Introduction

This project is the implementation of a simulation of one hand of the Dutch card game Klaverjassen. It is generally played with four players and uses 32 cards. A hand consists of eight tricks, where during each trick points can be obtained. The player that plays the highest card wins the trick and all the points attributed to the cards in that trick. The program is implemented using Python. To decide which card to play each of the four agents need to reason about their own cards and which cards the other players might have to win the trick. To be able to properly reason they need knowledge about the basic rules of the game and which cards the other players may have. At the start of the hand each player is only certain about their own cards, but as the game progresses more information becomes available. Public announcement logic is used to deal with the representation and updating of knowledge for each player. The visualisation of the knowledge is achieved by drawing Kripke models for each cards.

Download and run instructions

In addition to our program files, which can be downloaded by using one of the download buttons above, you will also need Python (either version 2.7 or 3.5) and the Pygame Module in order to run our program. To run our logical klaverjas agents app, unzip the folder after downloading it and execute the main.py script with python. On Mac/Linux run command: python main.py from the command prompt. On windows the standard Python installer associates the .py extension with a python file, so you should be able to double click main.py in order to run it.

The Game

Klaverjassen is a strategic card game frequently played among Dutch students. The game is played with two teams of two players. The first team which reaches a total of 1500 points wins the game. The game consists of a number of hands in which points can be gained. The objective of each hand is to collect more points than the other team. Every card from 7 and up is used for the game, this comes down to a total of 32 cards. These 32 cards are divided evenly between Each player, this means that everyone receives eight cards at the beginning of each hand. Each player can only see their own cards. A hand consists of eight tricks, players have to play one card each trick.

Main Rules

Points are scored by winning tricks. The player that plays the highest card in a trick receives all of the cards played that trick and the points associated to the cards. The ranking of the suit cards is displayed in table 1. Every hand the cards of one of the four suits are trump cards. As displayed in the third and fourth column of table 1 the trump cards have a different ranking and value than the regular suits. All trump cards also rank higher than the cards from other suits. Trumps can be decided in a number of ways, players can bid on a suit with the number of points they think they will aquire that hand. The highest bid wins and the team with the highest bid will play. This means they have to obtain at least the number of points of their bid. If they don’t acheive this, they will play wet. This means that the opposing team wil receive all the points for that hand. The trump can also be chosen at random, now, one by one, every player can say if they want to play, or if they pass. In this project, for the sake of simplicity, the trump is decided at random every hand and team South, North always plays.

Trick Rules

Every trick, a number of rules have to be followed by the players. At the beginning of every hand the person that can start playing a card at the first trick is determined in a clockwise order. This person can decide which suit will be asked that trick by playing the card of a certain suit. Every other player has to follow suit. If a player is not able to follow suit and the highest card on the table, at that moment, belongs to one of the players of the other team, he has to play a trump card. If the player has no trump cards, any other card can be played. When a trump card is played, all other players have to play a higher trump, if they are able to. Some bonus points can be earned by a roem system, which we do not elaborate on here. Winning the last trick of a hand awards 10 bonus points. When the starting player’s team does not accumulate more than half of the points during a complete hand, all points in that game are awarded to the opposing team. This is called playing wet.

Bonus Points (Roem)

For each hand there are a number ways to obtain bonus points. The first one, already explained above, is playing the other team wet. When a team does not achieve their point goal, they are played wet. This results in the other team gaining all points obtained that hand. This includes the points of every card as well as all other bonus points obtained during each trick of that hand. When one team wins every trick of that hand they have a pit, this gives the winning team an additional 100 bonus points.

During each trick certain card combinations on the table are also points for the team winning that trick.

• King and queen of trump: 20 points
• Three successive cards of the same suit: 20 points
• Four successive cards of the same suit: 50 points

Public Anouncement Logic and Kripke Worlds

To acquire the most points in a hand it is essential to stay in control. This means a player has to play every trick in such a way that he obtains the highest number certain tricks. Certain tricks are tricks where the starting player is assured of winning when starting that trick with a certain card. One tactic for doing this is starting with asking the trick suit when the player is in possession of the highest trick card. This means the other players also have to play their trick cards. This results in a lower chance of the players of the other team playing a trump when they do not have the asked suit. In other words, the strategic aspect of playing the klaverjas game is obtaining knowledge about the cards of the other players. Using this knowledge, players are able to devise which cards to play to certainly win a trick, and therefore obtain points. Every card played generates new knowledge available to all of the four players. Combining this public knowledge with the cards the players hold in their hands, the private knowledge, every player has a different set of certainties and uncertainties. In other words, the knowledge of every player is different. To analyse the increase in knowledge while the game progresses we employ the framework of Public Announcement Logic (PAL). Public announcement logic is widely used in multi-agent systems for modelling knowledge and announcements. For the language definition and an elaborated explenation of public announcement logic we refer to Chapter 4 in the book Dynamic Epistemic Logic written by Hans van Ditmarsch. In our klaverjas simulation we use the PAL framework to visualise the knowledge and beliefs of each player. It also provides us with a way to see the basis of the reasoning of each agent. At the start of each hand players are only able to see their own cards, they are certain about which player posesses these cards. Because all agents know the basic rules of the klaverjas game, they know that every card available in the game is possessed by another player. For example we can consider the case that South does not possesses the ace of spades, he knows that West OR North OR East must have this card. This is modelled by using Kripke models. Every Kripke model displays possible scenarios of a card for each player. Every time a card is played a public announcement is made and the Kripke models change, overall knowledge is increased.

Object Oriented View of Logical Klaverjas Playing

The Cards:

Cards are modeled like a tuple holding the suit, the name of the card and the point value. For example:(‘hearts’, ‘king’, 4) is the tuple representing the king of hearts cards which is worth 4 points. As stated above, a klaverjas game consists of a number of hands until one team reaches 1500 points. Our program simulates one hand of the whole klaverjas game since every hand all knowledge about cards is reset. This means that South always plays the first card in our simulation, and only team one (South and North) can play wet.

Team Class:

This is a data class holding only the number of the team (1 or 2) and the names of the players in it.

Trick Class:

This class holds multiple attributes for each round, which include: each played cards, score of the round, the winning player, the highest card, which suit is trump and the order players played a card in. It also holds a function that handles the adding of a new card to the round. The card and player are added to the attributes, the value of the new card is added to the score and if the card trumps the others or is of higher value the winner and high card attributes are also updated. The last functions check the bonus (roem) that might be provided at the end of the round, and adds these to the score.

Player Class:

Variables:

• team, a Team class instance
• closed_cards, a list holding the closed cards as tuples
• open_cards, a list holding the open cards as tuples
• own_cards, the combination of open_cards and closed_cards
• turn, a integer representing the turn order in a trick
• name, the name of the player
• all_cards, list of tuples holding all cards in the game
• knowledge, a list holding tuples of the form (name, card, played), where name are the names of the other players, card can be any tuple representing a card and played is a Boolean representing if a card is played or not. This list holds all items a players knows for certain
• possibles, a list of the same form as the knowledge list. But this list holds all the cards the player is uncertain about. This means that if a player (South) does not know whether the ace of spades is held by West, North or East, than this card is represented thrice in the list, as (‘West’, ( ‘Spades’, ‘Ace’, 11), False), (‘North, ( ‘Spades’, ‘Ace’, 11), False) and (‘East, ( ‘Spades’, ‘Ace’, 11), False).

Functions:

Play_card() is the function called when a player needs to play a card. It receives the trump and the trick if there is any yet. It will then first select the playable cards of the player by calling playable() from the rules_config.py file, after that it will select the best card from this list by calling find_best_card() from the tactics.py file (both these functions are explained later). Play_card() will then remove the found card from either the open_cards or closed_cards list. Then the function returns that card and the thoughts as found by the tactics.py function. Functions for this class are: Play_card() is the function called when a player needs to play a card. It receives the trump and the trick if there is any yet. It will then first select the playable cards of the player by calling playable() from the rules_config.py file, after that it will select the best card from this list by calling find_best_card() from the tactics.py file (both these functions are explained later). Play_card() will then remove the found card from the open_cards or closed_cards list, depending on in which it was in, and then returns that card and the thoughts (the reason why that card was chosen) as found by the tactics.py function.

Create_possibles() creates the possibles list. It looks at all the cards that are in the all_cards list and not in the knowledge list and creates three instances (for all the other players) in the possibles list for each card.

Update_possibles() looks at the played cards in a trick and makes inferences based on that cards:

• When a card is played, the card status changes from possible to knowledge, this means that all instances in the possibles list holding that card are removed.
• Next, when a player has played a card that is not of the same suit as the first played card, it can be concluded that that player does not have the asked suit anymore, so all instances holding that players name and that suit in the card tuple are removed from the possibles list.
• When the last played card is from a player that is not on the team winning the current trick, and he played a non-trump card, a number of options arise: If trump cards are played in this trick it can be inferred that the last playing player doesn’t have a higher trump card than the trump cards on the table. If there were no trump cards played and the player still didn’t play a trump card, it means that he has no trump left at all. Therefore all suitable combinations are removed from the possibles list.
• If a player played a card that in rank is one lower than the highest already played card, this means that he/she cannot play a lower value card (in our setting of the game, this is not always true in a real klaverjas game), so the player does not have any other cards of that suit left, and the suitable combinations are removed from the possibles list. For example: South starts with the ace of spades and West follows with the ten of spades. This means he has no other spades cards, and all combinations of West and spades are removed from the possibles list
• Finally, if a card is found only once in the possibles list it becomes definate knowledge. The card is then removed from the possibles list and added to the knowledge list. For example, South has two trump cards left, and because East and West have not responded with trump cards when these were played, South knows the remaining trump cards are all in North’s possession.

Rules_config.py

This file holds all information about the actual game, so the names of the suits are stored here, as well as the names of the players, the ranking and points of trump and non-trump cards. The number of players, the number of tricks and the number of open and closed cards are also stored here. The default setting of the number of closed cards is 8, this can be reduced so that players have more knowledge about the cards of the other players at the start of the game. The most interesting part of this file is the playable() function, that receives a list of cards, the team and the trick, if there is any.

• If there is no trick, all cards are immediately returned as this means that the first player can play any card from his/her hand.
• If trump is asked, a list of higher trumps is first returned.
• If this does not exist a list of lower trump cards is returned.
• If this also doesn’t exist all cards are returned.
• When suit is called and the player still has suit left, all suit cards are returned.
• If the player does not have suit left and is on the losing team, all (higher) trump cards are returned, if available.
• in all other cases all cards are returned.

Tactics.py

This file holds three functions, the first being unplayed_trumps(), which returns all trump card that can still be played by any of the layers. The second function KM_suit searches for all instances in the knowledge and possibles lists of a player having a certain suit and returns this as a sorted list on the rank. So this function is called like KM_suit(‘South’, ‘West’, ‘hearts’) and will return a sorted list with all instances in the knowledge and possibles lists of South where (‘West’, (‘Hearts’, _, _)False) is true. The most important and biggest function in tactics.py is find_best_card(), which receives the playable cards of a player, that player instance and the trick instance. This function analyses the knowledge of the player and determines which card to play by going trough a number of options. If there is only one playable card, that one is played. The options are different for each player in a trick, i.e. if a player can start and play the first card he can choose which suit will be asked, the other player have to follow suit.

For the starting player:

If there are still trump cards in play, and

• If the player has the highest ranking trump card and knows or thinks one of the opponents have at least one trump card left, the player will play their highest trump card.
• If the player knows that his teammate has the highest trump card, one of the opponents has a trump card left and the player himself has a trump card left, he will play his trump card.
• The player thinks both opponents still have a certain suit, and the player thinks they do not have a higher ranked suit card than he has, he plays that highest ranked suit card. For example: South has the ten of spades and thinks both East and West still have spades but not higher than the ten, he will play the ten. If there are no trump cards in play anymore, the first player will search for a card that is higher than any cards the opponents can have, or he will will play a card of which the opponents do not have suit anymore.

For the second player:

If trump is called and the player still has trump cards, multiple options are available.

• If the second player thinks the third player doesn’t have trump anymore, it will play the lowest trump card that is higher than the one played by the first player (if this is available).
• If the second player thinks the third player still has trump, it will play a card of which he thinks is higher than what the third player can play. If that is not the case as well, the second player will play his lowest available trump card.
• If the second player does not have trump anymore, he will play his lowest ranked available card.

If trump is not called the following options are available:

• When the second player has to play trump he plays his lowest ranked trump card. When he doesn’t have to play trump he thinks about what his opponent and teammate may have.
• If he thinks the third player (his opponent) doesn’t have suit anymore, he plays a card that is higher than the card of the first player, but only if he also thinks the third player does not have trump.
• If he thinks the third player still has suit, he plays his highest card if he thinks that it is higher than both the first card played and the highest possible card from the third player. When the second player thinks his teammate has an even better card there is an exception to this last option. He now plays hist lowest ranked card. In all other situations the second player doesn’t think he or his teammate can win this trick, and thus plays his lowest card.

For the third player:

Again, this player looks at his own cards, the cards played and what he thinks the fourth player still has left. Only if the third player is sure that he can win the trick (so the fourth player will not have a higher suit card, or no suit and trump left) he will play the highest card playable, in all other cases he will play the lowest card playable.

For the fourth player:

This player knows if he can win this trick with his available cards or not, so he will try to win the trick with the highest card capable of that if the other team is currently winning the trick. If he cannot win or his team already wins this trick he will play his lowest playable card.

Main.py

Excluding graphical details in this explanation, these can be found below in the visualisation section. main.py is where the match is played by our logical agents. In this file the current trump suit is chosen at random, the player instances are initialized and the cards are shuffled and distributed among the players. When this is done the knowledge of each player is created on the basis of their own cards and the open cards on the table, if there are any. When this is done, each player assesses what he thinks is possible, and then South starts the match by playing his first card. In eight rounds, after each card is played the reasoning of the player is shown. After each card, each player updates their knowledge and their uncertainty. After each round, the winner of the round is shown at the bottom of the text field, and the scores are added to the correct team. After 8 rounds the programs shuts itself down automatically, but first calculates if the first team accumulated more than half of the points in the game. If they did, they keep the points. If they don’t, the other team receives all the points.

Visualisation

Game Display

In main.py the game is rendered to the game display using Pygame. Pygame allows the drawing of stock images (such as the cards in the card playing gui, see below), basic rectangles and lines and text to a game display object, which is the foundation for the visualisation of our logical agents playing klaverjas. The game display consists of three parts, the card playing GUI in the top left, the Kripke model diagram box on the right, and the message box in the bottom. The card playing GUI and the message box are explained below. The Kripke model diagram box is explained in the next section, about the Kripke model diagrams.

Card Playing GUI

The card GUI, pictured above, is mainly visualised to make the progress of the game insightful to human observers and provide viewing ease. In the card playing GUI the entire game is played, card by card, the cards of the currently playing player are visible, as well as the open cards of the other players, if there are any. A small delay is implemented with each turn before the played card gets put into the center, this is done to create the visual effect of a player putting a card in the center. The card playing GUI also displays some extra information, including the score, number of open cards, the trump suit and instructions for the human observer to go to the next turn or skip to the end of the game.

Message Box

The message box (outlined in red above) is refreshed each turn. In the message box the thoughts, or reasonings, of the current player are printed as well as the public announcements of that turn. The thoughts of a player are the inferences made in tactics.py about which card would be the most advantageous to play in the current situation, and public announcements are played cards, and inferences all players can make based on played card. Such as the fact that one player no longer has any cards of a certain suit, if he can’t follow suit, or that he also doesn’t have any trump if he can’t play a trump card.

Kripke model diagrams of the of the agents’ card knowledge

At every moment during the game it is possible to see what the players know and hold for possible regarding the cards. After each trick, the user/spectator can select a card via a dropdown menu in the window on the right. A schematic S5 Kripke model is then drawn for the selected card with the draw_model function in model.py, which calls on the player.knowledge and player.possible tuples for each card to get the relations between the worlds. As card ownership is mutually exclusive in the klaverjas game (every card in the game is dealt to exactly one player), players never hold any worlds for possible where this is not the case, so for any card C with the corresponding propositional atoms:

1. p1: south owns C;
2. p2: west owns C;
3. p3: north owns C;
4. p4: east owns C.

the S5 model only includes one of the states:

1. (p1 = T, p2 = F, p3 = F, p4 = F);
2. (p1 = F, p2 = T, p3 = F, p4 = F);
3. (p1 = F, p2 = F, p3 = T, p4 = F);
4. (p1 = F, p2 = F, p3 = F, p4 = T).

In the beginning of the game, South plays its lowest card instead of one of its higher ranked cards (like the 10 of hearts). To understand this choice, let’s look at what South knows or holds for possible about the location of the ace of hearts (a card higher than his ten of hearts).

Relations in the diagram pictured above are modeled by the colored lines, each color corresponds to a different player. As we can see, South (who has no information except for his own cards, seeing as it’s the beginning of the game), still holds it for possible that either West, North or East has the ace of hearts, and decides to play it safe by not playing its ten of hearts. As a matter of fact, East is the actual owner of the ace of hearts. This is symbolized by the golden outline around the Kripke world where East is the owner of the card. East is also also the only player who currently knows this. Because this is an S5 model it is implicit that there is a reflexive relation between all worlds and themselves, however we decided to make this relation explicit for the real world, because otherwise there would not be any visible relation for an agent when it knows the owner of the card, and we thought showing the relation of the true world to itself might make the model a little bit more clear to observers.

When players play a card they make a public announcement that they were the owner of that card, if we look at the model for seven of clubs after South has played it, we can see that every player now knows that ‘South owns seven of clubs’, and all worlds where this is false are no longer part of the model.

During the game more and more inferences are made by the players about the remaining cards of the other players based on what they play. Pictured above is the model for the ten of clubs from the same game as earlier, but now a few rounds in, right after South is unable to follow suit on clubs, publicly announcing he has none. We can see that players East and North no longer hold it for possible that ‘South owns ten of clubs’ after this announcement.

Future Work

Klaverjassen is more detailed than represented by the program in this project. Therefore we mention a number of expansions that would improve this program. A selection of these expansions include:

1. letting Players be aware of roem and stuk, so that they may play different cards to gain bonus points for themselves or sacrifice some points to not let the opposing team gain bonus points.
2. Increase the number of hands from 1 to 16, or let a game continue until one of the teams has more than 1500 points after a hand.
3. Implementing signing and the understanding of this (this would come with a believe system, not just knowledge interpretation)
4. Different game modes, which could mean that the starting player is not forced to play with a certain trump. This could result in a game mode where the first player may choose a suit to be trump, in a game mode where players ‘bid’ to what they want to be trump or in other modes
5. Implementing different strategies for players. All players are very cautious now and will not take risks, while taking risks sometimes could lead to better results for the players.
6. Sometimes players should not play their lowest cards when they know their partner will win, but instead play a higher card to not lose that points another round.
7. Letting the observer play as one of the agents.

• Joram Koiter (s2240173)
• Tim Oosterhuis (s2234831)
• Rogier de Weert (s1985779)