I have been trying to find a algorithm to strongly solve the game Teeko. The game is played on a 5x5 board were each player has 4 pieces and attempts align them in any direction or create a square out of them. (assume there is no drop phase)
I have tried solving the game by using a negamax with alpha beta pruning and other optimizations like a transposition table but that has not seemed to have worked because the solver would usually get stuck in loops were neither player wants to deviate from there strategy as it would result in them loosing. From my research I have found stuff like Nash Equilibrium as a potential solution but I cant figure out how to implement it. Furthermore, I have found that the game has been solved and found that the with prefect play it result in a draw previously: https://pcarrier.com/teeko/text/teeko.results.txt
Are there any algorithms that might be able to give the same result as minimax and hanlde repeating positions and how could I implement it and are there any other algorithms that give the same result as minimax?
Minimax (or Negamax) is well capable of handling repeating positions using transposition tables, as you mention in your question. Transposition tables are complicated to implement though so maybe you have a bug?
The problem with minimax is that you either:
NEed to solve it until the game is completed to get a score. This is possible for simple games like tic-tac-toe, but not for more complicated games like chess.
Score each node using some heuristic function, which is the case for e.g. chess.
I am not sure about Teeko, is it possible to get to all leaf nodes with minimax and alpha beta pruning? Could you do other things to reduce the search tree, like transpotision tables or other cut offs? If so then minimax is a great option.
Is it possible to create some kind of evaluation function for this game? It seems hard to me, but maybe that is because I know too little about the game. Is it better to have central squares? Better to get 2 in a row than to spread out pieces? Evaluation function is something you could have a look at if you are a good player of the game, or find good sources online.
Related
How many plies deep can I realistically search using minimax in connect 4?
Is it possible to search through the entire game starting at turn 1?
If not, on what turn is it feasible to search the board fully?
Based on personal experience I can tell you that from the starting position, if you really fine tune your algorithm, with a coarse evaluation, and a good transposition table, you can get around 11 ply deep. If you want to include techniques that are not theoretically sound (but are good in practice), such as Late Move Reductions and Futility Pruning, 15 ply might be feasible.
When a column of the board fills up, the branching factor decreases from 7 to 6. This greatly increases how deep you can go. Depending on how full the board is, it would take between two to three columns full before you could search to the end of the game.
I work on a project which demands to use A* algorithm. In this project you select your player with the left click and you guide him in the map with the right click, like the gameplay of thousand strategy game. The graphics are 2D, a little like the game Don't Starve and the game is developped with SFML / C++.
I need to use A* for the deplacement of the player, indeed if an obstacle appears on his road he has to avoid it. But for the moment, i don't know how to apply a grid to the map, i want to place any tree / rocks and other stuff anywhere in order not to see the grid cells. For now the open list is only composed of pixels, which is not the good solution I think ^^, the algorithm is pretty slow. If you have any solution for a realistic rendering while keeping a fast algorithm I'd be happy to hear it. :)
Thank you in advance,
Do you have a screenshot?
The pathfinding grid, and rendering grid can be different. Zelda used different sized tiles for movement and rendering.
navigation mesh
This may be overkill for your map structure, but you may use a navigation mesh.
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edit: If you haven't read it, Amit has a great resource: http://theory.stanford.edu/~amitp/GameProgramming/
What you're looking for is discretization. Behind this obscene name stands a simple principle : you can't deal with an infinite amount of data.
You need then to perform a transformation on your world : instead of allowing your character/unit to go at any location (x and y being real numbers), you can divide your world into some sort of a grid (this is what the navigation mesh and waypoints are doing), and only allow your char to go on these cells (or points, you can see it as you want). This is discretising : you are going from continuous values (real coordinates) to discrete values (integer coordinates / point). The more precise you go, the nicer it'll look.
After doing this, assigning moving costs between cells/points is rather simple, and performing A* on it as well.
I'm currently making a game in the DirectX engine in c++. I'm using path-finding to guide an army of soldiers to a specific location. the problem is that I use raycasts to see if there is nothing in the way of my path, and this slows down the speed of the game. Is there a better way to do pathfinding?
I also have a problem with the moving of my army. Right now i'm using the average of soldiers' positions as the start point, which means all the soldiers need to go there first before moving to the end point. Is there a way to make them go to the end point without going to the startpoint?
Thanks for the help.
Have you tried something like A-Star? to navigate via nodes, or some sort of 2d-array representation of your map? written good it could possible be faster aswell as easier to do with jobs ( multithreaded ).
if you have a solider, who is at postion A, and needs to get to B.
just calulate the path from C(the avrage position what ever) to B. get the direction from a to b and do some sort of interpolation. ( havent done this, or tried it, but it could probablt work out pretty well!)
Are you hit-testing every object when you are raycasting?
That can be very expensive when you have many objects and soldiers.
A common solution is to divide your world into square grid cells, and put each object in a list of objects for that grid.
Then you draw an imaginary line from the soldier to the destination and check each cell what objects you need to hit test against. This way you will evaluate only objects close to the straight path and ignore all others.
I want to find path in 2d platform game, teeworlds. The player there can move left/right, jump, and use hook, that lets you move upward the wall or move under ceiling. Well, its hard becouse normal pathfinds like a* or bfs cant exist here, cuz you cant just move up. I need to find path btw 2 players so 1 can go to the second one. There are 3 types of tiles, collide, nohook (you cant hook it) and nothing (air). I have the map in format int map[w][h] where 0=air, 1=collide, 2=nohook. map isnt modified for whole game time.
I have completly no idea how to do that. If you can help me, I'd be pleased.
PS. The question is general about platform games, teeworlds is only one of them...
From the pathfinding algorithm's standpoint you could treat the climbable walls as if they were normal walkways, so the algorithm does not stop there.
I don't think I completely understand the possibilities in your game. But this is how it works in general:
Path finding algorithms work on graphs (directed, undirected, with costs or equal costs for all edges doesn't matter). All you have to do is model your graph according to your game's rules. I.e. if there is only a normal way between field i and j than cost(i,j) = normal, if there is an additional way to use a hook, it could would be that cost(i,j) = min(hook, normal) . and so on. Once you have a graph (i assume it has to be directed for your game) all the normal Pathfinding algorithms will work.
if there are requirements like "you can only use hook n-times", a multi-label dijsktra can work.
pathfinding algorithms work on graphs in general
movement from one cell to another means that there is a connection between two cells (for instance in four directions). But you can also link to some other cell (the ceiling).
A* as a general search algorithm can still be applicable here, you just need to find a way to represent your platform game path-finding problem as a general search problem. So while you might have been introduced to A* as an algorithm to find a path through a grid-like maze, that is just a specific case of such a general search problem.
The more general case being graphs, where edges represent moves or actions and nodes represent positions or states.
One way to use A* for the game you mention is by taking an example from this Infinite Mario AI. This implementation of A* works locally and is rerun every tick to get the most optimal actions at that exact moment which is great for a fast-paced game like Mario or the game you mention, but be mindful that this is different from A* when it's used to solve a maze, in which case the path is found only once and it is like a global plan to be followed until its end.
Use simple BFS method, preprocessing the pairs to nodes.
I apologize for the length of this question and give a pre-emptive thanks for anyone who reads through this!
So i've spent the last few days going over the GJK algorithm. I understand the general concepts behind it, and understand the most of the nitty gritties of its implementation in 2D thanks to the wonderful article by William Bittle at http://www.codezealot.org/archives/88 .
I've implemented his pseudo code (found at the end of the article) into my own c++ project, however i want to make a 3D implementation. My weakness comes into using the dot products to test the voronoi regions and the tripleProducts to get perpandicular lines. But im trying to read up more on that.
My problem comes down to the containsOrigin function. Im having trouble visualizing and accounting for the new voronoi regions that the z axis adds. I just can't seem to wrap my head around how to determine which regions contains the origin. I assume there is 4 I have to account for, each extending from the triangular planes that the comprise the 4 faces of the tetrahedron simplex. If the origin is not within any of those regions, then it is contained, and we have a collision.
How do i go about testing if it is contained in a particular voronoi region/ which triangular face is pointing in the direction of the origin?
The current 2D algorithm checks if a triangle is made, if not, then the simplex is a line and it finds the 3rd point. I assume the 3D algorithm with check if a tetrahedron is made, if not, then it will check for a triangle, if true then it will to find a 4th point to make a tetrahedron(how would i get this? using a normal in direction of origin?). If i trangle isnt made, it will find a 3rd point to make a triangle (do i still use triple product for this like in 2D?).
Any suggestions, outlines, resources, code augmentations, comments are much appretiated.
Depending on what result you expect from the GJK algorithm you might want to look at this nice tutorial from Molly Rocket: https://mollyrocket.com/849
Be aware though that his implementation only outputs intersection? yes/no. But it might be a nice start.