RULE #1
All players share a 250 card deck and a graveyard. You own every card you draw for purposes of things like Homeward Path.
RULE #2
Begin the game with 0 cards in hand.
This rule can be adjusted, personally I think starting with 3 cards is a lot more fun and makes it go quicker.
RULE #3
You must play every card in your hand as soon as legally possible. All optional modes are mandatory, to the extent that you can fulfill them (ex. casting Mnemonic Wall with an empty graveyard is legal, but if there’s any spells in the yard you must target one with Mnemonic Wall’s ETB trigger).
RULE #4
You must activate every activated ability of permanents you control once per turn per legal target as soon as legally possible. Always activate abilities from the bottom of the card up (for instance, if you satisfy Mosswort Bridge’s hideaway requirement you must activate it on upkeep, not the mana ability).
RULE #5
If a spell or ability has X in its mana cost, X is always 5.
RULE #6
You must attack with all legal attackers and block with all legal blockers whenever the option is presented to you.
RULE #7
All players have infinite life.
RULE #8
All players have infinite mana.
RULE #9
You lose this round if you commit a game rules violation.
RULE #10
Play the game until there’s a winner, that winner gets a point, then exile all permanents, all cards in the graveyard, and all cards in hands and start the next round. When the deck is empty, the player with the most points wins!
To show how testing this format is, here are some examples of how some games of Judge Tower can go.
Game 1, turn 1:
"Ok, untap, upkeep, draw. Mainphase 1, cast brainstorm-"
"You lose. Brainstorm is an instant so you have to retain priority in the draw step and cast it then."
Whatever, I didn't realize that. Game 2, a few turns in:
"Ok, untap, upkeep, draw, reveal Thunderous Wrath, cast it for its miracle cost targetting you."
"You lose, you it's an instant so you can respond to the miracle trigger by casting it, since the trigger does not occur until its already in your hand."
Awesome. Game 3. We've been casting a crazy number of instants or sorceries and my board is full of enchantments. I've been holding onto the card Dredge waiting for something to sacrifice.
"Ok, I'll play forest, tap it, cast dredge, sacrificing the forest-"
"Nope, you lose. Sacrifice isn't part of the cost, it's part of the resolution, and it doesn't target, so you could have cast it the second you drew it with nothing on the board."
So, yeah. The game's ridiculously brutal, but you learn quick, and you get better at the game's corner cases.
Extra Links
This was the first video released by card market about Judge tower, they also have another full length video playing it.
This is a youtube short explaining how judge tower works.