Homebrew 2d10 vs 1d20

Bell shaped curves (2d10, 3d6...) are good for non opposed rolls, where one side is variable (your skill/proficiency/ability to achieve the result) and the other (dificulty) is fixed. Since the variable side has a low variance/dispersion (when you're good at something that only depends on you, you're likely to succeed with regular frequency), the results are more predictable. Good for ability tests (non opposed rolls). The "take 10" rule goes in thia way, but it reduces the variance to 0, too drastic.
For tests where both sides are variable, like attacks or other opposed rolls, a linear result (1d20) is better since your skill is being tested against someone's else skill, so you want the results to be less predictable.
So if someone is open to abandon the d&d "1 roll to rule them all" rule from since 3e, I would recommend to use both rolls.
 

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Bell shaped curves (2d10, 3d6...) are good for non opposed rolls, where one side is variable (your skill/proficiency/ability to achieve the result) and the other (dificulty) is fixed. Since the variable side has a low variance/dispersion (when you're good at something that only depends on you, you're likely to succeed with regular frequency), the results are more predictable.
The results on the dice are more predictable. Whether the result of the skill check is more predictable depends entirely on the system built around the dice and the what the range of the variables is.

If the target is 8+ on 1d10 (fixed difficulty), basic proficiency provides +3, advanced proficiency gives +5 and expert gives +6, then advanced and expert characters succeed 80% and 90% of the time respectively. That's very predictable. Unskilled people fail 70% of the time, which is also quite predictable. You don't need a bell curve to have predictable outcomes.
 
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The results on the dice are more predictable. Whether the result of the skill check is more predictable depends entirely on the system built around the dice and the what the range of the variables is.

If the target is 8+ on 1d10 (fixed difficulty), basic proficiency provides +3, advanced proficiency gives +5 and expert gives +6, then advanced and expert characters succeed 80% and 90% of the time respectively. That's very predictable. Unskilled people fail 70% of the time, which is also quite predictable. You don't need a bell curve to have predictable outcomes.
I think your definition of predictable isn't what other people are talking about. "I as the person running the game can calculate the chance" being "predictable" isn't a super useful definition of "predictable", and definitely isn't the one being used here.

You could talk about being able predict how hard a challenge would be to a party when designing it. But you can also talk about "when a character tries to jump 10', how predictable if they make it"? A 0% chance and 100% chance there is predictable (always fail, always succeed), while a 50% chance (even if you know it is 50%) is in a sense "this is an unpredictable result".

How predictable the odds are vs how predictable the result of the task is, if that makes sense.

Careful about semantic arguments like this. They don't go far usually.
 

I think your definition of predictable isn't what other people are talking about. "I as the person running the game can calculate the chance" being "predictable" isn't a super useful definition of "predictable", and definitely isn't the one being used here.

You could talk about being able predict how hard a challenge would be to a party when designing it. But you can also talk about "when a character tries to jump 10', how predictable if they make it"? A 0% chance and 100% chance there is predictable (always fail, always succeed), while a 50% chance (even if you know it is 50%) is in a sense "this is an unpredictable result".
I'm really not sure what you're saying here.

Being able to know in advance how likely you are to succeed is very important when it comes to making decisions in character. Knowing how difficult a challenge is likely to be when planning an adventure is typically very useful to a GM. You seem to be suggesting this is not the case, which does not at all align with my experience.

I absolutely agree that 100% and 0% chances are the most predictable, while 50% chances are the least predictable/most swingy. The aligns entirely with my point.

How predictable the odds are vs how predictable the result of the task is, if that makes sense.
I genuinely do not understand the distinction you're drawing here. The odds tell you how predictable the result of the task is. These are the same thing, to me. I note that you, too, used the odds in your example, in exactly the same way that I did in mine.

I used the phrase, "the result of the skill check". To me, this is entirely synonymous with "the result of the task", on the assumption that the output of the skill check tells us the result of the task.

Careful about semantic arguments like this. They don't go far usually.
Again, I really don't understand what you're trying to warn me about here. I'm happy to work with any definition of "predictable" people want but, while it's clear you don't like the definition I'm using, I do not have any idea how your definition differs.

In the post you quoted, I provided an actual rule example of a 1d10 skill system and claimed it provides predictable results. Do you disagree with this? If so, can you explain why it doesn't meet your definition of predictable?
 
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