A Rainbow attack, sometimes called a Mix, increases your attacking power and decreases your casualty rate. A simple 100k attack(clearing)mix will generally consist of:
95k archers, 1k workers, 1k warriors, 1k scout, 1k Pike, 1k Sword. Notice this mix is ALL your infantry. You can get a little creative with this mix to suit your needs and personalities, such as 3k workers/warriors, 1 scout/sword and pike, 1997 Transporters 92k Archer (this is a good attack formation for a Lvl10 NPC farming expedition).
Loyalty waves need to be a mix as well. I personally like 15karcher and 1k scout for my loyalty waves. This wave is very fast and effective. Others will use a 10k Warrior/15k Archer mix, which is slower but will give you a little more prestige. Either way, you will need a lot of loyalty waves to capture an NPC or Historical NPC and Loyalty Waves are designed to drop loyalty quickly.
Cat/Cav Waves are used on defenses heavy on Archer and Archer Towers. A very powerful horse wave looks like 70k cataphract/20k cavalry/10k scout. Notice you still have a mix of troops. With a high attack hero this wave can do serious damage to a defenders Archers: 100k, 150k 200k and even as high as 300k archers can be defeated with this mix (dependent on your hero vs thier hero).
Spam waves (I call them RETARD waves) are designed to take out a defenders mix (sword, pike and warriors), or defensive abatis. They will also give the defender Honor while reducing yours. 1k archer/100 scouts sent over and over will reduce the number of pikes/swords and warriors. These are the first waves sent. Next comes 1k cav/100 scouts to clear out the abatis. You will need 20, 40, 60+ waves of each depending on what the troop strength is. Remember, you must make sure your archer spam waves remove pike and sword BEFORE sending in your cav spam, otherwise these attacks will not work.
Once your spam waves have cleared the pike/sword and abatis you are left with only archer towers and archers which your cat/cav wave clears (or significantly reduces). Then comes your clearing wave to mop up the city.
*** On any attack on another player, expect to loose your heros!!!! Your King/Queen is yours for life, but all other hero are susceptible to capture:::Most especially during SPAM Waves ***