1 Mana mutual card filtering isn't always that bad, right? Plus you have the chance of Flame Rifting someone if you win. It's a win-win! Unless you lose.

I want to give a strong incentive to discard high-cost cards, since usually most players are inclined to discard lands rather than high-cost cards. Why does Standoff target rather than just choose, as in clash? Because there are going to be a couple of cards in the set that will give you Hexproof, letting you avoid Standoffs.

Should say "A player loses the standoff if he or she discarded the card with..."

As it is, it doesn't specify what card is being referred to. WHile it's fairly obvious to anyone who is familiar with the game, a completely new player might think it means the card they drew rather than the one they discarded.

It is a little less clear in this case than the wording on Clash, which was what I was going off of. There are some space issues, but I do like your wording better.

You could just go "if his or her discarded card was the lower..."