Certain cards work better with certain other cards. Sometimes it is because their special powers amplify one another. Sometimes it is because they make up for each other's weaknesses. Certain cards also usually don't work well together because the effects of one card make the other card less likely to trigger. Of course any card combination might make sense in certain special circumstances. Below I have listed a bunch of cards. Below each card in the "Harmony" section I list other cards that enhance the special effects of this card. In the "Discord" section I list cards that detract from the effects of this card.
Feel free to add you own to the list. I'm sure I've missed a few.
Keep in mind, this is not meant to be a rulebook. It's just a guide to help new players (and maybe some old players) get some ideas for new strategies.
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I'll start with the cards designed to work well with (or poorly with) a large set of other cards.
CD = Cool Down
Slashing Strike
Harmony: Any melee attack unit, especially those with a CD of 9 or greater.
Discord: Everything else.
Overpower
Harmony: Any magic attack unit, especially those with a CD of 9 or greater.
Discord: Everything else.
Shadow Assault
Harmony: Any piercing attack unit, especially those with a CD of 9 or greater.
Discord: Everything else.
Amplifier
Harmony: Any special attack unit, especially those with a CD of 10 or greater.
Discord: Everything else.
Vengeance
Harmony: Any high health unit.
Discord: Any low health unit.
Priest
Harmony: Any spell card that isn't destroyed after activation.
Black Widow:
Discord: All other Hell Legion units.
All area attack units have a harmony with Dancer.
All piercing attack units have a harmony with Mermaid.
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Now for everything else
Apprentice Swordsman
Harmony: Mermaid
Cyclops
Harmony: Cyclops (Duh)
Panda Man
Harmony: Sister Apprentice, Archangel's Courage
The Crusader
Harmony: The Crusader (double duh), Archangel's Courage
Kendoka Girl
Harmony: Deterrence
Discord: Nine-Tailed Fox
Monk
Harmony: Faerie Dragon, Archangel's Courage, Poison Rain, Elves Seduction, Goddess of War
White Tiger Taoist
Harmony: Blindfold
Poison Rain
Discord: Mermaid
Haste
Harmony: Haste
Archangel's Courage
Discord: Archangel's Courage (diminishing returns)
Flaming Arrow
Harmony: Frost Wyrm, Deterrence (situation dependent)
Discord: Frost Wyrm, Deterrence
Pit Trap:
Discord: Faerie Dragon, Poison Rain, Goddess of War, Elves Seduction
Frosthunter
Harmony: Mermaid
Unicorn
Discord: Mermaid
Hot Ninja
Harmony: Haste, Deterrence
Aphrodite
Discord: Poison Rain, Faerie Dragon, Goddess of War, Elves Seduction
Dragon General
Harmony: Haste, Kendoka Girl, Summer Time, Deterrence
Blizzard
Harmony: Deterrence, Frost Trap, Frost Wyrm, Ice Elemental
Assassination
Harmony: Deterrence, Frost Trap, Frost Wyrm, Ice Elemental
Frost Bolt
Discord: Faerie Dragon, Poison Rain, Goddess of War, Elves Seduction
Frost Trap
Discord: Deterrence, Frost Wyrm, Ice Elemental
Magic Overwhelm
Discord: Sabotage (Seriously, I once lost a match after playing both of these because the Sabotage destroyed the enemy spell too early in the fight.)
Godesses' Favor
Harmony: Archangel's Courage, Sister Apprentice, Duke Vamp
Red Dragon
Harmony: Archangel's Courage, Sister Apprentice
Ultimate Seal
Discord: Kendoka Girl, Nine-Tailed Fox, Deterrence
Vengeance
Harmony: Archangel's Courage, Sister Apprentice
Jenifer
Discord: Mermaid
Blademaster
Discord: Faerie Dragon, Poison Rain, Elves Seduction, Deterrence