Subject: Mathematics
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LinusUser is Offline


26 Mar 2008 9:19 PM  

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?





Great AlanUser is Offline


27 Mar 2008 9:04 AM  
Indeed,I don't completely understand what you say,that's too 'theoretical'.But I know that you're talking about the 'mathematical calculation'.The latter means you anticipate how many troops will be lost or gain in the operation.'Calculation' is vital in Risk(and even in other strategic game).As Sun Tze said,'The winner aim for victory first and then fight,the loser fight and then aim for victory.'Without calculation,then you can't have an excellent move.

Well,'Mathematic Calculation' is so simple,don't need to say a lot,just like below:
1)If you want to take a continent,count the loss and the gain from continent value
2)Count do you have sufficient troops to defend your terrtories.If not,consider the 'strategic withdrawal',retreat to more defensible terrtories.It helps you to gather more troops to operate more effectively
3)When you want to conquer someone,count how many cards he have,then you know that it is worth or not
4)When you find that after you have a treaty with X player,X player can mobilize enough troops to overwhelm the others but you can't,better not have a treaty with him(It simpily destroy 'balance of power' and finally only benefit him if you do so)

In conclusion,if you can calculate carefully when playing Risk,you rarely make any mistakes.Then that is enough for you to gain the victory(Believe me,victory is not difficult in Risk).In addition,I hope that you can give some replies to my posted article.
LinusUser is Offline


27 Mar 2008 8:36 PM  

i do not just want to calculate the pro and cons of a single attack. i want to calculate a dynamic strategie. i want to build up system that can decide what move leads to biggest succest in any situation.

Ehsan HonaryUser is Offline

Site Admin

01 Apr 2008 3:55 AM  
Thanks Linus for providing your analysis. It seems at an early stage. There has been some work in regard with mathematically calculating the value of each territory in relation with others based on the number of neighbours it has, the continent bonuses, number of adjacent borders and so on. I guess you are thinking along these lines except you want to go further and formulate everything.

Bear in mind that Risk is a fundamentally different game in comparison with other games such as chess where you can analyse moves mathematically turn after turn. A lot depend on the psychological state of players. A frightened or an annoyed player acts emotionally which is difficult to accurately predict using the kind of maths you talk about.

Have you thought about these. You can clarify your post a lot more by providing examples.

Ehsan Honary
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