Hanabi Strategy

When I introduce new players to Hanabi (buy from Amazon), I describe it as mix between Solitaire, Mastermind, and Bridge, except where everyone plays on the same team. This post will focus on the Bridge-like qualities of Hanabi.

The twist in Hanabi is that you don’t get to see your cards, you only get to see everyone else’s cards. In order to teach other players about their cards you hint information (colors or numbers) to them. Each turn in Hanabi you have three options: 1) play a card, 2) discard a card, or 3) hint to your partner.

Similar to the bidding systems used in Bridge, we’ve developed a series of strategies and rules to optimize our hint-giving. Since developing the strategy is kind of the fun part of Hanabi, I wouldn’t suggest reading them until you’ve had a chance to play. I’ve also tried to write them down in such a way that you can incorporate them into your own strategy one at a time, if you’re just looking for a touch of inspiration.

The strategies are tricks that we’ve developed for getting around common situations.

 Strategy 1. The Hint to Play

The Rule: Hint the cards that you want your partner to play. Unless the situation is dire (your partner is about to discard a card which hasn’t been played yet and of which there is only one copy left in game), play the cards that you are hinted.

The Explanation: In a game there are 25 playable cards, and 35 discardable cards. You’ll only get about 18 hints before you run out of turns. Even if you use these hints to get more hints, you’ll still only have the turns to use about 18 of them. The difficult part of Hanabi isn’t winning, it’s winning in the limited number of turns. To do this, you have to get cards on the table, not build up a stash of hints. Furthermore, since there are so many discardable cards (and they can be discarded in any order), it’s safer to assume a card you know nothing about is discardable rather than playable. This also allows for the not receiving of a hint to act as a hint to discard.

 Strategy 2. The Hint to Hint (forced)

The Strategy: Use a hint of non-playable 5’s to force the player who received the hint to also give a hint (and obviously to not discard the 5’s). If you receive a hint of non-playable 5’s, then you are forced to hint. Do not play or discard.

The Explanation: This strategy allows you to hint to your partner that they should both not play and not discard. It also acts as a way of requesting your partner to hint you information about your own hand. If they hint to you, then you know you have something to play. If they hint to someone else, then you know you can safely discard.

The reason 5’s are hinted to pass this information is because there is only one copy of each 5 in the game, and hinting them also lets your partners know not to discard them (and is guaranteed to be useful information later in the game). If you want to hint 5’s to a person without any 5’s, you can use the “zero 5’s” hint, or consider using a hint of non-playable 2’s or 3’s.

**Example**: You don't know anything about your hand, and none of your partners have any playable cards. You hint 5's to the player on your left.

 Strategy 3. The Hint to Discard (optional)

The Strategy: Use a hint of 4’s (more likely in the first half of a game) or discardable 1’s (more likely in the second half of a game) to let the player who received the hint know what to discard if they think that discarding is their best option.

The Explanation: This strategy allows you to ask your partner if you have any playable or non-discardable cards. If you have playable cards, your partner should hint them to you. If you don’t have playable cards, but you do have cards that can’t be discarded, then your partner should hint those to you. If you have neither playable nor non-discardable cards, then your partner will discard, which signifies to you that you should discard also. This strategy is useful for the situation where cards must be discarded in order to draw a card needed to make progress in the game.

The reason 4’s are chosen for this purpose in the beginning half of the game is because they are the most likely mid-card to be redrawn (in the process of playing 2’s and 3’s) before they’re needed. If you need to discard a card that would eventually be playable, it’s best to discard a 4.

**Example**: Nobody in the game has a playable card, and you are in a forced hint situation.

 Strategy 4. The Leader Paradigm

The Strategy: At all points in the game there should be a de facto leader. The leader should be the person with the least playable, least discardable hand, and they should be the person giving hints to the players with more playable, more discardable hands. When the current leader has no hints left to give, the leader role should transition to the next player without playable or discardable cards.

The Explanation: The leader paradigm is useful because it helps visualize the progression of the game through the assignment of roles. Throughout the game there will be players who have playable cards (and should be receiving hints to play), players who have discardable cards (and should not be receiving hints to play, which act as hints to discard), and players who have neither playable nor discardable cards (and should be giving hints, so as to save their cards for when they’re needed in the future). In fact, a clear strategy for transitioning between these roles can easily substitute for logical deduction and a sound memory.

Our strategy for doing this depends upon the number of players in the game. If there’s three players, the first player assigns the role of leader by hinting 1’s to the player they don’t want to be leader. The leader is then forced to hint, and will continue hinting until they having no useful hints left to give, at which point they will pass the role of leader by hinting 5’s to the person they wish to take the role of leader. The new leader is forced to hint, and should make sure that the old leader isn’t in a position to discard a non-discardable card on their next turn. This role of passing leadership could theoretically extend until the end of the game, but often doesn’t because of either because there are an excess of cards to discard.

The leader signals that there are an excess of cards that need to be discarded (in order to draw a card needed to make progress), by hinting 4’s or non-playable 1’s. This is essentially the leader’s way of asking if they can discard on their next turn. This pattern of discarding continues until someone draws a playable card (or reaches a point where they are in imminent danger of discarding a non-discardable card), at which the next player to play will assign the role of leader by either making the necessary hint or not making the necessary hint. If they make the necessary hint, then they are taking the role of leader. If they don’t make the necessary hint, then they are assigning the role to the next player to play.

The rules are designed to be rigidly followed on an individual level to optimize the chance of putting yourself in easily solvable situations.

 Rule 1. Arrange Your Hand

The Rule: Arrange your hand from right to left with the most playable cards on the right and the most discardable cards on the left. When given a hint, pull the hinted cards to the appropriate side (maintaining their original order). Pull any cards you know to be discardable to the far left.

The Explanation: Arranging your hand will let your teammates see what your next playable and discardable moves will be, which lets them pass more information with each hint (or lack of a hint).

**Example**: Your partner has (from their right to left) R1, B1, G1, G2, G3 where the R1 and B1 are discardable. You hint the green cards, which gives your partner three playable moves (G1, then G2, then G3) for the price of one hint.

 Rule 2. Draw Strategically

The Rule: After playing a card (from the right), draw a card and add it to the left side (but obviously keep your known discardables even further left). After discarding a card (from the left), draw a card and add it to the right side (but obviously keep your known playables even further right).

The Explanation: The card that you draw after playing a card (from the right) will be the card in your hand that you know least about, so it should go in the left (most discardable) position. This makes sense for several reasons. First, because of the distribution of cards in the deck, in almost all cases a drawn card has a higher chance of being discardable than being playable. Second, if the card is playable it should be hinted as such before played, so placing it on the right doesn’t earn you anything but placing it on the left earns you a un-hinted discard if the card is discardable. Third, the hints given to play cards also serve as hints to what the other cards in your hand aren’t, so the drawn cards become the cards you know least about.

The card you draw after discarding a card is the card most likely to be playable, so it should be placed in the right (most playable) position. If you’re discarding then it probably means you haven’t been given hints to play, which probably means you have no playable cards in your hand, which means that the card you draw (which might be playable) is the card in your hand most likely to be playable.

 Rule 3. The Order of Operations

On the off chance that I ever program this, I just thought I’d write down the order of operations that a player should go through when they decided what move to make.

If you’re the leader, hint to…

  1. the next person with non-discardables in the discard position
  2. the person with playables
  3. the person with the least number of playables their…
  4. unknown playables.
  5. non-playable 5’s, and renounce the leader position.
  6. non-playable 1’s, and renounce the leader position.
  7. non-playable 4’s, and renounce the leader position.

If you’re not the leader…

  1. If you’ve been hinted non-playable 5’s, then follow the leader instructions.
  2. If you’ve been hinted non-playable 1’s or non-playable 4’s, then…
    1. If the previous leader has unknown playables, then hint them their unknown playables.
    2. If the previous leader has non-playable non-discardables in the discard position, then hint them their non-playable non-discardables in the discard position.
    3. If the previous leader has non-discardables in the discard position, then hint them non-playable 5’s, 1’s, or 4’s.
  3. Play the card in the most playable position.
  4. Discard the card in the most discardable position.
 
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