The AI in The Octagon Theory-Intro

The Octagon Theory (TOT) is a two-player board game in which the goal is to push the opponents pieces off the edges of an octagonal field or in the hole in the middle. For a game with few rules it is surprisingly complex and offers strategic depth which makes it challenging to master for an AI opponent.

With the advent of mobile gaming and the popularity of board games on this platform the need for efficient AI for such games has increased in the last years. Board games are an interesting field because of their discrete nature and the often immense branching of their search tree which makes them hard to solve by brute force. Learn more about the state of the art in this field in our Monte Carlo-Tree Search Article.

We sat down with Daniel Huffman, the inventor and programmer behind the game, to talk about his approach for the computer opponent which is able to challenge even experienced players.

Introduction

Q: Can you describe the gameplay of the octagon theory and the goals you had in its design?

Daniel Huffman (DH): The Octagon Theory (TOT) was very loosely inspired by the Japanese sport of Sumo where the goal is to knock one's opponent to the ground or push the opponent out of the ring. So TOT is a two-player 'pushing' game. 
You and your opponent basically take turns rotating and placing directional pieces of various strength on the board attempting to knock the opponent's pieces off the board. When the pre-decided number of game turns counts down to zero, the player with the most pieces on the board is the winner.

TOT gameplay. Red Player places a piece and pushes one of his blue opponents off the board.

Along with the Sumo inspiration it was very important to me for TOT to be a very pure and simple game that didn't need a rule book. A game that could be learned by just watching it being played once or twice. But of course I also wanted it to be deep.

I think most of the classic board games like chess, checkers, backgammon, go, etc. all fit within that simple but deep description. And I think that's the reason that they all have lasted down through the ages. And it is more important to me for TOT to be considered as one of the classics and to be played forever than it is for TOT to become an instant sales success. I want TOT to be my legacy.

Q: Which strategies and ways to play can one apply in this game?

DH: If you play in a purely offensive way you'll probably lose. I consider a defensive/offensive mix the best. Always start by securing the strongest positions on the board. Of course those are the positions that are furtherest from the board edges and the center hole. And instead of always trying to push opponent pieces towards the edges or off the board in one move, try to slowly setup the opponent pieces by slowly forcing them into a pattern which will allow later use of one of your stronger pieces to 'kill' three or more opponent pieces with one move. And timing is important too... don't wait until too late in a game to use the stronger pieces for two reasons...

1. You may run out of turns before you can make good use of all your stronger pieces. and

2. The board may become too crowded to make effective use of your stronger pieces.

And don't get the impression that placing a piece near the edge is always a bad move. If the pattern of pieces on the board is right, with 'cannoning' you can place your piece in just the right edge position to 'kill' opponent pieces that are located on far edges of the board.

Of course blocking tactics are useful at the right time and with the right pattern. 
Also I have to mention that I keep learning new strategies the more I play TOT. The funny thing is I had no idea how deep the strategy could be when I designed the game. It seems to have taken on a life of its own. It's probably because of the addition of the one, two, and four-pieces (directional). The original Apple II version of TOT that I made back in the mid-1980's had only one piece...the non-rotatable 8-piece. And an unlimited number of them. So in the new version of TOT I think strategy depth has increased exponentially.

Since the game is so new I think most players have yet to develop any advanced or deep strategies. But what I have seen is very aggressive gameplay - trying to always push the opponent's pieces off the board, without giving any thought to securing safe positions if it means not being able to attack the opponent. Also timing is wrong - they may wait until too late to use the stronger pieces - the pieces that can push two to eight opponent pieces in one move. And they forget to use piece rotation and 'cannoning' effectively.

Also when playing online I notice that some players will mimic my moves because they think since I designed the game that I must be making the best moves. In this case I'll sometimes make illogical moves just to confuse my opponent and make him/her get hung up on trying to figure out why I made that move.

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