I want to develop a *RISK board game*, which will include an AI for computer players. Moreover, I read two articles, __this__ and __this__, about it, and I realized that I must learn about *Monte Carlo simulation* and *Markov chain* techniques. And I thought that I have to use these techniques together, but I guess they are different techniques relevant to calculate probabilities about transition states.

So, could anyone explain what are the important differences and advantages and disadvantages between them?

Finally, which way you will prefer if you would implement an AI for the RISK game?

__Here__ you can find simply determined probabilities about outcomes of a battle in the risk board game, and the brute force algorithm used. There is a tree diagram to which specifies all possible states. Should I use Monte Carlo or Markov chain on this tree?