A friend recently raised a question about dice mechanics, and while I won't go into the details, it sparked some thoughts about dicepools.
The broad idea was something transparent, allowing degrees of success for comparison, and not requiring maths at the table.
When avoiding maths, I tend to think of dicepools as a starting point. I don't know if this will work out but let's give it a shot.
The idea I have in mind is, for now, a pretty basic one. You'd roll a handful of dice, looking for values of X or more. Immediately we hit the downside that this isn't actually all that transparent - odds for dicepools are not all that intuitive. Okay. Let's blatantly ignore that for now and move on...
For comparisons, we could say that higher values are better. So the target might be fixed at a 4+, but when the margin of success matters, your 5+ beats their 4+. For an opposed roll, this can essentially set the target difficulty.
Okay, for a five-die pool looking for rolls of 4+, we have 97% chance of getting 1 or more, then 81%, 50%, 19%, and finally a mere 3% chance of getting 5 successes.
Looking for 5+, we go 87%, 53%, 20%, 5% and 0.4%. A group of n 4s is always less probable than a group of n-1 5s and more probable than n 5s. For example, going by sheer rarity, 4x4s should beat 3x5s, but lose to 4x5s.
Looking for 6+, we go 60%, 20%, 4%, 0.3% and 0.01%. A group of n 6s is always less probable than a group of n+1 4s or 5s, or a group of n 5s. It doesn't work entirely neatly, though - 3x6 is less likely than 4x5, but 2x6 is just as likely as 3x5, and 1x6 is more likely than 2x5.
Keeping things simple
One straightforward way of handling opposing rolls would be to have dice cancel out. Let's say you roll 4, 4, 5, 6, 6 and the opponent rolls 4, 6, 6, 6. The opponent's first two 6s cancel out both of yours. Their third 6 cancels your 5 (since it's higher) and their 4 cancels one of your 4s. This leaves you the victor with a single roll of 4.
In this model, having a bigger pool should make you more reliable at overcoming opponents. Sure, the novice might get a lucky 6, but if you're rolling more dice, you're more likely to roll some 6s and cancel it out. Conversely, if you're putting up a defence (or setting the difficulty of a challenge) you're more likely to roll a high number that the novice will struggle to cancel.
Is this significantly different from just having a dicepool without that comparison? I'm not sure...
Skill numbers
Okay, let's think about another approach. What if rather than contributing to the size of your pool, your skill determined the target number you were going for? I feel the more intuitive way to do this is rolling equal to or less than your skill, because descending numbers being better was bad when it was THAC0 and hasn't improved since.
So if you have a skill of 1, you need to be rolling 1s. If you have a skill of 3, anything from 1-3 is a success. We'd compare these like blackjack, so your successful 3 beats the opponent's successful 2.
I feel like I slightly prefer this, because higher skill makes you more reliable at getting successes, rather than extending the maximum number of successes you can achieve.
This could be part of the classic Attribute vs. Skill model, with Attributes + circumstantial bonuses determining the size of your pool, and Skill making it easier to get successes. I'm not sure that's necessary, but it's an option. One downside there would be that having both as adjustable axes makes things less transparent, at least when creating characters: you'd potentially need to think about the impact of both on a particular ability.
