I'm a long-time proponent of the participants of such matches being handed a single brick before they go into whatever closed room or arena has been agreed upon. Also leave a third brick in the middle of the area. It creates a certain degree of strategy. It also livens up the "just hugging" part of the fight that many UFC or boxing matches kinda devolve into.

Do you throw the brick? Use it to block a thrown brick? Use it add a blunt weapon? Plus you need to get that third brick, but doing so exposes you to getting hit with a brick as you bend down to get it. There's so many choices it's like rock, paper, scissors except it's just brick, brick, brick.