• Announcements

    • khawk

      Download the Game Design and Indie Game Marketing Freebook   07/19/17

      GameDev.net and CRC Press have teamed up to bring a free ebook of content curated from top titles published by CRC Press. The freebook, Practices of Game Design & Indie Game Marketing, includes chapters from The Art of Game Design: A Book of Lenses, A Practical Guide to Indie Game Marketing, and An Architectural Approach to Level Design. The GameDev.net FreeBook is relevant to game designers, developers, and those interested in learning more about the challenges in game development. We know game development can be a tough discipline and business, so we picked several chapters from CRC Press titles that we thought would be of interest to you, the GameDev.net audience, in your journey to design, develop, and market your next game. The free ebook is available through CRC Press by clicking here. The Curated Books The Art of Game Design: A Book of Lenses, Second Edition, by Jesse Schell Presents 100+ sets of questions, or different lenses, for viewing a game’s design, encompassing diverse fields such as psychology, architecture, music, film, software engineering, theme park design, mathematics, anthropology, and more. Written by one of the world's top game designers, this book describes the deepest and most fundamental principles of game design, demonstrating how tactics used in board, card, and athletic games also work in video games. It provides practical instruction on creating world-class games that will be played again and again. View it here. A Practical Guide to Indie Game Marketing, by Joel Dreskin Marketing is an essential but too frequently overlooked or minimized component of the release plan for indie games. A Practical Guide to Indie Game Marketing provides you with the tools needed to build visibility and sell your indie games. With special focus on those developers with small budgets and limited staff and resources, this book is packed with tangible recommendations and techniques that you can put to use immediately. As a seasoned professional of the indie game arena, author Joel Dreskin gives you insight into practical, real-world experiences of marketing numerous successful games and also provides stories of the failures. View it here. An Architectural Approach to Level Design This is one of the first books to integrate architectural and spatial design theory with the field of level design. The book presents architectural techniques and theories for level designers to use in their own work. It connects architecture and level design in different ways that address the practical elements of how designers construct space and the experiential elements of how and why humans interact with this space. Throughout the text, readers learn skills for spatial layout, evoking emotion through gamespaces, and creating better levels through architectural theory. View it here. Learn more and download the ebook by clicking here. Did you know? GameDev.net and CRC Press also recently teamed up to bring GDNet+ Members up to a 20% discount on all CRC Press books. Learn more about this and other benefits here.
Sign in to follow this  
Followers 0
CaymanS

Game AI for card game

4 posts in this topic

Hi,

 

I have written several perfect knowledge games (chess, checkers, othello, etc.) but I would like to better understand the common mechanisms that are utilized when dealing with card games - where the AI opponent doesn't have knowledge of what cards an opponent is holding (and no, I do not want the AI to cheat).

I don't understand how I can build a game tree (and then minimax, etc.) without knowing the cards the opponent is holding. The only thing I can think of is to use probabilities to make meaningful guesses as to what the opponent has.

The AI in something like the electronic version of Magic the Gathering appears to make very good choices but I'm just not sure how it works.

I'd really appreciate it if someone might shed a little light on this for me.



All the very best,
CS
 
0

Share this post


Link to post
Share on other sites

I think minimax won't help you at all here. Monte Carlo methods, however, should do the job nicely.

 

The first thing you need to have is a probabilistic model of how players make decisions that can be evaluated very fast. It doesn't have to be perfect; you can actually start with something that assigns equal probabilities to all the choices available, and then make obviously bad moves much less likely and obviously good ones much more likely. Always normalize the probabilities to make sure they add up to 1.

 

Armed with this fast probabilistic model, you proceed to run simulations as follows:

 (1) Create a random permutation of cards that matches the cards you have seen so far.

 (2) Replay the hand from the beginning up to the current point. Multiply the probabilities of all the decisions the players have made (use the fast probabilistic model for this). The resulting number is called the likelihood of the observed decisions given the card permutation from (1).

 (3) Now play a hypothetical move, among the moves you are considering (we'll discuss how to pick this move later, but for now think of it as a random move).

 (4) Play the hand to the end, using the fast probabilistic model for all future decisions.

 

Accumulate statistics of how often you win or lose with each move selected at (3). Some simulations are more relevant than others: Use the likelihood computed in (2) as the weight of the simulation.

 

After you have played a number of simulations, you'll have a pretty good idea of what moves are promising and which ones aren't, and evaluating the bad moves many times over is just a waste of time. So when you get to (3) you want to give the strong moves a larger probability of being picked. There is a theoretical construct that is very close to this situation, called a multi-arm bandit, and the theory developed for those can be useful. In particular, there is a policy called UCB1 that is described in an early paper about the computer go program MoGo, which consists of picking always the move that maximizes a formula that goes something like this (from memory):

 

expected_reward[i] + (1/sqrt(number_of_simulations[i])) * log(1+total_number_of_simulations) * some_constant

 

 

So you need to keep track of how many simulations have been played for each move and also the total number of simulations. I think you should "count" these simulations weighted by the likelihood, so you are actually using the sum of the likelihoods of the simulations instead of the count.

 

When you run out of time, you can play the move with the highest expected reward, or the move that was tried the most times in your simulations. Or you may want to take a little more time for this move if these two criteria don't agree.

 

That should be enough to get you started. As you certainly know if you have programmed AI for board games before, there are many decisions to be made as you build your program. For instance, it might be better to generate card permutations in (1) using some version of importance sampling, because for some games the average likelihood of a random card permutation might be very very low. Or you may want to reuse the situation from (1) to evaluate several moves...

 

Do you have a particular card game in mind?

Edited by Álvaro
2

Share this post


Link to post
Share on other sites

That article is quite good.  Are there similar online resources that could be recommended?  Perhaps approaching a different problem - board game, other card games, etc.?  Just trying to get a good grasp of the topic.

0

Share this post


Link to post
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!


Register a new account

Sign in

Already have an account? Sign in here.


Sign In Now
Sign in to follow this  
Followers 0