yeah, statistics class gave me some ideas too when I took the class, I forgot about them so I can''t tell you how well they work, but go for it!

Yes, there is a large overlap between statistics and machine learning. Chi-square and similar statistics have been used directly in machine learning algorithms for years. In my data mining work, for instance, one tool I use to look for relationships in data uses a statistical calculation to decide whether individual variables are worth further investigation or not.

[edited by - Predictor on February 1, 2003 8:45:05 AM]

Independence between variables is only interesting if you want to compute mutual probabilities. In case of independent variables you can simply multiply their individual probabilities. This is something you want to know when you work on raw data, like measurements or values in a large database.

The example of the armor strength only tells you that the armor will reduce the damage inflicted. This is something that''s already known by the programmer (it''s what the armor is used for). If you want to simplify the AI you should look at higher level abstract concepts that are not immediately clear to the programmer, like "life expectancy under enemy fire". The value of LifeExp depends on the units hip points (hp), the units armor strength (as) and the enemies weapon strength (ws). If you can compute LifeExp you can make a simple AI like:

if ( LifeExp(your_as,your_hp,his_ws) > LifeExp(his_as,his_hp,your_ws) ){  // you will win    Attack;  }else{  // you will loose    RunAway;  // or GetHelp;  } 

The point here is that LifeExp should DEPEND on as, hp and ws. You can make the units more interesting by giving them different speeds and give the weapons different ranges. These can also be included in LifeExp. Including something like unit color in LifeExp can be useless when there is NO correlation between color and LifeExp. Then you shouldn''t use it. If you generate test fights between different units with different equipment then you can use chi-square to test for dependencies between LifeExp and the attribute. If they are independent then you can ignore them.
The other way around is also possible. As a game designer you want to balance your units. If you find out that one unit is too weak compared to the other units, then you can find out which attributes has to be changed (changing an independent attribute is pointless). For a simple game you can guess which attributes have to be changed. For very large RTS of RPG games with dozens of units, armor and weapons statistical tricks like chi-squared become essential for balancing the game.

BTW: machine learning == statistics with cool buzzwords

Tazzel3D:

Unfortunately you haven''t come up with anything new, although you should not be discouraged by that, since you have realised an important use for the notion of statistical in/dependence.

In/dependence in systems of variables has long been studied in AI. In the past 20 years Belief Networks have been used to represent these systems and they have been applied to games, however the use of statistical representations of causality extends back hundreds of years to the work of Pascal, Bayes, Gauss and others.

To give you a little more to think about (and to research if you desire), you can arrive at independence in a slightly more efficient manner.

Take a set of variables for which you have collected data on the frequency of events (occurrences of values of the variables). You can easily compute the mean vector for the set and the covariance matrix. The inverse of the covariance matrix is the correlation matrix of the set. Zero elements in this matrix represent independent variables. It is natural, although not strictly correct, to infer that non-zero elements represent causal relationships between variables. They don''t though, merely correlations between events of that value (perhaps due to a common cause).

If you were to draw a diagram with each variable in the set as a node (circle) and each non-zero entry a line between its two corresponding nodes, then you would have created a graph representation of the set of variables.

A particular form of such a graph, known as a DAG (Directed, Acyclic Graph) is the basis of a Bayesian belief network and can be used for all manner of very interesting artificial intelligence tasks.

If you''re interested in using this sort of thing in games I highly recommend that you read up on Bayesian networks. A very good - and very accessible - starting point is Finn Jensen''s book, ''An Introduction to Bayesian Networks''. Russell & Norvig''s ''Artificial Intelligence: A Modern Approach'' also gives a good introduction, although it isn''t quite as accessible as a first read. There''s an abundance of material online and I''d be happy to point you in a particular direction if you want more information on something specific.

Cheers,

Timkin

If you want to learn this stuff, you''re better off getting a hold of a book... they usually give a more complete view of a topic... and it''s good to have them in your bookshelf later on, as a reference. If you''re just starting out, I would recommend Finn Jensen''s book. You don''t need to understand too much probability theory to get into it... and it has clear examples that you can work by hand.

Cheers,

Timkin

A search for "belief networks" returned a large number of results on Google. Here''s one that looks good for an introduction. I''m reading it myself right now.

http://www.anc.ed.ac.uk/~amos/belief.html