In the game of klaverjassen knowledge and beliefs play a big role. At the most basic level of knowledge the player knows its own cards and the cards that have been played. The knowledge of which cards have been played is common knowledge among the players as these cards are played openly to the table.
Knowledge one level deep is the basic form of knowledge about the other players. Knowledge about the cards of other players is obtained from inference and not direct observation. There is only one type of fact the player can really know and that is whether or not another player does not have a card of a certain color. In the game a player has to play a card of the color currently being played if it can. If it plays a different card it is known this player does not possess the requested color.
A player can also have believes about cards other players have. These believes come from the way people play certain cards. Several possible things are:
1) A player wants to take a trick when it can. Therefore, it is likely it has the higher card as well when it starts out with a card from a certain color that is 1 or 2 lower than the highest still in play
2) Seinen
Seinen can work both from the player’s partner as well as the opponent. Players only sein if their partner has currently the highcard of the trick and if the player can't serve the asked color of the trick. If the partner plays a low card (7,8,9) of a certain color it wants to send the message it also has the high card of that color. If the partner throws a medium card, e.g. jack, queen or king, when the player has the highcard of the trick it might mean the partner does not have any good cards of that color.
Seinen from the opponent work much in the same way: If an opponent seins to his partner it has the high card of a color it is known to you as well. In this case this information (the belief that that opponent has the highcard) can be used to avoid that color.
In klaverjassen believes about seinen you get from your partner are usually acted upon, unless you know your partner does not sein or can’t have a certain card. Ofcourse it is also possible that you can't act upon a sein, simply because you do not have the cards to do so.
In klaverjassen most knowledge and believes that are two (or more) levels deep are implicit. This particularly holds for believes about seinen. Because there is no two way communication, the player who gives the sein will have to assume it is understood by its partner, and also that it has been picked up by the opponents. The player receiving the sein also has no way of verifying the sein was an actually sein or just the only card his partner could play. These believes only become knowledge when the person who the sein went to acts on its believe and plays the color asked for by his partner.
This implicit knowledge can also be used to trick other players. If, for example, a player acts as if it seins with a low card of a certain color his opponents might avoid that color. This is beneficial if the player had no other cards of that color. It can also work if, after the sein, the partner plays this color after which the player can play his medium trump which otherwise would have been lost.
Kripke-Models are a good way of representing all possible situations that might occur. A world could be present for each possible distribution of cards. Every time a new piece of knowledge becomes known, worlds could be removed. In such a system believes could be a measure of strength of the connections. When connections are too weak worlds could be deleted as well. Based on these worlds a player could then see which card would be the best one to play by seeing if he has anything that can beat everything that is at its opponents.
Unfortunately this method is not feasible for klaverjassen. As the deck consists of 32 cards at the start of a round and only 8 of those are known, 13824 (24^3) worlds would be needed per player to represent all the knowledge.
Building Kripke-Models can be done for the last few tricks of the game. Would we build a complete model of the last three tricks, “only” 729 (9^3) worlds would be needed. This amount can be reduced even further when using knowledge obtained in the other tricks to delete worlds that can’t be true.