Introduction Welcome to the Referential Sieve system for Hanabi! Why should you learn Referential Sieve? It's powerful: Even with just the Basic Conventions, players can usually get a perfect score and avoid discarding more than one or two useful cards. It's simple: This document is pretty short! It's different: If you haven't played Referential Sieve before, you probably haven't seen either of the ideas in its name before. The word "Sieve" in the name means that we prefer to discard newer-drawn cards. The word “Referential” means that when we want someone to play or discard a card, we don’t clue it directly, instead we clue an adjacent card.

Introduction One of the key ideas of Reactor is that we can split up two pieces of information in our Hat Guessing clues: the sum of the slots of the actions and the types of actions. For example. in a 3p game, a reactive color clue calls for 1 play and 1 discard and a reactive number clue calls for 2 plays. In general, how much information about the types of actions do we need to encode? Without finesses, we just need to encode whether the number of plays is odd or even, because each player's decision is only whether to discard/clue or play which adds 0 or 1 to the total number of plays. The problem is that with finesses, Bob has to decide the actions of both himself and the player with the one-away card: either they both discard/clue, Bob plays and the other discards/clues, or they both play (adding 0, 1, or 2 to the total number of plays). Adding 0 or 2 have the same effect on the parity (oddness/evenness) of the total, so Bob doesn't know which to decide. Instead of communicating the parity of the number of plays (which is the same as the number mod 2), we can communicate the number mod 3, that way adding 0 and 2 have different effects on the total. Discard slot 4 = lock (4p-specific) In a 4-player game, if a player has no plays or safe discards, we can assign them a "discard slot 4" instruction. When a player receives such an instruction, they know that it actually means to give a clue (they are basically locked). Unfortunately, this means we have no way of telling slot 4 to discard.

We follow all/most conventions of https://hackmd.io/Ui6LXAK3TdC7AKSDcN20PQ Overruled/clarified/extra conventions PTD Alice does not have PTD if either: A) Players have only taken Urgent Actions since her chop was drawn and they see that there's an Okay Clue to give B) The player who last took a non-Urgent Action saw a Necessary Clue to give and that giving it would not force a useful discard Urgent Action:

These conventions were developed by @timotree3 in May 2021 in collaboration with @indego, @Lel0uch-H, @melwen, MarkusKahlsen, and HelanaAshryvr as an alternative to IAMJEFF's Score Hunting Guide. Some big differences include: Safer playstyle, e.g. save stalls More powerful Focus Inversion and Self-Color Bluffs A powerful convention for unlocking a locked partner These are still my personal favorite 2p conventions with a discard-oldest assumption, but now that Sieve and Referential Sieve have been invented, I recommend those for 2p. Basic conventions The following H-Group conventions are turned on:

# mod 8 action person clued clue 0 (8) discard slot 1 1 player away 1 or 4

# mod 8 action person clued type card 0 (8) discard chop 1 player away number