Descriptions of the Games used in the AI 2012 Competition
The GDL Files provided here are the ones that were used in the actual competition in December 2012. Some of these games were subsequently modified to fix errors or rebalance. Final versions of the games will be uploaded to the Dresden GGP Server when they are complete.
GDL I Games
Connect 3 Decomposition
Multiple games of connect 3, which is a simplified version of Connect 4. This game is split into 3 boards, each of which can be won separately.
The rules in this game legally allow players to play on any of the three boards each turn, but a further analysis is necessary to show that only one colour is specified in the state for each player each turn. So, if a player plays a colour that is not one of the ones currently available for play, the next state is not changed.
This game was intended to test a player’s ability to decompose the three separate games and win them separately as well as their ability to differentiate between moves that were legal and useful against moves that were legal but not useful.
It seems that most players were able to tell which boards they were currently allowed to play on, however, those that did not understand (and hence played on the incorrect colours) were more likely to lose early in the game. The most interesting result was players who could put one of the boards into a state where whoever played next would be at a disadvantage. At this stage players would intentionally play the “incorrect” move so that they would not place themselves at that disadvantage. This would often lead to stalemated games if both players realised that playing on a particular board would lead to their opposition winning.
Hold your Course
A very simple number guessing game that tests a player’s ability to decipher the rules of the game and use a single planned out strategy from start to finish. In the first round players “deal” a number. For the next 10 rounds, they must choose that same number every round in order to win. If at any time, they stray from that number, they will lose the game.
A simple analysis of the GDL will show quite clearly how to win at this game, but the branching factor of the game (30^10) makes it very difficult for random simulation methods to actually find the one and only one path that leads to victory.
It turns out that none of the current competition players managed to succeed at this game.
Irrelevant Multiboard Connect 3
Another Connect 3 variant. This time there are 6 boards and each of the players can play one piece on any of three of the boards each turn. Analysis of the rules will show that it is only important to win on two of the six boards, the other four are irrelevant.
This game was designed to test whether players can both decompose the 6 boards into separate games as well as understand that though the search space of possible moves is very large, only a small portion of it is significant.
Like in our other Connect 3 game, a single board can end up in a situation where whichever player plays next will end up at a disadvantage to the other player. In many games, the only reason any of the irrelevant boards were played on was that players were trying to avoid giving away an advantage on one of the “stalemated” boards.
In other games, a more capable player would nearly always beat a player that made a mistake and played on one of the irrelevant boards early in the game.
Rock Paper Scissors
This game was indeed a standard implementation of Rock Paper Scissors. The special element of the game was the “robot player”. We implemented a player who would appear as an opponent but play in a very specific way. For the ten rounds of the game, the robot player would always play “Paper”.
This setup was designed to test a player’s ability to notice their opponent’s predictable behaviour and react accordingly.
None of the competition players showed an ability to predict their opponent’s behaviour.
Removalists is a cooperative game of carrying heavy objects. Each object is very difficult to carry alone (takes 15 steps) but only takes 1 step if both players carry it at the same time. There is also the option to “broadcast” the name of one of the objects, which could be used to signal the intention to carry an object, but the rules do not force a player to follow through with a broadcast intention.
This game was designed to test a player’s ability to detect a cooperative game and to work alongside the other player to maximise both their scores. It also allows communication between the players, however this may require the ability to model and predict an opponent’s (teammate’s) behaviour to be useful.
Like Rock Paper Scissors, this game was played with an automated “robot player” teammate. This teammate would automatically help the player if the player was carrying something and the robot was not. Otherwise, it would broadcast its intent to carry one of the objects, then pick it up in the following turn.
None of the players managed to score highly in this game. Most games resulted in the players and the robots carrying different objects and wasting a large amount of time. We were watching in particular for situations where the robot had an object in transit and the player had the ability to join the robot in carrying and hence score points very quickly.
Small Dominion (GDL I Version)
This is a simplified version of the game Dominion by Donald X Vaccarino. There are only Victory and Treasure cards in this game and the normal randomness of drawing cards from a deck has been abstracted away.
This game was designed to test players’ ability to differentiate between a short term and long term goal. To score the highest, it is necessary to acquire the higher value treasure cards before attempting to buy the higher value victory cards.
This version of Dominion did not turn out to be a significant enough challenge for our players. The optimal strategy was found very easily by all players and (once the game was balanced properly) resulted in 50-50 ties consistently.
Surrounding the Tiger (Tiger vs Dogs)
This is an asymmetric abstract board game where one player plays as a tiger while the other player controls 16 dogs. The aim of the tiger is to kill 6 of the dogs, while the aim of the dogs is to completely surround the tiger so that it has no possible moves in its next turn. The Tiger kills a pair of dogs if it places itself on a line such that there are dogs adjacent to it on either side, but there are no other dogs directly behind either of those dogs on the same line.
After several games played, it appears that the dogs have an advantage in this game. The game was played in pairs of rounds with players swapping roles. This usually resulted in both players winning as the dogs and losing as the tiger. There might be a way to balance this game by setting a round limit and the tiger winning if it can survive until the limit.
GDL II Games
The Banker and The Thief
A game of deception for two players. In this game, there are five banks that the banker can place money in, one of which is randomly determined to be the “primary” bank. The thief can see all the deposits made by the banker and after their ten deposits are complete, the thief will raid one of the five banks. The banker will score based on the amount of money that then remains in their primary bank. The thief will score the amount they stole only if they stole from the primary bank.
This game was designed to test the idea of players with hidden goals and opponent modelling. The banker must predict what the thief will do and deposit in such a way as to not show obviously which bank is their primary. The thief must try to determine which bank is the banker’s hidden goal by judging the banker’s actions.
Battleships in Fog
A very simplified variant of Battleship that includes some ideas about revelation and gathering of information. Each player has a 2x1 cell ship randomly placed on their own board of 4x4 cells. Each turn, they may either fire (at any cell on their opponent’s board), move (to any position that shares at least a single cell with their current location) or scan (which reveals 3 possible ship locations of their opponent, one of which is definitely the opponent). Each player can always see their own position, and will know if they’ve been hit or if they hit their opponent. An interesting side effect of firing is that your opponent will receive the same information as if they scanned when you fire. This means that repeatedly firing without moving is very likely to give away your position.
This game was designed to test a player’s ability to reason about their opponent’s knowledge. Reading the rules shows that after being fired upon, a player has a choice of only 6 cells that their opponent might be in. A player should then play in such a way as to try to keep their position secret while determining their opponent’s position, or else move from a position once they’ve been given away.
A simple GDL implementation of the common casino card game, Blackjack. In this version of the game, there is a single deck of 52 cards and two players play two rounds each.
This game was used to test probabilistic reasoning in a computationally difficult environment. It is infeasible to enumerate all possible decks so players will need to reason about the average likely future card values to make their choices in the game.
Hidden Goals Connect 3
Like our other Connect 3 games, this was played on more than one board (in this case two). This variant of the game also uses hidden goals. In the first turn of the game, the random player assigns a value of either “win” or “lose” to the first player on the first board and to the second player on the second board. Players win by completing their goal on their own board and stopping their opponent from completing the goal on the other board.
This game tests a player’s ability to judge an opponent’s possible goal based on their behaviour and also a player’s ability to play in a certain way to deceive their opponent into helping them complete their goal.
A simple version of Minesweeper using only a small 4x4 or 5x5 grid and 2 or 7 mines (there are two versions).
This game tests a player on reasoning using partial information that makes different legal moves relatively safer or more dangerous than each other.
A very simple game where the random player chooses a number between 1 and 32. The player can then either ask if the number is less than another number or declare which number they think is the secret number.
This game, though simple, is a test of whether players can understand the idea of making moves for information gathering purposes. A certain amount of mathematical reasoning would also be necessary to optimally search for a number.
A GDL II version of the game Dominion by Donald X Vaccarino . There are only Victory and Treasure cards in this game and hand size has been reduced to 3 for simplicity.
This game was used for its complexity in the randomness of every hand. It also tested a player’s ability to play a longer term game, building up resources rather than a greedy solution that would end up in a worse position at the end of a game.