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Hanabi — named for the Japanese word for "fireworks" — is a cooperative game in which players try to create the perfect fireworks show by placing the cards on the table in the right order. (In Japanese, hanabi is written as 花火; these are the ideograms flower and fire, respectively.)
The card deck consists of five different colors of cards, numbered 1–5 in each color. For each color, the players try to place a row in the correct order from 1–5. Sounds easy, right? Well, not quite, as in this game you hold your cards so that they're visible only to other players. To assist other players in playing a card, you must give them hints regarding the numbers or the colors of their cards. Players must act as a team to avoid errors and to finish the fireworks display before they run out of cards.
To get enough information, you need not only the explicit information from the clues, but also to have a mental model of what algorithm the other players are using to interpret the information they have, so you can base deductions about why and when they gave the particular clue, rather than giving a different clue, or a clue to someone else, or doing something else (such as playing or discarding).
It turns out that one of the most desirable properties for an algorithm to have is its predictability - how easy it is for other players to accurately model what you'll actually do, based upon their clues, when trying to follow the algorithm.
Compare the following two algorithms:
A1
1. If the player to your left is about to play a wrong card, or discard a needed card, alter their behaviour (either by giving them a clue, or by leaving them in a situation where they have to spend their turn giving the player to their left a clue).
If and only if 1. isn't applicable, then do:
2. If you have certain knowledge that at least one card in your hand is safe to play, then play one of them
If and only if neither 1. nor 2., are applicable, then either do:
3. Discard a card you are certain will never be safe to play
or
4. Give someone a clue that changes what their default 'next to discard' card is
or
5. Give someone a clue that changes what their default 'next to play' card is
or
6. Discard your own 'next to discard' card, which might be something that could have been useful later on, but hopefully isn't critical.
or
7. Give an informational clue, hopefully in a way which, while it doesn't change someone's default behaviour, makes it easier for someone else to then later give a clue that will change behaviour.
A2
The same as A1 except it specifies that if you have two cards you are certain are safe to play, you play the one on the right of your hand.
Algorithm A2 is more prescriptive than A1 and less flexible. There are situations where you'd like to do something else. For example, if you can play a Green 2, because the next player to your left has a Green 3, and you want to enable them to play it, rather than play a card which doesn't enable anything yet. But, if you're going to break the algorithm sometimes, is it better not to have the algorithm specify at all what to do in that situation, so other people know they can't make reliable deductions about what you will do?
Clive, you said you'd written a blog post about this somewhere?
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Hanabi