Ok, first let's see what we all agree upon:
We need Greenland, and we have to make sure we really get it this turn, so that binds 6 out of 12 armies. 6 remaining, and we need to invest them effectively.
Assuming Imp has 17 armies at his disposal, he outnumbers our reinforcements almost 3 to 1. Of course unless he reads our little discussion he won't be aware of that fact, he will most likely assume he is up against 12+x.
South America:
Imp has to assume we get at least 12 reinforcements.
We have 1 in Argentina and 29 in Brazil.
He has 1 in Columbia and 6 in Venezuela.
Scenario 1 - biggest stack vs biggest stack:
Imp's perspective:
We put 12 in Brazil, total 41. He puts 17 to Venezuela, total 23.
We attack with 40 vs 23 ->
99% chance of success
he loses 23
we lose 16.1
net gain = 7
World's perspective:
We put 6 in Brazil, total 35. He puts 17 to Venezuela, total 23.
We attack with 34 vs 23 ->
0% chance of success
we lose 16.1
he loses 20.4
net gain = 4
Scenario 2 - split forces vs split forces:
Imp's perspective:
We put 12 to Brazil and attack Col and Ven with 20 each and thus try to complete SA in this turn. Imp can put 11 to Col and 6 to Ven and have 12 in both of them (not very likely, I admit, but anyway).
We attack 2 times with 20 vs 12 ->
86% chance of success per attack; chance of both attacks succeeding = 74%
we lose 2x 8.4 = 17
he loses 2x 12.0 = 24
net gain = 7
World's perspective:
In order to complete SA, we have to take Bolivia as well. This binds another 4 of our reinforcements, leaving only 2 to put to Brazil for a total of 30. We attack Col and Ven with 15 each and thus try to complete SA. Imp can put 11 to Col and 6 to Ven and have 12 in both of them (not very likely, I admit, but anyway).
We attack 2 times with 15 vs 12 ->
0% chance of success per attack; chance of both attacks succeeding = 0%
we lose 2x 8.4 = 17
he loses 2x 9 = 18
net gain = 1
There are of course, endless more combinations thinkable, but for me this boils down to:
a) We don't yet have the strength to take Greenland AND SA at the same time.
b) As long as we attack with ~27+ we don't risk losing more armies than Imp.
c) If we split our forces now, we give up the advantage of having an unpredictable stack of armies, capable of taking any territory it wants.
d) If we don't split-attack, we can effectively deny him SA.
West Africa:
I half expected Imp to already be present in Nigeria. The fact that he is not, together with Lybia being a wasteland, tells us he is at least 2 turns away from completing West Africa, unless he took a detour around Nigeria through Niger to get to Ghana, which is absolutely not likely.
I therefore revise my earlier statement: as of now, it is not necessary to move into West Africa in force. It would be nice to do so in smaller numbers, so we can possibly threaten East Africa/South Africa in 2 turns, but taking Nigeria can wait another turn IF we leave enough troops in Brazil to outnumber him in West Africa next turn.
Central America:
Taking Ven or Col would bring us into a position to get into CA next turn, which always is a big plus.
Antarctica:
If we don't blockade now we WILL have to deploy troops there next turn, else he can take that bonus freely.
Conclusion:
....
I have no idea :-)