Objective-c – Writing an AI for a turn-based board game

(Edit: 8/8/2013) - I've written some sample code: Ultimate Tic-Tac-Toe, where I have a generic implementation of min/max game search. The code is written in a silly variant of C++, called prepp.

Your best resource would be a college-level course on Artificial Intelligence. The classic textbook is "Artificial Intelligence: A Modern Approach" by Russel & Norvig

I'll try to give you a breakdown of the key concepts.

Game state - this is a set of variables which can be used to determine:

• The estimated "Value" of the current state
• Is the game over?

Value - the "value" of a particular state is a function of that state evaluated by the current player, let's call it f(x). Another name for this function is the "heuristic" function. It determines the best possible value that the current player could achieve, given board state, x. How you model x is up to you, but x should encompass everything used in the natural flow of the game. So, in your case, x may be an 8x8 matrix of values mapped to pieces on the board. And, f would be a function that gives the "Value" of that board configuration for the Red player (or some such.)

A possible simplification to consider in a 2-player turn-based game is to encode the "current player" as part of the state. This adds state to input to the heuristic function. So, instead of f(x), we have f(x, player). However, that can be simplified by rolling player into x. Either way, f will always return the "Value" for the same player, but according to who's turn is next.

To clarify by (simplified) example, f in chess should nearly always return a very high score if white can kill black's queen. But if black will have the possibility of killing white's queen in the next move, then f should return a very low number.

Note that so far there is no mention of the tree-searching part of minmax. f is always defined based on the current state. So, when I said "black will have the possibility...", what I mean is that your heuristic function can determine, for example, that given x, there is a line of sight (diagonal, horizontal, or vertical) between a black bishop, or rook, to white's queen. The heuristic for chess should be sophisticated enough to know that this alone creates a threat, and therefore it should be scored accordingly when computing the total value of f.

Before I get to minmax, note that A* is an optimization for searching the space of possible x values. But, you should not worry about optimization until you fully understand and have implemented minmax.

So, the minmax algorithm is a way to organize your AI's decision-making process. The things you'll need to be able to do in order to implement minmax:

• Generate valid game states from an existing game-state x.
• Stop looping or recursing after a particular depth has been reached.
• Remember the "Value" for each level recursion by passing it back to the caller.

The basic flow starts by understanding, whose turn is it? As I mentioned earlier, f will always return high values to indicate success for player 1, and low values to indicate success for player 2. At each deeper level of recursion, player will allow you to understand whether to choose the minimum or maximum of the potential values discovered through your recursion.

Let me say that another way. There are two reasons to actually evaluate f(x).

1. You want to know if the game is over at state x.
2. You have reached the deepest level of recursion and you'd like to evaluate what the score will be if the game progressed this far.

So, your code would do something like this:

function minmax(x, player) returns value

• My current state is x, and the next player to move is known. I know this because
  • function choose-move told me so. (see below)
  • I was called recursively by myself. (see below)
• Is the game over? Ask f(x). If it returns positive infinity, then white has won. If it returns negative infinity, then black has won. If your game has a stalemate option, or has an end score (perhaps as part of a larger game), then you will simply have to make up a way to represent winning + score as a return value of f. Or, if you want to separate it out, just make a new function g(x) which does this. If the game is over, return that value to your caller. If the game is not over, continue.
• From x I will enumerate all possible x'. In an 8x8 game, there may be a few, to tens or hundreds of possible valid moves from any single game state. This depends on your game's rules.
• If the deepest level of desired recursion has been reached,
  • For each x', call f(x', player). For each call, we associate its return value with the particular x' we had passed in.
• Else
  • For each x', recursively call minmax(x', other-player). (Note that other-player is the opposite of player at this point.) For each call, we associate its return value with the particular x' we had passed in.

At this point, all possible next moves should have a "value" associated with them.

• If player is player 1, choose the maximum value from all values associated with all x', and return that value. That is the best that player 1 will be able to do from this game state.
• If player is player 2, choose the minimum value from all values associated with all x', and return that value. That is the best that player 2 will be able to do from this game state.

end function minmax

function choose-move(x, player) return *next_state*

• My current state is x, and we're trying to figure out what player's next move should be.
• Check whether the game is over, as described above.
• From x I will enumerate all possible x'. (You should be able to re-use whatever code you had to do this in minmax.
  • For each x', call minmax(x', player). For each call, we associate its return value with the particular x' we had passed in.
• If player is player 1, choose the maximum value from all values associated with all x', and return that value. That is the best that player 1 will be able to do from this game state.
• If player is player 2, choose the minimum value from all values associated with all x', and return that value. That is the best that player 2 will be able to do from this game state.

end function choose-move

Your driver code will just need to call choose-move, and it should return the next game board. Obviously, you can also encode the return value as a "move" instead of a state, for a different representation.

Hope this helps. Sorry for the long-winded explanation, I just had some coffee.