an approach to a mathematical solution
i'm a math student from germany so please excuse my english.
i'm very interested in risk's mathematical backround. i've tried to create some basic ideas to solve risk mathematically. while analysing the gameplay i came to the same solution again and again: i need a highly dynamic system. that's my first idea. imediatly my second idea came up: this hugh dynamic complexity must be back tracked to it's roots. so i wanted to figure out some basic laws.
i tried to formulate some of those basic laws. at first i divided the complexity in "static" and "dynamic".
the static complexity is the easiest part of my journey. it contents: every static countable amount befor starting the game ( i.e. amount of extra units for any continent, any land's amount of borders, etc) and dice probabilities. with all static data a "static statistic" of lands and continents can be computed (the tricky part: all data must be subjectivly weighted).
now with this static statistic i try to manage the hard part: formulating the "dynamic complexity". this can be divided in 2 parts: game and meta-game.
with "game" i mean the whole board (how much players, who ownes which country and with how much units). the "game" 's math is not that complicated: i just put the game data in relation to the static statistic to compute a "dynamic game statistic".
now we enter the core problem: the meta-game. in my eyes meta-game is defined as tactics, strategy and diplomatics. the whole meta-game is based on static and dynamic game statistics. meta-game means analysing the statistics, isolate goal-patterns and form goals.
how to do this?
there are some laws:
every of any oponent's behaviour is related to a goal he tries to achieve.
goals are atomic goals (conquer a country) or composed goals (conquer a continent, strenghten a border, damage an opponent ... ) .
so by analysing the statistics the opponents' goal-patterns can be reveald.
that's enough data to characterise a player's behaviour and to compute threat statistics between every player.
now with all the data (static game, dynamic game and dynamic meta-game), almost every relevant data is collected, to formulate own goals and to rank those goals with achieving-probabilities and profits. so a "best" move can be computed.
two things left:
first: to pack a hugh statistic in a single number (i.e which country to attack) ,the data must be weighted (i.e a continent's amount of borders is more important then this continent's amount of bordering continents). those weights must be dynamic (i.e different sets of weights can result offensive or defense behaviour).
second: a knowledge base is needed for high level solutions. there must be stored a pool of goal patterns and a pool of weights that result most effective behavior according to the current game situation.
i tried to reduce the complex gameplay to those few words. now i ask you for feedback! did i describe every important aspect?