I've got a game that uses special dice for its resolution. Basically when making an opposed check, each side rolls a bunch of them based on the relevant trait, and whoever rolls most points wins. The margin by which you win matters for resolution, usually.
I'd like to simulate the resolution on regular dice. Specifically, I'd like to be able to play, and let others play, without buying more of these special dice.
Problem to solve
I'm stumped because the dice symbols don't line up easily. Effectively, the special dice are marked [-1, 0, 0, 1, 1, 2] with a minimum score of 0 for any roll. (The actual dice have symbols on them. An X, two blank sides, two sides with a sword and one side with two swords. This game is played by my children, who count swords and remove one for each X. They don't understand negative numbers, so more X'es than swords just means you score 0. But this does matter for the feel of the game, so I want to keep that rule)
Because the margin of victory matters, I can't just replace it with "whoever rolls higher", and because of the -1 on the die there's a bigger chance of rolling nothing than normal.
Can anyone see a way to match (or at least get very close) to the resolution mechanic used here, while using easy to get dice? I'm okay with them not being 6-sided, but I would like something with a regular distribution.
Number of dice thrown is usually 2-6 per side.