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  • minimax depth first search game tree

    - by Arvind
    Hi I want to build a game tree for nine men's morris game. I want to apply minimax algorithm on the tree for doing node evaluations. Minimax uses DFS to evaluate nodes. So should I build the tree first upto a given depth and then apply minimax or can the process of building the tree and evaluation occur together in recursive minimax DFS? Thank you Arvind

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  • MiniMax function throws null pointer exception

    - by Sven
    I'm working on a school project, I have to build a tic tac toe game with the AI based on the MiniMax algorithm. The two player mode works like it should. I followed the code example on http://ethangunderson.com/blog/minimax-algorithm-in-c/. The only thing is that I get a NullPointer Exception when I run the code. And I can't wrap my finger around it. I placed a comment in the code where the exception is thrown. The recursive call is returning a null pointer, what is very strange because it can't.. When I place a breakpoint on the null return with the help of a if statement, then I see that there ARE still 2 to 3 empty places.. I probably overlooking something. Hope someone can tell me what I'm doing wrong. Here is the MiniMax code (the tic tac toe code is not important): /* * To change this template, choose Tools | Templates * and open the template in the editor. */ package MiniMax; import Game.Block; import Game.Board; import java.util.ArrayList; public class MiniMax { public static Place getBestMove(Board gameBoard, Block.TYPE player) { Place bestPlace = null; ArrayList<Place> emptyPlaces = gameBoard.getEmptyPlaces(); Board newBoard; //loop trough all the empty places for(Place emptyPlace : emptyPlaces) { newBoard = gameBoard.clone(); newBoard.setBlock(emptyPlace.getRow(), emptyPlace.getCell(), player); //no game won and still room to move if(newBoard.getWinner() == Block.TYPE.NONE && newBoard.getEmptyPlaces().size() > 0) { //is an node (has children) Place tempPlace = getBestMove(newBoard, invertPlayer(player)); //ERROR is thrown here! tempPlace is null. emptyPlace.setScore(tempPlace.getScore()); } else { //is an leaf if(newBoard.getWinner() == Block.TYPE.NONE) { emptyPlace.setScore(0); } else if(newBoard.getWinner() == Block.TYPE.X) { emptyPlace.setScore(-1); } else if(newBoard.getWinner() == Block.TYPE.O) { emptyPlace.setScore(1); } //if this move is better then our prev move, take it! if((bestPlace == null) || (player == Block.TYPE.X && emptyPlace.getScore() < bestPlace.getScore()) || (player == Block.TYPE.O && emptyPlace.getScore() > bestPlace.getScore())) { bestPlace = emptyPlace; } } } //This should never be null, but it does.. return bestPlace; } private static Block.TYPE invertPlayer(Block.TYPE player) { if(player == Block.TYPE.X) { return Block.TYPE.O; } return Block.TYPE.X; } }

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  • MiniMax not working properly(for checkers game)

    - by engineer
    I am creating a checkers game but My miniMax is not functioning properly,it is always switching between two positions for its move(index 20 and 17).Here is my code: public double MiniMax(int[] board, int depth, int turn, int red_best, int black_best) { int source; int dest; double MAX_SCORE=-INFINITY,newScore; int MAX_DEPTH=3; int[] newBoard=new int[32]; generateMoves(board,turn); System.arraycopy(board, 0, newBoard, 0, 32); if(depth==MAX_DEPTH) { return Evaluation(turn,board);} for(int z=0;z<possibleMoves.size();z+=2){ source=Integer.parseInt(possibleMoves.elementAt(z).toString()); System.out.println("SOURCE= "+source); dest=Integer.parseInt(possibleMoves.elementAt(z+1).toString());//(int[])possibleMoves.elementAt(z+1); System.out.println("DEST = "+dest); applyMove(newBoard,source,dest); newScore=MiniMax(newBoard,depth+1,opponent(turn),red_best, black_best); if(newScore>MAX_SCORE) {MAX_SCORE=newScore;maxSource=source; maxDest=dest;}//maxSource and maxDest will be used to perform the move. if (MAX_SCORE > black_best) { if (MAX_SCORE >= red_best) break; /* alpha_beta cutoff */ else black_best = (int) MAX_SCORE; //the_score } if (MAX_SCORE < red_best) { if (MAX_SCORE<= black_best) break; /* alpha_beta cutoff */ else red_best = (int) MAX_SCORE; //the_score } }//for ends return MAX_SCORE; } //end minimax I am unable to find out the logical mistake. Any idea what's going wrong?

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  • Minimax algorithm: Cost/evaluation function?

    - by Dave
    Hi guys, A school project has me writing a Date game in C++ (example at http://www.cut-the-knot.org/Curriculum/Games/Date.shtml) where the computer player must implement a Minimax algorithm with alpha-beta pruning. Thus far, I understand what the goal is behind the algorithm in terms of maximizing potential gains while assuming the opponent will minify them. However, none of the resources I read helped me understand how to design the evaluation function the minimax bases all it's decisions on. All the examples have had arbitrary numbers assigned to the leaf nodes, however, I need to actually assign meaningful values to those nodes. Intuition tells me it'd be something like +1 for a win leaf node, and -1 for a loss, but how do intermediate nodes evaluate? Any help would be most appreciated.

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  • How to utilize miniMax algorithm in Checkers game

    - by engineer
    I am sorry...as there are too many articles about it.But I can't simple get this. I am confused in the implementation of AI. I have generated all possible moves of computer's type pieces. Now I can't decide the flow. Whether I need to start a loop for the possible moves of each piece and assign score to it.... or something else is to be done. Kindly tell me the proper flow/algorithm for this. Thanks

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  • How to utilize miniMax algorrithm in Checkers game

    - by engineer
    I am sorry...as there are too many articles about it.But I can't simple get this. I am confused in the implementation of AI. I have generated all possible moves of computer's type pieces. Now I can't decide the flow. Whether I need to start a loop for the possible moves of each piece and assign score to it.... or something else is to be done. Kindly tell me the proper flow/algorithm for this. Thanks

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  • How to implement Pentago AI algorithm

    - by itsho
    Hi, i'm trying to develop Pentago-game in c#. right now i'm having 2 players mode which working just fine. the problem is, that i want One player mode (against computer), but unfortunately, all implements of minimax / negamax are for one step calculated. butin Pentago, every player need to do two things (place marble, and rotate one of the inner-boards) I didn't figure out how to implement both rotate part & placing the marble, and i would love someone to guide me with this. if you're not familiar with the game, here's a link to the game. if anyone want's, i can upload my code somewhere if that's relevant. thank you very much in advance

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  • How do i start with Gomoku?

    - by firstTry
    I read about Gomoku that it can be implemented using Minimax and Alpha-Beta Pruning algorithms. So, i read these algorithms and now understand how the game will be solved. But when i sat to down to code, I am facing problem how to approach it. As in , How to design the prototype functions like getNextMove or Max(Move) ? How will the next move searched? Till when should i apply the minimax algorithm. I know i can find the code online, but i want to do it myself. Can anyone please point me in the right direction?

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  • Checker AI in visual basic not working [on hold]

    - by Eugene Galkine
    I am trying to a make checkers in visual basic with ai. I am using the minimax algorithm (or at least what I understand of it) and it works, except the ai is retarded and plays like it is trying to loose and I tried to switch around the min and the max but the results are IDENTICAL. I am pissed of and have been trying to fix it for over a week now, I would really appreciate it if someone could help me out here. I have 3 years experience of programming (in Java, only about of month of VB experience) and I always am able to solve all my errors on my own so I don't know why I can't get this to work. The program is not at all optimized or anything at this point and is over 1.2K lines long, so here is the entire vb project instead: https://www.dropbox.com/sh/evii0jendn93ir2/9fntwH2dNW I would really appreciate any help I could get.

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  • tic tac toe game ai as3

    - by David Jones
    I'm looking into creating a simple tic tac toe/noughts and crosses game in actionscript3 and am trying to understand the ideas behind the ai used in a game like this. I've seen some simplistic examples online but from what I've read a game tree or something like minimax is the best way to go about this. Can anyone help explain or reference any good examples of this? I've seen that there is a library called as3ds - data structures for game developers which has a number of classes that might help tie this together? Any info/examples or help is much appreciated

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  • How important is a single-player mode in a 2-player game?

    - by Davy8
    So say you have a 2 player game, taking Chess as an example (except it's an original game with no ready-to-go AI available). Let's say there's also a social-aspect to the meta-game, so let's say it's a Chess game on Facebook where you can challenge your friends. How important is it to have a single-player mode, knowing that an AI will need to be created (I've done minimax AI for tic tac toe, but nothing too sophisticated)? Is it important enough that it should be in the initial launch of the game? Can it wait for a future iteration (knowing that being hosted on the web means the game can be updated at any time)?

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  • Reversi/Othello early-game evaluation function

    - by Vladislav Il'ushin
    I've written my own Reversi player, based on the MiniMax algorithm, with Alpha-Beta pruning, but in the first 10 moves my evaluation function is too slow. I need a good early-game evaluation function. I'm trying to do it with this matrix (corresponding to the board) which determines how favourable that square is to have: { 30, -25, 10, 5, 5, 10, -25, 30,}, {-25, -25, 1, 1, 1, 1, -25, -25,}, { 10, 1, 5, 2, 2, 5, 1, 10,}, { 5, 1, 2, 1, 1, 2, 1, 5,}, { 5, 1, 2, 1, 1, 2, 1, 5,}, { 10, 1, 5, 2, 2, 5, 1, 10,}, {-25, -25, 1, 1, 1, 1, -25, -25,}, { 30, -25, 10, 5, 5, 10, -25, 30,},}; But it doesn't work well. Have you even written an early-game evaluation function for Reversi?

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  • Tic-Tac-Toe game AI

    - by David Jones
    I'm looking into creating a simple tic tac toe/noughts and crosses game in Actionscript3 and am trying to understand the ideas behind the AI used in a game like this. I've seen some simplistic examples online but from what I've read a game tree or something like minimax is the best way to go about this. Can anyone help explain or reference any good examples of this? I've seen that there is a library called as3ds - data structures for game developers which has a number of classes that might help tie this together? Any info/examples or help is much appreciated.

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  • Getting the index of the returned max or min item using max()/min() on a list

    - by KevinGriffin
    I'm using Python's max and min functions on lists for a minimax algorithm, and I need the index of the value returned by max() or min(). In other words, I need to know which move produced the max (at a first player's turn) or min (second player) value. for i in range(9): newBoard = currentBoard.newBoardWithMove([i / 3, i % 3], player) if newBoard: temp = minMax(newBoard, depth + 1, not isMinLevel) values.append(temp) if isMinLevel: return min(values) else: return max(values) I need to be able to return the actual index of the min or max value, not just the value.

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  • techniques for an AI for a highly cramped turn-based tactics game

    - by Adam M.
    I'm trying to write an AI for a tactics game in the vein of Final Fantasy Tactics or Vandal Hearts. I can't change the game rules in any way, only upgrade the AI. I have experience programming AI for classic board games (basically minimax and its variants), but I think the branching factor is too great for the approach to be reasonable here. I'll describe the game and some current AI flaws that I'd like to fix. I'd like to hear ideas for applicable techniques. I'm a decent enough programmer, so I only need the ideas, not an implementation (though that's always appreciated). I'd rather not expend effort chasing (too many) dead ends, so although speculation and brainstorming are good and probably helpful, I'd prefer to hear from somebody with actual experience solving this kind of problem. For those who know it, the game is the land battle mini-game in Sid Meier's Pirates! (2004) and you can skim/skip the next two paragraphs. For those who don't, here's briefly how it works. The battle is turn-based and takes place on a 16x16 grid. There are three terrain types: clear (no hindrance), forest (hinders movement, ranged attacks, and sight), and rock (impassible, but does not hinder attacks or sight). The map is randomly generated with roughly equal amounts of each type of terrain. Because there are many rock and forest tiles, movement is typically very cramped. This is tactically important. The terrain is not flat; higher terrain gives minor bonuses. The terrain is known to both sides. The player is always the attacker and the AI is always the defender, so it's perfectly valid for the AI to set up a defensive position and just wait. The player wins by killing all defenders or by getting a unit to the city gates (a tile on the other side of the map). There are very few units on each side, usually 4-8. Because of this, it's crucial not to take damage without gaining some advantage from it. Units can take multiple actions per turn. All units on one side move before any units on the other side. Order of execution is important, and interleaving of actions between units is often useful. Units have melee and ranged attacks. Melee attacks vary widely in strength; ranged attacks have the same strength but vary in range. The main challenges I face are these: Lots of useful move combinations start with a "useless" move that gains no immediate advantage, or even loses advantage, in order to set up a powerful flank attack in the future. And, since the player units are stronger and have longer range, the AI pretty much always has to take some losses before they can start to gain kills. The AI must be able to look ahead to distinguish between sacrificial actions that provide a future benefit and those that don't. Because the terrain is so cramped, most of the tactics come down to achieving good positioning with multiple units that work together to defend an area. For instance, two defenders can often dominate a narrow pass by positioning themselves so an enemy unit attempting to pass must expose itself to a flank attack. But one defender in the same pass would be useless, and three units can defend a slightly larger pass. Etc. The AI should be able to figure out where the player must go to reach the city gates and how to best position its few units to cover the approaches, shifting, splitting, or combining them appropriately as the player moves. Because flank attacks are extremely deadly (and engineering flank attacks is key to the player strategy), the AI should be competent at moving its units so that they cover each other's flanks unless the sacrifice of a unit would give a substantial benefit. They should also be able to force flank attacks on players, for instance by threatening a unit from two different directions such that responding to one threat exposes the flank to the other. The AI should attack if possible, but sometimes there are no good ways to approach the player's position. In that case, the AI should be able to recognize this and set up a defensive position of its own. But the AI shouldn't be vulnerable to a trivial exploit where the player repeatedly opens and closes a hole in his defense and shoots at the AI as it approaches and retreats. That is, the AI should ideally be able to recognize that the player is capable of establishing a solid defense of an area, even if the defense is not currently in place. (I suppose if a good unit allocation algorithm existed, as needed for the second bullet point, the AI could run it on the player units to see where they could defend.) Because it's important to choose a good order of action and interleave actions between units, it's not as simple as just finding the best move for each unit in turn. All of these can be accomplished with a minimax search in theory, but the search space is too large, so specialized techniques are needed. I thought about techniques such as influence mapping, but I don't see how to use the technique to great effect. I thought about assigning goals to the units. This can help them work together in some limited way, and the problem of "how do I accomplish this goal?" is easier to solve than "how do I win this battle?", but assigning good goals is a hard problem in itself, because it requires knowing whether the goal is achievable and whether it's a good use of resources. So, does anyone have specific ideas for techniques that can help cleverize this AI? Update: I found a related question on Stackoverflow: http://stackoverflow.com/questions/3133273/ai-for-a-final-fantasy-tactics-like-game The selected answer gives a decent approach to choosing between alternative actions, but it doesn't seem to have much ability to look into the future and discern beneficial sacrifices from wasteful ones. It also focuses on a single unit at a time and it's not clear how it could be extended to support cooperation between units in defending or attacking.

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  • How to find minimum cut-sets for several subgraphs of a graph of degrees 2 to 4

    - by Tore
    I have a problem, Im trying to make A* searches through a grid based game like pacman or sokoban, but i need to find "enclosures". What do i mean by enclosures? subgraphs with as few cut edges as possible given a maximum size and minimum size for number of vertices that act as soft constraints. Alternatively you could say i am looking to find bridges between subgraphs, but its generally the same problem. Given a game that looks like this, what i want to do is find enclosures so that i can properly find entrances to them and thus get a good heuristic for reaching vertices inside these enclosures. So what i want is to find these colored regions on any given map. The reason for me bothering to do this and not just staying content with the performance of a simple manhattan distance heuristic is that an enclosure heuristic can give more optimal results and i would not have to actually do the A* to get some proper distance calculations and also for later adding competitive blocking of opponents within these enclosures when playing sokoban type games. Also the enclosure heuristic can be used for a minimax approach to finding goal vertices more properly. Do you know of a good algorithm for solving this problem or have any suggestions in things i should explore?

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  • TicTacToe strategic reduction

    - by NickLarsen
    I decided to write a small program that solves TicTacToe in order to try out the effect of some pruning techniques on a trivial game. The full game tree using minimax to solve it only ends up with 549,946 possible games. With alpha-beta pruning, the number of states required to evaluate was reduced to 18,297. Then I applied a transposition table that brings the number down to 2,592. Now I want to see how low that number can go. The next enhancement I want to apply is a strategic reduction. The basic idea is to combine states that have equivalent strategic value. For instance, on the first move, if X plays first, there is nothing strategically different (assuming your opponent plays optimally) about choosing one corner instead of another. In the same situation, the same is true of the center of the walls of the board, and the center is also significant. By reducing to significant states only, you end up with only 3 states for evaluation on the first move instead of 9. This technique should be very useful since it prunes states near the top of the game tree. This idea came from the GameShrink method created by a group at CMU, only I am trying to avoid writing the general form, and just doing what is needed to apply the technique to TicTacToe. In order to achieve this, I modified my hash function (for the transposition table) to enumerate all strategically equivalent positions (using rotation and flipping functions), and to only return the lowest of the values for each board. Unfortunately now my program thinks X can force a win in 5 moves from an empty board when going first. After a long debugging session, it became apparent to me the program was always returning the move for the lowest strategically significant move (I store the last move in the transposition table as part of my state). Is there a better way I can go about adding this feature, or a simple method for determining the correct move applicable to the current situation with what I have already done?

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  • Finding minimum cut-sets between bounded subgraphs

    - by Tore
    If a game map is partitioned into subgraphs, how to minimize edges between subgraphs? I have a problem, Im trying to make A* searches through a grid based game like pacman or sokoban, but i need to find "enclosures". What do i mean by enclosures? subgraphs with as few cut edges as possible given a maximum size and minimum size for number of vertices for each subgraph that act as a soft constraints. Alternatively you could say i am looking to find bridges between subgraphs, but its generally the same problem. Given a game that looks like this, what i want to do is find enclosures so that i can properly find entrances to them and thus get a good heuristic for reaching vertices inside these enclosures. So what i want is to find these colored regions on any given map. My Motivation The reason for me bothering to do this and not just staying content with the performance of a simple manhattan distance heuristic is that an enclosure heuristic can give more optimal results and i would not have to actually do the A* to get some proper distance calculations and also for later adding competitive blocking of opponents within these enclosures when playing sokoban type games. Also the enclosure heuristic can be used for a minimax approach to finding goal vertices more properly. A possible solution to the problem is the Kernighan-Lin algorithm: function Kernighan-Lin(G(V,E)): determine a balanced initial partition of the nodes into sets A and B do A1 := A; B1 := B compute D values for all a in A1 and b in B1 for (i := 1 to |V|/2) find a[i] from A1 and b[i] from B1, such that g[i] = D[a[i]] + D[b[i]] - 2*c[a][b] is maximal move a[i] to B1 and b[i] to A1 remove a[i] and b[i] from further consideration in this pass update D values for the elements of A1 = A1 / a[i] and B1 = B1 / b[i] end for find k which maximizes g_max, the sum of g[1],...,g[k] if (g_max > 0) then Exchange a[1],a[2],...,a[k] with b[1],b[2],...,b[k] until (g_max <= 0) return G(V,E) My problem with this algorithm is its runtime at O(n^2 * lg(n)), i am thinking of limiting the nodes in A1 and B1 to the border of each subgraph to reduce the amount of work done. I also dont understand the c[a][b] cost in the algorithm, if a and b do not have an edge between them is the cost assumed to be 0 or infinity, or should i create an edge based on some heuristic. Do you know what c[a][b] is supposed to be when there is no edge between a and b? Do you think my problem is suitable to use a multi level problem? Why or why not? Do you have a good idea for how to reduce the work done with the kernighan-lin algorithm for my problem?

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  • What's the best/most efficent way to create a semi-intelligent AI for a tic tac toe game?

    - by Link
    basically I am attempting to make a a efficient/smallish C game of Tic-Tac-Toe. I have implemented everything other then the AI for the computer so far. my squares are basically structs in an array with an assigned value based on the square. For example s[1].value = 1; therefore it's a x, and then a value of 3 would be a o. My question is whats the best way to create a semi-decent game playing AI for my tic-tac-toe game? I don't really want to use minimax, since It's not what I need. So how do I avoid a a lot of if statments and make it more efficient. Here is the rest of my code: #include <stdio.h> #include <stdlib.h> #include <string.h> #include <time.h> struct state{ // defined int state; // 0 is tie, 1 is user loss, 2 is user win, 3 is ongoing game int moves; }; struct square{ // one square of the board int value; // 1 is x, 3 is o char sign; // no space used }; struct square s[9]; //set up the struct struct state gamestate = {0,0}; //nothing void setUpGame(){ // setup the game int i = 0; for(i = 0; i < 9; i++){ s[i].value = 0; s[i].sign = ' '; } gamestate.moves=0; printf("\nHi user! You're \"x\"! I'm \"o\"! Good Luck :)\n"); } void displayBoard(){// displays the game board printf("\n %c | %c | %c\n", s[6].sign, s[7].sign, s[8].sign); printf("-----------\n"); printf(" %c | %c | %c\n", s[3].sign, s[4].sign, s[5].sign); printf("-----------\n"); printf(" %c | %c | %c\n\n", s[0].sign, s[1].sign, s[2].sign); } void getHumanMove(){ // get move from human int i; while(1){ printf(">>:"); char line[255]; // input the move to play fgets(line, sizeof(line), stdin); while(sscanf(line, "%d", &i) != 1) { //1 match of defined specifier on input line printf("Sorry, that's not a valid move!\n"); fgets(line, sizeof(line), stdin); } if(s[i-1].value != 0){printf("Sorry, That moves already been taken!\n\n");continue;} break; } s[i-1].value = 1; s[i-1].sign = 'x'; gamestate.moves++; } int sum(int x, int y, int z){return(x*y*z);} void getCompMove(){ // get the move from the computer } void checkWinner(){ // check the winner int i; for(i = 6; i < 9; i++){ // check cols if((sum(s[i].value,s[i-3].value,s[i-6].value)) == 8){printf("The Winner is o!\n");gamestate.state=1;} if((sum(s[i].value,s[i-3].value,s[i-6].value)) == 1){printf("The Winner is x!\n");gamestate.state=2;} } for(i = 0; i < 7; i+=3){ // check rows if((sum(s[i].value,s[i+1].value,s[i+2].value)) == 8){printf("The Winner is o!\n");gamestate.state=1;} if((sum(s[i].value,s[i+1].value,s[i+2].value)) == 1){printf("The Winner is x!\n");gamestate.state=2;} } if((sum(s[0].value,s[4].value,s[8].value)) == 8){printf("The Winner is o!\n");gamestate.state=1;} if((sum(s[0].value,s[4].value,s[8].value)) == 1){printf("The Winner is x!\n");gamestate.state=2;} if((sum(s[2].value,s[4].value,s[6].value)) == 8){printf("The Winner is o!\n");gamestate.state=1;} if((sum(s[2].value,s[4].value,s[6].value)) == 1){printf("The Winner is x!\n");gamestate.state=2;} } void playGame(){ // start playing the game gamestate.state = 3; //set-up the gamestate srand(time(NULL)); int temp = (rand()%2) + 1; if(temp == 2){ // if two comp goes first temp = (rand()%2) + 1; if(temp == 2){ s[4].value = 2; s[4].sign = 'o'; gamestate.moves++; }else{ s[2].value = 2; s[2].sign = 'o'; gamestate.moves++; } } displayBoard(); while(gamestate.state == 3){ if(gamestate.moves<10); getHumanMove(); if(gamestate.moves<10); getCompMove(); checkWinner(); if(gamestate.state == 3 && gamestate.moves==9){ printf("The game is a tie :p\n"); break; } displayBoard(); } } int main(int argc, const char *argv[]){ printf("Welcome to Tic Tac Toe\nby The Elite Noob\nEnter 1-9 To play a move, standard numpad\n1 is bottom-left, 9 is top-right\n"); while(1){ // while game is being played printf("\nPress 1 to play a new game, or any other number to exit;\n>>:"); char line[255]; // input whether or not to play the game fgets(line, sizeof(line), stdin); int choice; // user's choice about playing or not while(sscanf(line, "%d", &choice) != 1) { //1 match of defined specifier on input line printf("Sorry, that's not a valid option!\n"); fgets(line, sizeof(line), stdin); } if(choice == 1){ setUpGame(); // set's up the game playGame(); // Play a Game }else {break;} // exit the application } printf("\nThank's For playing!\nHave a good Day!\n"); return 0; }

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  • Strategy and AI for the game 'Proximity'

    - by smci
    'Proximity' is a strategy game of territorial domination similar to Othello, Go and Risk. Two players, uses a 10x12 hex grid. Game invented by Brian Cable in 2007. Seems to be a worthy game for discussing a) optimal strategy then b) how to build an AI Strategies are going to be probabilistic or heuristic-based, due to the randomness factor, and the high branching factor (starts out at 120). So it will be kind of hard to compare objectively. A compute time limit of 5s per turn seems reasonable. Game: Flash version here and many copies elsewhere on the web Rules: here Object: to have control of the most armies after all tiles have been placed. Each turn you received a randomly numbered tile (value between 1 and 20 armies) to place on any vacant board space. If this tile is adjacent to any ally tiles, it will strengthen each tile's defenses +1 (up to a max value of 20). If it is adjacent to any enemy tiles, it will take control over them if its number is higher than the number on the enemy tile. Thoughts on strategy: Here are some initial thoughts; setting the computer AI to Expert will probably teach a lot: minimizing your perimeter seems to be a good strategy, to prevent flips and minimize worst-case damage like in Go, leaving holes inside your formation is lethal, only more so with the hex grid because you can lose armies on up to 6 squares in one move low-numbered tiles are a liability, so place them away from your main territory, near the board edges and scattered. You can also use low-numbered tiles to plug holes in your formation, or make small gains along the perimeter which the opponent will not tend to bother attacking. a triangle formation of three pieces is strong since they mutually reinforce, and also reduce the perimeter Each tile can be flipped at most 6 times, i.e. when its neighbor tiles are occupied. Control of a formation can flow back and forth. Sometimes you lose part of a formation and plug any holes to render that part of the board 'dead' and lock in your territory/ prevent further losses. Low-numbered tiles are obvious-but-low-valued liabilities, but high-numbered tiles can be bigger liabilities if they get flipped (which is harder). One lucky play with a 20-army tile can cause a swing of 200 (from +100 to -100 armies). So tile placement will have both offensive and defensive considerations. Comment 1,2,4 seem to resemble a minimax strategy where we minimize the maximum expected possible loss (modified by some probabilistic consideration of the value ß the opponent can get from 1..20 i.e. a structure which can only be flipped by a ß=20 tile is 'nearly impregnable'.) I'm not clear what the implications of comments 3,5,6 are for optimal strategy. Interested in comments from Go, Chess or Othello players. (The sequel ProximityHD for XBox Live, allows 4-player -cooperative or -competitive local multiplayer increases the branching factor since you now have 5 tiles in your hand at any given time, of which you can only play one. Reinforcement of ally tiles is increased to +2 per ally.)

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  • Find optimal strategy and AI for the game 'Proximity'?

    - by smci
    'Proximity' is a strategy game of territorial domination similar to Othello, Go and Risk. Two players, uses a 10x12 hex grid. Game invented by Brian Cable in 2007. Seems to be a worthy game for discussing a) optimal algorithm then b) how to build an AI. Strategies are going to be probabilistic or heuristic-based, due to the randomness factor, and the insane branching factor (20^120). So it will be kind of hard to compare objectively. A compute time limit of 5s per turn seems reasonable. Game: Flash version here and many copies elsewhere on the web Rules: here Object: to have control of the most armies after all tiles have been placed. Each turn you received a randomly numbered tile (value between 1 and 20 armies) to place on any vacant board space. If this tile is adjacent to any ally tiles, it will strengthen each tile's defenses +1 (up to a max value of 20). If it is adjacent to any enemy tiles, it will take control over them if its number is higher than the number on the enemy tile. Thoughts on strategy: Here are some initial thoughts; setting the computer AI to Expert will probably teach a lot: minimizing your perimeter seems to be a good strategy, to prevent flips and minimize worst-case damage like in Go, leaving holes inside your formation is lethal, only more so with the hex grid because you can lose armies on up to 6 squares in one move low-numbered tiles are a liability, so place them away from your main territory, near the board edges and scattered. You can also use low-numbered tiles to plug holes in your formation, or make small gains along the perimeter which the opponent will not tend to bother attacking. a triangle formation of three pieces is strong since they mutually reinforce, and also reduce the perimeter Each tile can be flipped at most 6 times, i.e. when its neighbor tiles are occupied. Control of a formation can flow back and forth. Sometimes you lose part of a formation and plug any holes to render that part of the board 'dead' and lock in your territory/ prevent further losses. Low-numbered tiles are obvious-but-low-valued liabilities, but high-numbered tiles can be bigger liabilities if they get flipped (which is harder). One lucky play with a 20-army tile can cause a swing of 200 (from +100 to -100 armies). So tile placement will have both offensive and defensive considerations. Comment 1,2,4 seem to resemble a minimax strategy where we minimize the maximum expected possible loss (modified by some probabilistic consideration of the value ß the opponent can get from 1..20 i.e. a structure which can only be flipped by a ß=20 tile is 'nearly impregnable'.) I'm not clear what the implications of comments 3,5,6 are for optimal strategy. Interested in comments from Go, Chess or Othello players. (The sequel ProximityHD for XBox Live, allows 4-player -cooperative or -competitive local multiplayer increases the branching factor since you now have 5 tiles in your hand at any given time, of which you can only play one. Reinforcement of ally tiles is increased to +2 per ally.)

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