earlier in the game.

* What are the optimal strategy?
* What is your expected score in that case?
* What score can you guarantee?
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Pierre Beri
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Optimal strategy might look like what you guys actually did: you play, arnau attempts (because if you clue you lose too much time) and if it’s a bomb, then he will later be more prudent, watching carefully what you pick to know if he has w5. Max score 29 with a bit of luck it seems.
 
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Jeff Thornsen
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You need to play 6 cards to get a 30.
With only 3 cards left in the deck, the best you could do is play 5 cards for 29 points total.
Since florrat has lots of cards that need to get played, he should keep playing and let amau spend clues to stall.

florrat should assume his unmarked 4 is the G4, although it might be R4.

The G3, G4, and W5 are the only cards that amau could possibly draw/play, so to get to 29 will require that amau draws these in the right order.

Fortunately, florrat can already see that amau has the G3.

Spoiler (click to reveal)
Guaranteed to work:
1. florrat Play M4
2. amau clues the uncolored 4 as Green if possible, otherwise clue 4 if somehow the uncolored 4 is the R4 and the G4 is in the new slot, otherwise clue 5 for the White 5, otherwise clue something else (Red or White) to indicate florrat's new cards are not playable and the cards we need (G3/G4/W5) are still in the deck.
3. Play M5 (+1 clue)
4. amau plays his newest card, which happens to be G3.
5. florrat plays G4 or W5 (he's guaranteed to have one of them, and amau would have clued where it is in step 2)
6. amau plays his newest card again if he drew G4 or W5 (luck of draw).
Guaranteed to score 28, but might score 29 if amau draws G4 or W5 after playing G3.
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Hint: you can guarantee 29.
 
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Jeff Thornsen
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ok, I see it now. It's hard to visualize the future board state with all possible options.

Spoiler (click to reveal)

1. florrat Play M4
2. amau clues something (G4 or W5 if possible)
3. Play M5 (+1 clue)
4. At this point, there is 1 card left in the deck, so amau will have 2 possible scenarios which both end up scoring 29:
4a: if florrat doesn't have either the W5 or G3, amau will know that he has one of them and the other is the last card in the deck. amau has no choice but to play his newest card, since giving a clue would be useless (florrat has nothing currently playable). If amau has the G3 (which he does), then score 29 by playing G3 --> G4 --> W5. If amau has the W5, then score 28 by playing W5 --> nothing --> G3.
4a: If florrat has the W5, clue it. florrat plays W5, triggers game end, amau plays G3, florrat plays G4.

It's kind of interesting because amau doesn't know he has G3, so amau can't guarantee a score of 29 from what he currently sees (if G3 is last card in deck, max score is 28 no matter what), but florrat can see the G3 already.

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Byron S
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Do you know that the uncolored 4 is NOT green? It's impossible to tell from the image, but quite possible given the cards showing, and would make the logic much cleaner.
 
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Jeff Thornsen
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I think the entire premise of the puzzle is that prior game events are such that florrat 'unofficially' knows that he has the G4 and not the R4 in that slot.

I think the logic works out even if florrat is holding R4 or any other possible ordering of the cards.

florrat will basically just play M4 and M5 no matter what, and amau will be forced to give clues or play based on which cards florrat draws. Eventually amau will play the G3 at a time that enables a score of 29, with the G5 unplayed.
 
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We have a winner!

It's indeed interesting that arnau doesn't know we can guarantee 29, but his optimal strategy will lead to 29 anyway.

In the game I was convinced that the uncolored 4 was green (and it was), but it's not necessary to assume that for the puzzle, as Jeff said.

The only new case is if the G4 and W5 are the bottom two cards of the deck. Then I (florrat) play M4, arnau clues red or green to show that my 4 is not green, I play M5. Now I have no playable card, so arnau plays. Now I see that arnau draws either the G4 or the W5. In either case, I conclude that my newest card is playable, because arnau didn't clue a playable card one turn earlier. So I play it, and arnau plays his newest card.
 
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