+1 to the link TBest put there; I think Norman's guide is about as helpful as it gets when it comes to a general heuristic for managing armies and making sure that they're all "working" armies.
I'd recommend getting good on 0% SR first since in 0% SR everything but your opponent is 100% predictable. You will know in advance whether or not your attack will succeed (if you know how many armies are attacking and defending) and similarly you can figure out how many armies you need to attack given the defending army count (2 requires 3, 3 requires 5, 4 requires 6, etc.).
Opponent-Independent Army Management
So before you even think about the opponent-dependent aspect of strategy, just look at the empty map and figure out the most efficient way to expand. For example, here's a map from a recent 1v1 (ignore the picks made- I couldn't figure out how to not display them; not my picks either):
If you know your base income (5 on Strategic 1v1), your starting army size (4), and the number of starting territories (3), you can easily plan your early expansion in advance. For example, if you begin in Iceland (#3 on the map), you just need to deploy a total of 5 armies there to take the bonus in 2 turns (8->2 leaves you with 7 alive; 3->2 and 3->2 take the territory and leave you with 2 alive on each). You can also control the path these armies take so that your surviving armies are in a particular position when you finish.
But it's also not a situation of one bonus at a time. Notice that some starts border other bonuses- the East Africa start, for example, borders the West Africa start. If you got both of these starts, then you can take the West Africa bonus in 2 turns with a deployment of 4 (3->2 leaves 2 alive; +2 lets you attack with 3->2 again leaving 2 alive and taking the bonus). Notice that not every such border situation results in the same type of combo- if you combo'd Southeast Asia (#1- Myanmar start) with East China (Taiwan start), you still won't be able to take the East China bonus in less than 3 turns just because it would take you at least 3 turns to go from either of your starts to the most distant territory (Beijing) in the bonus.
And since you have 3 starts, you can even plan ahead on a higher level. You can, for example, start in Scandinavia, West Africa, and
East Africa and take both Scandinavia (requires a deployment of 5 for 2 turns) and West Africa (requires 4) in 2 turns with 1 army left over from your base income. You can plan your early expansion out during just the pick stage! But also keep in mind that the game doesn't end in 2 turns- if you start in Scandinavia, you will not have great expansion options in that part of the map once you take the bonus - West Russia has a wasteland, Europe is inefficient (7 territories for a +5 bonus), and Greenland is efficient (6 territories for +5) but big and requires a minimum of 3 turns to fully take. But even that planning you can do early on.
Really, there's three key features you should look at on the map when considering expansions:
- bonus efficiency (# of territories : bonus value).
- start/combo locations (in terms of minimum turns to take the bonus)
- surrounding bonus efficiency/wasteland status
The ideal bonus/combo (without considering your opponent) is one that is efficient, can be taken relatively quickly (early income can make or break the game, since 2 extra armies are much more impactful when you only have 10 armies total vs. 100 armies), and does not limit your expansion opportunities afterwards.
One final note before I talk about the opponent-dependent side of the game (which makes things more fun and complex). Remember this graph you get at the end of a game? # Armies controlled vs. turn?
It's not a perfect representation of who's winning or losing (geography + the way your armies are distributed on the board also into play) but it provides a useful way to think about expansion and over-expansion. Expanding to take a bonus is a dip on that graph- you'll be burning some armies to take the bonus, so that's a negative slope. But once you have the bonus, you start to get income from it and the slope becomes more positive. Keep in mind that usually
if you take a little bit longer to take a bonus, you're able to save a little bit on army deployment (or even total army cost)- if you take Scandinavia in 3 turns instead of 2, for example, you'll be doing an 7->2 (leaves 6); 5->2 (4); 3-2 (2) attack series over 3 turns instead of an 8->2 (7); 2*3->2 (2) series- you can afford to deploy one less army in the bonus
and can deploy that army elsewhere. If you have a good reason to use armies elsewhere, slowing down can pay off.
So think of expansion as an investment. You spend A armies to take a bonus that gives you +B armies/turn. It'll take B/A turns (rounded up) for your investment to be made up. Throw in geographic considerations- like the specifics of army deployment/reuse- and you're able to figure out how valuable it is to actually take a bonus. If you're facing your opponent at a border and you could take a +5 bonus in 2 turns by deploying 8 armies there instead of on the front, you're now able to figure out the short-term (army cost) vs. long-term (bonus) aspect of your decision and figure out whether expansion is a good call or could cost you the game. (Also keep in mind that you may get card pieces from expanding- that +5 reinforcement card is also an investment return to think about). The beauty of this small aspect of the game is that you can figure out most (>0% luck or WR) or all (0% luck SR) of it in advance, right at the pick stage.
Opponent-Dependent Army Management
There's no way to keep this part of the game from being noisy, and so you can't figure it all out in advance. This part of the game is essentially what turns Warzone into a strategy game- from a simple optimization problem that can be solved by an algorithm to a tricky decision-making scenario where you don't have all the information you need to figure out the outcomes of your decisions.
This part is too complicated to explain in a single forum post (plus most of what I've said is redundant anyway) and I'd recommend looking at the guide TBest linked above to get a better grasp of it, but there's still a useful bag of tricks to consider + you can apply some of the ideas from opponent-independent army management to this aspect of the game.
But some basic tricks:
- Think of armies/deployments/expansion as investments (pretty much along the lines of the first half of this post).
- Move order matters. Sometimes you benefit from making sure your movement happens early on- like when you're running away from a more powerful stack to a territory your opponent probably didn't deploy in. Sometimes you want to go late- like when you want to attack your opponent but aren't sure if you'll have more armies than them, so you don't want to be in a situation where your attack fails and then they're able to take your territory due to the armies you lost. Make sure the order you submit your moves in makes sense- or at least think about which moves should be early moves and which ones should be late-turn moves.
- Don't waste armies. If you've got 2's or 3's lying around that you aren't going to use to attack anything, moving them around can give you extra delays (+ reinforcements if you move them toward the front or wherever you're expanding). If you're not expanding super-fast, you could also benefit from moving armies toward a single bonus instead of trying to take all the bonuses that you border. This also matters for attacks- if 8 armies take 5, there's often no point to attacking with 9 instead (although having 1 more surviving army on that territory after your attack is something you might want sometimes).
- Geography matters. If you have about even armies on a 3:1 or 2:1 border with someone (3 or 2 of their territories border 1 of yours) and the ratio of their income to your income isn't as high (it's a bit trickier in practice than this rule, but since your incomes likely won't get that far apart in most games it's an okay rule-of-thumb) then they're at a disadvantage when it comes to preventing you from taking at least 1 of those territories. If those 2 or 3 territories are in bonuses that they control, you now have pretty good odds of breaking that bonus. This is also useful for counter-picks- notice, for example, that the southernmost territory in East China has a 2:1 border with the easternmost territories of Southeast Asia. Controlling that southernmost territory gives you pretty good odds of breaking their Southeast Asia bonus. You might find it advantageous to convert 1:1 borders into more favorable ratios by moving around- for example, if you're in West
China and have a 1:1 border with Pakistan (or Afghanistan- the westernmost bonus in Southeast Asia), you can trade that for a 3:1 border by taking Tibet. This makes breaking their bonus a lot easier.
As far as figuring out the number of armies goes (which is pretty much the question you actually
asked here), in 0% SR that's easy. If you're expanding, you already know the math from part 1. If you're defending, think about how many armies you think they'll be able to attack you with (or will attack you with). You want to have at least just enough armies there to survive that attack (so if they're attacking with 6, for example, you want to have at least 5 defending so they can't just kill you off). If you can't do that, try running (if move order favors you- check History- people that went early last turn are likely going to move later this turn). If you're attacking, just do the same thing but in reverse.
For WR, just use the Analyze Attack tool to figure out ranges instead of exact values. The same principles work though.
Good luck! Also check out the guide!