Face the Hydra was one of the three "Horde Decks" created by Wizards during the original Theros block. It was designed for groups of players to play with sealed decks, and was likely inspired by the fan-created Zombie Horde EDH format. It's a cooperative format where a team of players faces down a deck that runs itself. The game works exactly as a normal game, except for these rules:
The Hydra deck loses if there are no Heads on the board at the end of any turn.
Players don't attack the Hydra deck, but attack individual Heads that the Hydra deck controls. Each creature can only attack one Head in a combat phase, but multiple creatures can attack the same Head. Creatures can attack both tapped and untapped heads.
The players share a turn instead of taking separate turns.
The players go first and don't draw on their first turn.
They Hydra Deck consists of only Head Creatures and Sorceries.
Whenever a Head dies, the Hydra deck reveals the top two cards. For both of those cards, if either are Heads, they enter the battlefield.
If a Head would leave the battlefield and go to any zone other than the graveyard, it dies instead.
If the Hydra player would be dealt damage or lose life, instead deal that much damage to a head of the players' choice.
Ignore effects that are impossible for the Hydra player. (E.g. drawing/discarding cards.)
If the Hydra player must make a choice, the players make the choice instead.
During the Hydra player's turn:
The Hydra untaps all their heads.
The Hydra player reveals the top card of their library and casts that spell.
The Hydra player's Head cards damage all the players. Hydra Head creatures each deal 1 damage; other creatures (Elite Creature - Head) each deal 2 damage.
At the end of the Hydra player's turn, some of the Elite Heads have additional effects.
At the beginning of the game, the players choose a number of starting heads and the Hydra player begins with that many Hydra Head creatures in play.
Not in the original rules: When the Hydra deck needs to flip a card but cannot, the graveyard is shuffled into the library. (I believe this is the most reasonable thing to do.)
Acknowledgments
Thank you to the following who playtested and/or helped me fix things: