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Homer2101

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For the sake of completeness:

http://www.eu4wiki.com/Army#Composition

As has already been posted, in most circumstances the ideal combat stack is:
(1) Two to six cavalry units, not exceeding your cavalry support limit;
(2) Enough infantry to fill your combat width;
(3) A full combat width of artillery; and
(4) Reserve infantry up to the supply limit to fill out casualties.

The double cost of cavalry makes cavalry-heavy armies inefficient in most circumstances. Cavalry is usually superior to infantry when the new cavalry units show up due to increasing military tech level, but it will then become outclassed by newer infantry units. If you have the income to support lots of cavalry, then the calculus naturally changes.

Artillery should never see combat casualties and massively boosts your combat and siege effectiveness. The limit for artillery is not manpower but income, and it's all too easy to go bankrupt trying to support a huge artillery train in the early game. Your combat width depends on terrain, so as has been said above, it's perfectly possible to economize on artillery. I usually try for full combat width because I cannot always guarantee an engagement in low-width defensive terrain and prefer to not lose engagements due to insufficient artillery support.

The exception to the cavalry rule is hordes and some Eastern-tech countries like Poland. Poland/Commonwealth gets huge bonuses to cavalry combat strength and cost. Hordes are hordes.

By the second half of the game period, assuming you are playing as a major power and fighting the likes of France or a properly-fed Austria, you will want reinforcement stacks following your combat stacks for major battles. A reinforcement stack is simply a pure-infantry stack that is sent in to reinforce your combat stacks and provide fresh full-strength regiments.

If your manpower pool is not very deep, and you're fighting equal powers, by the second half of the game infantry regiments should be drawn from mercenaries to reduce stress on your manpower pool.
 

nicechinos

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For the sake of completeness:

http://www.eu4wiki.com/Army#Composition

As has already been posted, in most circumstances the ideal combat stack is:
(1) Two to six cavalry units, not exceeding your cavalry support limit;
(2) Enough infantry to fill your combat width;
(3) A full combat width of artillery; and
(4) Reserve infantry up to the supply limit to fill out casualties.

The double cost of cavalry makes cavalry-heavy armies inefficient in most circumstances. Cavalry is usually superior to infantry when the new cavalry units show up due to increasing military tech level, but it will then become outclassed by newer infantry units. If you have the income to support lots of cavalry, then the calculus naturally changes.

Artillery should never see combat casualties and massively boosts your combat and siege effectiveness. The limit for artillery is not manpower but income, and it's all too easy to go bankrupt trying to support a huge artillery train in the early game. Your combat width depends on terrain, so as has been said above, it's perfectly possible to economize on artillery. I usually try for full combat width because I cannot always guarantee an engagement in low-width defensive terrain and prefer to not lose engagements due to insufficient artillery support.

The exception to the cavalry rule is hordes and some Eastern-tech countries like Poland. Poland/Commonwealth gets huge bonuses to cavalry combat strength and cost. Hordes are hordes.

By the second half of the game period, assuming you are playing as a major power and fighting the likes of France or a properly-fed Austria, you will want reinforcement stacks following your combat stacks for major battles. A reinforcement stack is simply a pure-infantry stack that is sent in to reinforce your combat stacks and provide fresh full-strength regiments.

If your manpower pool is not very deep, and you're fighting equal powers, by the second half of the game infantry regiments should be drawn from mercenaries to reduce stress on your manpower pool.
It's neither accurate nor complete. Battle width is not needed when enemy doesn't have full width. It doesn't take maneuver into account.
 

G_Morgan

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Late game cavalry is a waste of money. What you want is combat width worth of cannons. 1.2 * combat width of infantry. Supporting stacks of pure infantry. This strategy starts to become viable at mil tech 13.

You can substitute combat width with the number of enemy infantry and cavalry regiments in a stack if you are fighting a small enemy. Personally in that circumstance I pull out spare cannons first but keep the spare infantry in place as far as possible.
 

Homer2101

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It's neither accurate nor complete. Battle width is not needed when enemy doesn't have full width. It doesn't take maneuver into account.

If your opponent cannot field full-width combat stacks to challenge your own, then the power balance is so asymmetrical that any optimizations are pointless to begin with and the enemy army can simply be steamrolled. Similarly, if you can guarantee a certain terrain-based combat width, then it makes sense to balance an army's composition around that. My experience is that such situations are not guaranteed and that it is best to assume that the maximum possible combat width will come into play. The alternative is to risk facing an enemy army whose cavalry will roll up your flanks. Which is why you want to have a wider battle line than your enemy -- so that you can hit his flanks with multiple cavalry units.

Maneuver by itself does not make cavalry superior, except on the flanks where maneuver actually matters. A regiment can engage only one other regiment, regardless of its type. Maneuver determines how far off-center the regiment can engage, and so comes into play mostly on the flanks and only for armies of different width, because it allows the larger army to roll up the smaller army's flanks by having multiple flanking regiments engage one enemy regiment.

There are, as others and I have said, situations where having more than the minimum cavalry necessary to get flanking bonuses is advantageous. Hordes and Poland are the best examples. But for the typical country, there's no point in paying double for a marginal and temporary advantage after the first hundred years of gametime, if not earlier.