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Context for those that don't know the game: 1. Each player has a set of tiles that each have a particular color and a particular number. 2. The tiles a player

Context for those that don't know the game: 1. Each player has a set of tiles that each have a particular color and a particular number. 2. The tiles a player has are known only to other players (they are placed to face away from the player) 3. On your turn, you may either place one of your tiles, or give a hint to another player about their tiles. 4. Hints can only take the form of "you have exactly K tiles of C color <indicate the K tiles>" or "you have exactly K tiles of N number <indicate the K tiles>". There are some rules for how many hints can be given and ways to "earn back" more hints to give. 4b. You can make more deductions than what the hints provide. There are a fixed number of each tile. e.g. There are 2 RED-4 tiles. So if you can see that two other players both have a RED-4 tile, this means that you cannot have a RED-4 tile. So if someone gives you the hint that you have a *-4 tile, you know it is not RED. But the two players with the RED-4 tiles cannot see their own, so they cannot make this deduction. But if you act in a way that shows that you have made the deduction, and they are really smart, they can observe your act and deduce that you would have only made that act if you knew that you didn't have a RED-4 tile. And since they can only see 1 other RED-4 tile, they can deduce that they must hold the other. 5. No other communication is allowed. 6. In the center of the table there are stacks for each color that start empty. The goal of the game is to populate the stacks by playing the color tiles of that stack in increasing number. (e.g. RED-1, RED-2, RED-3 ...). If a player tries to play a tile that is invalid (e.g. the RED stack is only up to RED-2 and the player selects their RED-4 tile), a counter is incremented. 7. The game ends when the counter reaches a threshold or all tiles are played. The score is equal to the number of tiles played. Higher is better. I have long thought that it should be possible to write an AI that does superhuman hint-giving and deduction, provided that all of the AIs can collude beforehand. That is, if all of the AIs have a giant lookup table that essentially says "If the board is in this particular state, and I give hint H, that actually means FOO" where FOO contains more bits of information than hint H would by itself.

defen 8y ago
> 5. No other communication is allowed. When playing with friends / casuals I've found that this is the one that trips people up (if you want to play strictly by the rules) - no, you can't ask if there are any reds left. You can't ask what hint Alice gave to Bob on her previous turn. You can't just say "Only one yellow 4 left, let's be careful" etc.
- gamegoblin 8y ago
  When playing with casuals I actually don't mind communicating deductions that could strictly be made with a very simple application of the rules, such as your example. If someone discards a RED-4, there isn't a deep chain of logical reasoning to arrive at the conclusion that only 1 is left. The best to teach casuals, I have found, is to play a round where you actually invert it have the experience player announce all of their reasoning (to demonstrate to the casuals the type of deductions that can be made).
  - defen 8y ago
    That's true, for teaching purposes it does help to simplify, as long as people know that they're not playing by the "real" rules (so when they play again without you, they play correctly). I don't remember the specific details, but the times I've seen it be an issue are when people give different answers to a question since they've each deduced different things about the board state.
- esrauch 8y ago
  > You can't ask what hint Alice gave to Bob on her previous turn This sounds like reading the rules too stringently and not by their intent if you ask me, since it is asking only about information that the person is supposed to know. It would be like saying if someone asks what the rules of the game are you aren't allowed to answer because none of the rules explicitly state that you can convey information about the rules of the game.
  - kd5bjo 8y ago
    There is at least one game where knowledge of the rules is restricted from the players: https://en.m.wikipedia.org/wiki/Paranoia_(role-playing_game) https://en.m.wikipedia.org/wiki/Paranoia_(role-playing_game)
    - ggggtez 8y ago
      Considering we are discussing card games, Chairman Mao would have been the more logical game to bring up. Unlike paranoia, but like Hanabi, it's a game for insufferable people.
jakobnicolaus 8y ago
Thanks for your summary of Hanabi! You can find an example of your hypothetical AI in our recent paper: https://arxiv.org/abs/1811.01458 https://arxiv.org/abs/1811.01458. Note that all the conventions and rules are learned though, rather than hand coded. And your 'giant lookup table', is just a feedforward neural network. We also link out 300 games in case you are curious to see how it works.
- gamegoblin 8y ago
  Thanks for the paper, that is really interesting. For those who read my previous comment, an example of pre-game communication collusion that the AI in the paper invented was to decide that any hint involving red or yellow _also_ means that your most recently acquired tile is immediately playable. "Roughly 40% of the information is obtained through conventions rather than through the grounded information and card counting" (what I have been describing as "collusion" the paper describes as "conventions" but it amounts to the same thing -- you can pass a lot more information than the hints imply if you can plan ahead) That is super fascinating.
  - jakobnicolaus 8y ago
    yes - this was the focus of our method: Allowing agents to interpret the actions of others, while also learning to be interpretable when observed by other agents.
- abcanthur 8y ago
  I've only Hanabbed it up a handful of times (got 25 w strict play, no mistakes w my brother over Christmas!), but I've been of the conviction that there is too much emphasis on these "conventions," which either require a pregame explanation and agreement, or more often in-game argument (which is against the rules). I prefer an emphasis on card holding that constantly displays your knowledge of your own hand. To me this isn't against the communication rule, because the cards have to be on display. They can be held sideways, higher or lower, upside down (The cards are orientable on both faces, people don't notice this!), I hold them between certain fingers to remember number values. While that's just another convention, one can observe it develop from the beginning game state, and every time a player receives a clue, how they redo their hand. In summary, card holding is very effective/information rich and can be deduced without words, and seems to me perfectly natural to the game. This also relieves a lot of the cognition devoted to remembering what other people know about their own hands. When discussing a UI for a digital version of Hanabi, my brother and I discussed mostly how customizable the card holding would be, which would be exactly reflected to the other players.
thebzax 8y ago
There's a paper from just a couple years ago about turning hanabi (with >2 players) into a variant of the 100-prisoner hat color problem: http://helios.mi.parisdescartes.fr/~bouzy/publications/bouzy-hanabi-2017.pdf http://helios.mi.parisdescartes.fr/~bouzy/publications/bouzy... For the 5 player variant specifically, the concept is as follows: Out of the 8 moves each other player can make (play any of 4 cards, discard any of 4 cards), you figure out the best move, add them up mod 8, and make one of 8 hints (you have a color or number hint available for each player). Then each of the 4 other players deduces which move you wanted them to make by subtracting out everyone else's best move. There's some room for improvement on figuring out how to avoid one player mistaking another's best play (because it might be predicated on them playing a card they don't know they have first), or how to hint in ways which avoid that. A friend has put up an implementation up on github: https://github.com/chikinn/hanabi/blob/master/players/hat_player.py https://github.com/chikinn/hanabi/blob/master/players/hat_pl...
- SilasX 8y ago
  Nice! Any intuition on whether this is practical for humans to implement in a game? (Side note: in practice, it's almost impossible to avoid the illegal side-channel communication of watching the other players get nervous as you start to do something stupid, so really the only rules-faithful way is to play over a computer.) (Another side note: there's a game called The Mind[1] which is the board-game version of SleepSport -- the goal is to, without most kinds of communication, play cards from each players hand in increasing order. One way to win is to synchronize everyone's internal clock and play each card when that many seconds have passed.) [1] https://boardgamegeek.com/boardgame/244992/mind https://boardgamegeek.com/boardgame/244992/mind [2] https://stackoverflow.com/questions/6474318/what-is-the-time-complexity-of-the-sleep-sort https://stackoverflow.com/questions/6474318/what-is-the-time...
  - whatusername 8y ago
    (I think you meant to refer to "the Mind". "The Game" looks similar in some ways -- but your description is for "the mind".)
deleted 8y ago
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dbcurtis 8y ago
One of the interesting aspects of Hanabi is that there really isn't enough turns to fully hint. So with every hint, you must ask yourself not just "Why is s/he telling me this?", but "Why are they telling me this now?" At least in the group I play with, the hint is presumed to be immediately useful, but you may have to make some deductions and take some risk to make a play.
- ThrustVectoring 8y ago
  Hints made to other players can matter, too. Suppose you play after me, and I make a hint that you can see would make the next player play an unplayable card. You know that I wouldn't make that hint unless you had some course of action that would fix the situation. Since spending a hint to make you fix things via a hint is silly, that leaves playing the card you'd otherwise discard. So you can interpret a hint for an unplayable card you can see as a hint to play the oldest card in your hand. And it can go a level deeper, where the card you played blind is a 5 (or some other card incompatible with actually making the hinted card playable). Since they see that you thought the card wasn't playable, and then it didn't become possibly playable after your play, they now know that the card isn't playable and can be safely discarded. This isn't actually much better than just direct hinting, though, so the straightforward play is higher value. Both have advantages over straight hinting, though.
ggggtez 8y ago
Incorrect. The game is played by one player creating a finite state machine description. That player wins if they convince 4 people to follow it. The other players win if they realize they aren't playing a game.

defen 8y ago

> 5. No other communication is allowed. When playing with friends / casuals I've found that this is the one that trips people up (if you want to play strictly by the rules) - no, you can't ask if there are any reds left. You can't ask what hint Alice gave to Bob on her previous turn. You can't just say "Only one yellow 4 left, let's be careful" etc.

gamegoblin 8y ago
When playing with casuals I actually don't mind communicating deductions that could strictly be made with a very simple application of the rules, such as your example. If someone discards a RED-4, there isn't a deep chain of logical reasoning to arrive at the conclusion that only 1 is left. The best to teach casuals, I have found, is to play a round where you actually invert it have the experience player announce all of their reasoning (to demonstrate to the casuals the type of deductions that can be made).
- defen 8y ago
  That's true, for teaching purposes it does help to simplify, as long as people know that they're not playing by the "real" rules (so when they play again without you, they play correctly). I don't remember the specific details, but the times I've seen it be an issue are when people give different answers to a question since they've each deduced different things about the board state.
esrauch 8y ago
> You can't ask what hint Alice gave to Bob on her previous turn This sounds like reading the rules too stringently and not by their intent if you ask me, since it is asking only about information that the person is supposed to know. It would be like saying if someone asks what the rules of the game are you aren't allowed to answer because none of the rules explicitly state that you can convey information about the rules of the game.
- kd5bjo 8y ago
  There is at least one game where knowledge of the rules is restricted from the players: https://en.m.wikipedia.org/wiki/Paranoia_(role-playing_game) https://en.m.wikipedia.org/wiki/Paranoia_(role-playing_game)
  - ggggtez 8y ago
    Considering we are discussing card games, Chairman Mao would have been the more logical game to bring up. Unlike paranoia, but like Hanabi, it's a game for insufferable people.

jakobnicolaus 8y ago

Thanks for your summary of Hanabi! You can find an example of your hypothetical AI in our recent paper: https://arxiv.org/abs/1811.01458 https://arxiv.org/abs/1811.01458. Note that all the conventions and rules are learned though, rather than hand coded. And your 'giant lookup table', is just a feedforward neural network. We also link out 300 games in case you are curious to see how it works.

gamegoblin 8y ago
Thanks for the paper, that is really interesting. For those who read my previous comment, an example of pre-game communication collusion that the AI in the paper invented was to decide that any hint involving red or yellow _also_ means that your most recently acquired tile is immediately playable. "Roughly 40% of the information is obtained through conventions rather than through the grounded information and card counting" (what I have been describing as "collusion" the paper describes as "conventions" but it amounts to the same thing -- you can pass a lot more information than the hints imply if you can plan ahead) That is super fascinating.
- jakobnicolaus 8y ago
  yes - this was the focus of our method: Allowing agents to interpret the actions of others, while also learning to be interpretable when observed by other agents.
abcanthur 8y ago
I've only Hanabbed it up a handful of times (got 25 w strict play, no mistakes w my brother over Christmas!), but I've been of the conviction that there is too much emphasis on these "conventions," which either require a pregame explanation and agreement, or more often in-game argument (which is against the rules). I prefer an emphasis on card holding that constantly displays your knowledge of your own hand. To me this isn't against the communication rule, because the cards have to be on display. They can be held sideways, higher or lower, upside down (The cards are orientable on both faces, people don't notice this!), I hold them between certain fingers to remember number values. While that's just another convention, one can observe it develop from the beginning game state, and every time a player receives a clue, how they redo their hand. In summary, card holding is very effective/information rich and can be deduced without words, and seems to me perfectly natural to the game. This also relieves a lot of the cognition devoted to remembering what other people know about their own hands. When discussing a UI for a digital version of Hanabi, my brother and I discussed mostly how customizable the card holding would be, which would be exactly reflected to the other players.

thebzax 8y ago

There's a paper from just a couple years ago about turning hanabi (with >2 players) into a variant of the 100-prisoner hat color problem: http://helios.mi.parisdescartes.fr/~bouzy/publications/bouzy-hanabi-2017.pdf http://helios.mi.parisdescartes.fr/~bouzy/publications/bouzy... For the 5 player variant specifically, the concept is as follows: Out of the 8 moves each other player can make (play any of 4 cards, discard any of 4 cards), you figure out the best move, add them up mod 8, and make one of 8 hints (you have a color or number hint available for each player). Then each of the 4 other players deduces which move you wanted them to make by subtracting out everyone else's best move. There's some room for improvement on figuring out how to avoid one player mistaking another's best play (because it might be predicated on them playing a card they don't know they have first), or how to hint in ways which avoid that. A friend has put up an implementation up on github: https://github.com/chikinn/hanabi/blob/master/players/hat_player.py https://github.com/chikinn/hanabi/blob/master/players/hat_pl...

SilasX 8y ago
Nice! Any intuition on whether this is practical for humans to implement in a game? (Side note: in practice, it's almost impossible to avoid the illegal side-channel communication of watching the other players get nervous as you start to do something stupid, so really the only rules-faithful way is to play over a computer.) (Another side note: there's a game called The Mind[1] which is the board-game version of SleepSport -- the goal is to, without most kinds of communication, play cards from each players hand in increasing order. One way to win is to synchronize everyone's internal clock and play each card when that many seconds have passed.) [1] https://boardgamegeek.com/boardgame/244992/mind https://boardgamegeek.com/boardgame/244992/mind [2] https://stackoverflow.com/questions/6474318/what-is-the-time-complexity-of-the-sleep-sort https://stackoverflow.com/questions/6474318/what-is-the-time...
- whatusername 8y ago
  (I think you meant to refer to "the Mind". "The Game" looks similar in some ways -- but your description is for "the mind".)

deleted 8y ago

[deleted]

dbcurtis 8y ago

One of the interesting aspects of Hanabi is that there really isn't enough turns to fully hint. So with every hint, you must ask yourself not just "Why is s/he telling me this?", but "Why are they telling me this now?" At least in the group I play with, the hint is presumed to be immediately useful, but you may have to make some deductions and take some risk to make a play.

ThrustVectoring 8y ago
Hints made to other players can matter, too. Suppose you play after me, and I make a hint that you can see would make the next player play an unplayable card. You know that I wouldn't make that hint unless you had some course of action that would fix the situation. Since spending a hint to make you fix things via a hint is silly, that leaves playing the card you'd otherwise discard. So you can interpret a hint for an unplayable card you can see as a hint to play the oldest card in your hand. And it can go a level deeper, where the card you played blind is a 5 (or some other card incompatible with actually making the hinted card playable). Since they see that you thought the card wasn't playable, and then it didn't become possibly playable after your play, they now know that the card isn't playable and can be safely discarded. This isn't actually much better than just direct hinting, though, so the straightforward play is higher value. Both have advantages over straight hinting, though.

ggggtez 8y ago

Incorrect. The game is played by one player creating a finite state machine description. That player wins if they convince 4 people to follow it. The other players win if they realize they aren't playing a game.