Err.. 2/3 + 1/2 + 1/6 > 1...

No Maths scholar, but here's what I remember from my high school lessons

Ok, let's assume you spread your army 1/4 : 1/4 : 1/2 is A,B,C

You win A if your opponent's army there is <= 1/4

You win B if your opponent's army there is <= 1/4

You win C if your opponent's army there is <= 1/2

So...the probability that you win A & B is the probability that your opponent's army at A <= 1/4 and B <=1/4

Since your opponent is random, the probability of each combination he chooses is equal...that is the probability of him setting his army 1/4:1/4:1/2 is the same as the probability of 1/3:1/3:1/3. In other words, 1/(total possible combinations). From there you should be able to calculate the total combinations where A <= 1/4 and B <= 1/4. And from there, the probabilities