RISK?





Oh you play? Me too.. ckeck this out:



Mathematicians have the analytical tools to address two important questions about individual battles: If you attack a territory with your armies, what is the probability that you will capture this territory? If you engage in a battle, how many armies should you expect to lose depending on the number of armies your opponent has on that territory?



Baris Tan of Koc University in Istanbul, Turkey, tackled these questions in the December 1997 Mathematics Magazine. He applied a technique involving so-called Markov chains to calculate the required probabilities over the course of a long game with many battles.



Based on his analysis, Tan concluded that, when both attacker and defender have the same number of armies, the probability that the attacker wins is less than 50 percent. When there are twice as many attackers as defenders, the winning probability exceeds 80 percent. Moreover, the expected loss by the attacker is slightly lower than the number of defending armies. For example, if an attacker has 20 armies and a defender has 10 armies, the attacker would win the war with a probability of 98 percent and lose about 9 armies doing so.



more