Lets say you have 2 territories with 3 units, and you are trying to take 1 terrortory also with 3 units. Both territories border the 1 territory you are trying to take. Whats the best way to spread out your units when you get 3 and 4 units on your first turn?

3 units:
A) 6 - 3

B) 5 - 4

4 units:
A) 7 - 3

B) 6 - 4

C) 5 - 5

I would go for B and B, but let's wait what the mathematician geeks have to say.

I'll try my hand at a three bonus unit analysis.  It's more logic than math.

A) 6 - 3

B) 5 - 4

I don't think it matters how you distribute the bonus armies in that it won't impact whether or not you are able to take the territory. What will matter is the potential distribution of armies after the battle.  Let's look at some possibilities:

1.  You lose 2 on every roll:
In both cases, you will be able to attack with 3 dice twice, and in both cases you will end up with 3 -2 

2.  You win one and lose one on every roll.
In both cases, you will take the territory and end up with a 1-3 -3 distribution if you elect to move in with the minimum.

3.  You win 2 on every roll:
In one case  you will end up with a 3-3-3, and in the other you end up with 2-3-4 if you elect to move in with the minimum

Case 1 is the important one, no matter how you distribute your bonus armies, you will get to attack with 3 dice twice no matter what the outcome, and you will also have the opportunity to attack with 2 after that if you are desparate, so tactically speaking, there is no difference.

I agree with what M says and add my own perspective.

I look at it as a matter of 'activating armies'.  I have two rules (among many others):

1. Don't attack when odds dont favor

2. When odds favor attack as much as possible

3 armies v 3 armies (roll 2 v 2) is not favorable, dont attack.  4 (and higher) v 3 is favorable, so attack.  If I start with two countries (or more) of 3 each I want to 'activate' the units by raising the total above 3.  So if I have 6-3, I will only be attacking with 6 armies, if I go 5-4 I will be attacking with 9 armies.  So I wouldn't leave only 3 in a country. 

As to prefering 5-5 or 6-4, not sure, I will run an analysis if I get a chance next week, I have one started I need to finish. 

If we ignore strategic considerations and make some simplifying assumptions, the way to maximize your probability of success is as Toto says: 5-4 for 3 and 6-4 for 4. We'll assume you're only willing to use "attack with 3" and you're not worried about the potential for losing more armies. You only care about maximizing success and attacking with 3.

As M said, lose 2-lose 2 is the same for both setups. However, with a split, assuming you attacked from the 5 in the 5-4, you have 4-4 left. So, split-lose 2 leaves an attack from the 5-4 setup, but you are down to 3-3 if you started out in the 6-3 formation. So, most branches are equal, but in the split-lose 2 branch, the 5-4 setup gets an extra shot.

For 4 units, 6-4 should be best because a split is even with the 5-5 setup, but lose 2 puts us back in the 4-4 versus 5-3 situation: advantage to 4-4.

And 5-5 is better than 7-3 because lose 2 is equal while split puts you in the 6-3 versus 5-4 situation.

If you are willing to go all out (use more than just attack with 3), the analysis is much harder, but we did this on another site's forum, and found 5-4 to have the better chance of success, again because of the split-lose 2 case. I suspect it similarly works out to favor 6-4 if you go all out.

Also, I ignored the pure success case (defender loses 2) because the defender will be down to 1 unit and the attacker will have the same amount of free "attack with 3's" in all branches.