Heated Rivalry

41 cards because you can tutor for Amadeus Cho with Protect Humanity

Ancient Rivalry has two targets with Thor and Thor,

Try not to put Defeat the Hydra on the Lernean Hydra (unless you have a resource generator out to pay the so you are not spending a card from your hand for it.

I like using player side schemes, my decks usually have at least 2, but I always play 2 player, so clearing them is typically not an issue, just wish you could get player side schemes with Embody Pathos so most likely will grab Olympic Feud if it is early on, as the only Olympus card will be Hercules

My preferred order of gifts would be Sword of Peleus, Shield of Perseus, Nemean Lion Skin but it will depend ion current game state.

I am more than willing to deal with Ares to draw cards with Face the Past

Herc starts with an attack of 3, with Aggressive Conditioning and Combat Training it brings you up to 5. "Now I'm Mad" can get you to 6, having out Sword of Peleus or Golden Mace (even with 0 gifts) gives you a Weapon to exhaust with Mean Swing getting you to 9 on a basic attack. Any gifts you do have out will increase this with Golden Mace. Then potentially a last +1 from Specialized Training getting you Combat Specialist. For a maximum potential 13 damage from a basic attack, with piercing and overkill. Not accounting for a potential +2 from two copies of Lion of Olympus. Now this is a scenario that will most likely never happen, or only happen once every 10 or so games, because of how many cards it requires to be in play and the 3 cards needed in hand, but man it will be fun when it does happen.