What homebrew dice mechanic can I use for PvP in Amazing Tales?

Question

I've recently started playing Amazing Tales with my children. As a summary of basically all the mechanics of the game (it's pretty simple since it's targeting children), each character has four skills, each of which is assigned one die from the four available (d6, d8, d10, d12). When the GM wants to call for a skill check, he determines the appropriate skill, and the player rolls that die. A 3 or greater indicates success, and a 1 or 2 indicates failure. The GM then continues narrating, trying to keep the story interesting based on what happened.

The challenge I'm running into is that my children often want to play opposing sides. (That is, one will be the "good guy" and another will be the "bad guy" of whichever fictional universe they want to play in that day.) The rules as written pretty much assume that the entire party is on the same side, and doesn't have any sort of player-vs-player mechanic. But the stories we're coming up with are fun for the group, so I think that PvP is working for us. I think it'd help me with some of the narration, though, if we had some sort of "opposed roll" mechanic for when two players are trying to do something directly in opposition to each other.

My first instinct is to just pick an appropriate skill for each character, have the player roll the die for it, and the highest die wins. While that certainly accomplishes my objective, I'm a bit worried about it being too "swingy" if the dice are significantly different. That is, if the d6 skill of one player goes against the d12 skill of another player, then (if I did my math right) the d6 player would win ~21% of the time, and the d12 player ~71% of the time (with a tie the remaining ~8%).

I'm looking for something with a bit more "bounded accuracy" (if that's the right term), where having a better skill gives some advantage, but not a really big advantage. Maybe something where the favored player is likely to win more like 60% of the time, though I haven't really thought through what the ideal number would be.

My next thought is something like "1d20 + the skill die", where the d20 adds a lot of "randomness". But I'm not sure how close this meets my needs, and I know that adding more dice generally ends up ironically reducing the "randomness" by lowering the standard deviation, and I'm not sure how to fully evaluate how adding more dice to rolls helps with the overall probabilities. I will probably playtest this at our next session unless I get a better idea, though.

So I'm looking for an answer of what mechanics I can use to do a PvP opposed roll, with different skill levels of the players, within the simplified skill-checking system that Amazing Tales has.

Requirements:

1. Using a better skill should give some level of advantage, but not a big advantage. The odds should be 50%/50% if they're using the same skill, and somewhere near 60%/40% (though this is negotiable) if they've got the biggest gap in skill (d6 vs. d12).
2. Really simple and quick to calculate, since this is being used by children without much patience. Rolling two or three dice and adding them, or taking the highest, or something like that is about the most complex I want to get. If there's a lot of cases and rerolls of numbers or whatnot it gets tough to explain and would take us too much time during an exciting action scene.
3. I expect it should use the skill die itself in some way, just because that's the core of the system and it can be helpful to put the physical die on top of the skill on the character sheet. (That is, rolling some other die and just adding the skill die size seems like it's not in the spirit of the system, though perhaps something like it may work too.)

Answer 1

As it happens, your "d20 + skill die" mechanic gets pretty close to what you're asking for. It gives a 60.4% chance for a d12 to win and a 35.4% chance to lose against a d6, with 4% chance of a tie:

For an even simpler and even more "bounded" mechanic, you could have each player roll their skill die and a d20, but instead of summing them up, just let the player with the highest roll win. This gives the player with a d12 skill die a 52.6% chance of winning (and a 42.2% chance of losing) against a player with a d6 skill, with a 5.2% chance of a tie:

If that's a bit too balanced for you (as there's a risk that the players might feel that their skill dice don't really make any difference), you could replace the d20 with a d12, for a 60% of a d12 skill die winning and a 31% chance of it losing against a d6 (and a 9% chance of a tie):

The AnyDice program I linked above also gives the win/loss/tie probabilities for both mechanics for all combinations of (non-equal) skill dice, and with both a d12 and a d20 as the extra die. It should be fairly easy to modify if you want to e.g. test the effects of other types of extra dice with either mechanic.

(As a particularly noteworthy trick, replacing the result: 0 line in the code with result: d{} makes it return the eventual winner assuming that all ties are rerolled. In particular, the probability of a player with a d12 skill die eventually winning against a d6 is 62.9% using the "d20 + skill die" mechanic, 55.5% with the "highest of d20 and skill die" mechanic and 66% with with the "highest of d12 and skill die" variant.)

You may want to playtest these different mechanics and see what works best at your table. Personally, I'd probably try the "highest of d12 and skill die" mechanic first — it's simple, requires no math beyond comparing numbers, and the approximately two-to-one odds of a high-skill character beating a low-skill one just feel reasonably well balanced for the kind of game you're running. Remember that you don't want the advantage given by high skill dice to be too small, or your players could end up feeling like their character skills don't really matter in PvP.

Answer 2

Paired Success and Paired Failure from Parallel Goals

Here's a small adaptation of a framing mechanic that originally appeared in a game called shock: social science fiction. It doesn't change anything about the game mechanic you've detailed but it will slightly change the course of the game.

Once you've taken sides, one side gets the spotlight. Pick something chunky and easily passable to represent this.

Run the game as normal, but when the characters are opposing each other directly, whoever has the spotlight is the protagonist and says what they want to do first; then, the other side, the antagonist, says what they want to do. The only rule is that both the protagonist and the antagonist have to be able to succeed. This means that the protagonist can't annihilate the antagonist, but the antagonist can't directly contradict the protagonist.

So you can't have: "I steal the power diamond!" "I stop you!"

But you can have: "I steal the power diamond!" "I track you back to your hideout!"

Then roll as normal and adjudicate the results. If only one side fails, that side gets or keeps the spotlight and will be the protagonist next time. Otherwise, the spotlight swaps sides.