Advanced Battle Mechanics
PvE - Battles Against Bosses and Monsters
The What: You should send a large single compliment of same-level troops with a general. Check that your March's power (crossed swords near bottom right before sending) matches or exceeds the power of the monster you are attacking (shows as crossed swords when clicking "Attack" on the map). It is generally recommended to send Cavalry (Mounted Troops) against Monsters and Bosses as they have the highest attack to cost ratio.
The Why: Boss and Monster battles happen turn by turn with each of your troop levels fighting separately until either 10% or more of your troops are defeated (Defeat for you) or until one of your troop levels has a higher power (Victory for you).
Let's give an example: you want to battle a 100K power monster. You have a general with 50K power, Rank 1 troops at 10K power, Rank 2 troops at 30K power, and Rank 3 troops at 60K power. When you click on the monster to attack, Evony will automatically assign as many troops as your march will allow, so in this example, we'll say it assigns all of them, including your general: 50K + 10K + 30K + 60K for a total of 150K power. When the battle commences, the monster will first attack your general and Rank 1 troops. 100K vs 50K + 10K (total 60K). The 100K monster clearly "wins" this battle. Some of your Rank 1 troops will be wounded (or killed) and the monster will lose some power, let's say down to 95K. Next, the monster will battle your general and Rank 2 troops: 95K vs 50K + 30K (total 80K). Again, the monster has higher power and will kill or wound some of your Rank 2 troops, and itself will be wounded, let's say down to 85K power. The last battle in this case would then be the monster at 85K vs your general and Rank 3 troops 50K + 60K (total 110K). You would win this final battle, the match would be declared a Victory, and your troops return home with several wounded and/or dead.
The real batty part about this, though? If the monster was able to kill 10% or more of your total troop complement in those first two rounds, the entire battle would end in Defeat, you would not loot anything from the monster, and you'd return home with several wounded and/or killed troops. So to recap: sending all your ranks of troops will minimally end up with some wounded or killed soldiers and, maximally, might even lose you the whole battle.
If, however, you sent only your general and Rank 3 troops, the match is much cleaner. The 100K monster goes up against your 50K general and 60K Rank 3 troops: 100K vs 50K + 60K (total 110K). Since your total power is more than the monster's, your troops win the battle and return home without any wounded or killed troops! A much better outcome than sending all ranks in this case.
PvP - Battles Against Player Cities and Outposts and NPC Cities
The What: You should send "layered" troops. This means small amounts of all lower rank troops and as many highest-rank troops as you have. "Small amounts" is debated among players, but generally agreed to be between 100 and 1000. You should also send a mix of all four troop types (Ground Troops, Ranged Troops, Mounted Troops, and Siege Machines). Often a general will prefer a type of troop i.e. Edward the Black boosts the attack of Ranged Troops. If you lead a march with Edward the Black, once you have your layers (100-1000 of each type and rank) then you can add more high-level ranged troops for the best outcome with that general.
The Why: PvP matches use a round-robin style of battles. That is, each of your distinct troop and rank combinations will battle each of your opponents troop and rank combinations. A troop and rank combo will drop out of the round-robin tournament if it individually has 10% or more wounded or killed. Having layers will tire out your opponents' troops.
Let's give an example: you each have a 50K general. your opponent has 100K Rank 3 troops. You have 98K Rank 3 troops, 1K Rank 2 troops, and 1K Rank 1 troops. The match will start with their Rank 3 troops and general battling your Rank 1 troops and general. Both sides will take losses, let's say down to 99K for you opponent, and 200 of your Rank 1's wounded for you. Since this is more than 10% of your Rank 1 troops, this will cause your Rank 1's to stop fighting. Next up, your opponent's 99K Rank 3's and general vs 1K of your Rank 2's and general. Let's say your opponent is now down to 98K and your Rank 2's at 950 troops. Next round: your evenly matched 98K Ranks 3's and generals take losses down to 94K Rank 3's for both you and your opponent. Next, your opponent's Rank 3's have to battle your Rank 2's again bringing your opponent to 93K Rank 3's and your Rank 2's down to 900 troops. Since this is now a 10% loss of your Rank 2's, they will no longer fight in rounds, but the remaining battle will be between 93K of your opponent's Rank 3's and their general against 94K of your own Rank 3's and your general, resulting in a victory for you.
These numbers are entirely fabricated and considerably off from what would really happen (many rounds at smaller losses per round) but were meant to illustrate how rounds work in a battle and why troop layering is effective. Ultimately, the weaker layers pick off troops from your opponents' higher layers while preserving your own higher rank troops. When this is effectively done through all 4 troop types and all 15 possible layers, the effect is a victory for layered troops against a similar complement of single-rank troops.