Quote from: Alexander Kalinowski;1082333I was pointing out above that this is not the case. Let's think through it logically: a bell-curve means diminishing returns at the upper end - does this induce greater specialization or does it dissuade investments into having an even higher stat level... higher by a slight margin? It clearly is the latter. When you have reached a 75% skill, it becomes harder and harder to make any significant improvements and you're probably better off using your resources to improve other, lower skills by greater amounts.

It depends on other elements of the system that deal with situational modifiers. For example in Runequest skills above 100% allow one to split the skills and attempt two actions. The GURPS magic system has an impact on casting time and fatigue cost if you continue to push skill with the spell beyond 15.

It not possible to formulate an answer without the context of a larger system.

The advantage of a 2d6/3d6 is that it better reflect how skills work. That use of skills cluster toward the median. That low skill levels fail far more often then the effort to become competent.

As far as playability goes, the use of a bell curve make skill attempts more predictable while still leaving the possibility of outliers.

The the thing to watch out for with bell curves is how dramatic the central peak is. The more of a difference between peak and the outliers the more important even a +1 bonus becomes. The 4dF that Fate and Fudges uses has this issue.  In general 2d6 and 3d6 rolls allows for a progression of bonuses that works well in play.

Quote from: estar;1082346It depends on other elements of the system that deal with situational modifiers. For example in Runequest skills above 100% allow one to split the skills and attempt two actions. The GURPS magic system has an impact on casting time and fatigue cost if you continue to push skill with the spell beyond 15.

It not possible to formulate an answer without the context of a larger system.

Sure. But there is still merit to comparing linear versus bell-curve basic task resolution mechanics in a vaccuum. The biggest difference, in a vaccuum, is in the progression of success chances (of, say, 1d10 versus 2d6), which peter out with bell-curve mechanics. And that difference in success chance progression comes in during stat advancement (be it in chargen or during "leveling-up") and with the application of modifiers.

Yes, 2d6 or 3d6 rolls tending to be more average does make a difference if, for example, your system measures quality of success of a roll. But if it's only a binary success versus fail test, it doesn't matter with what kind of roll (average or not) you succeeded or failed with.

And if you're using exploding dice, the 'bell curve' is suspect.  On a standard 2d6 your median result in 7 (3.5 per die) and you have approximately a 17% chance of rolling it.  With exploding dice two of the combinations that result in a 7 (6,1 and 1,6) explode and become 8+.  Consequently, the odds of rolling a 7 drop from 17% to only 11% (Any Dice 2d6 Exploding).  In both instances, the odds of getting at least a 7 are equivalent (58%), but with exploding, you have a whopping 21% to have a 12 or better, compared to less than 3% when you take the true result.

Quote from: jan paparazzi;1081613I am considering a change with Unisystem from 1D10 to 2D6. I know Vortex uses that version. Why would you prefer 2D6? Is it the normal curve? Doesn't it become easier for skillfull characters in the long run?

I know why 1D10 was preferred originally. The system, especially the cinematic version, is supposed to feature variance, wild swings, and lots of  unpredictable results. Using 2D6 reduces the variance that might allow a mook, like my character in Buffy, a chance to succeed against a supernatural character. Even so, it only gives the mook an occasional win; it usually just delays the inevitable, usually through a really bad roll for the monster. But a delay means that the Slayer or someone else powerful can show up and save the day, and the mook's bacon.
So, as usual, it depends on what you want in your campaign. If you really want to reduce variance or want to reduce it for some situations, you could use averaging dice. That's one normal D6 and one where a 1 result counts as a 2 and a 6 result counts as a 5. I remembered that from wargames and used it occasionally in RPGs.

Quote from: deadDMwalking;1082367And if you're using exploding dice, the 'bell curve' is suspect.

Yeah, in that case it's not a classical bell-curve anymore anyway - given the curve's asymmetry.

Quote from: jan paparazzi;1081613I am considering a change with Unisystem from 1D10 to 2D6. I know Vortex uses that version. Why would you prefer 2D6? Is it the normal curve? Doesn't it become easier for skillfull characters in the long run?

The "normal curve" for 2d6 is more like a pyramid with straight slopes for the record

Ok, let me explain again what I mean. I am considering swapping 1D10 to 2D6-1 or 2D6-2 with unisystem. On a 1D10 vs 9 as a target number with stats plus skills equals 2 you need to roll at least 7 to make the roll. That means 7,8,9 or 10 will do. So it's 40 %. With a 2D6 vs 11 with stats plus skills equals 2 you need to roll at least 9 with 2D6. So 9, 10, 11 or 12. That's 4/36+3/36+2/36+1/36 = 10/36 = 27,8% chance. If it's vs difficulty 10 add another 5/36  making 15/36 = 41,6 %. So on low skills 2D6-2 is a lot worse than 1D10 and 2D6-1 does a little better.

On high skills 1D10 vs 9 with stats plus skills equals 6 you only need to roll 3 or higher. 1 and 2 won't do, so it's 80% chance of making the roll. On 2D6 vs 11 with stats/skills of 6 you need to roll at least 5 to make it. 2, 3 and 4 won't do so that's 1/36, 2/36 and 3/36 = 6/36 of rolling those. So that makes 30/36 of rolling everything else. That's equals 83,3% chance of making the roll. So it's already doing better on the high difficulty. 2D6 vs 10 has 33/36 = 91,7% chance of making it.

Ergo: Because of having a higher chance of rolling a median the 2D6 does better than 1D10 with high skilled characters and poorer with low skilled characters. So it's indeed what Estar says more predictable. The question is "Would you want that?", because the system already has competent characters make rolls quite often. Standard unisystem has competent characters making rolls increasingly easier the more competent you are (ranging from 0-100% with a steady increase of 10% for each skill/attribute increase) vs. for example a dice pool system like WoD (which also has a bell curve, but a different one) which has odds that go from 1 dice (30%) 2 dice (51%) 3 dice (65,7%) 4 dice (75,99%) etc. So you see that that system makes the difference between compentent and less competent characters smaller because of the bell curve. A straight 1D10 vs a target number doesn't do that. And a 2D6 vs a target number has a bell curve, but it seems that it makes the difference between compentent and less competent characters bigger. Because of higher chances of rolling a median. So what's wisdom? What is better and why?

Apologies for my rambling btw. It's complicated and my English is falling appart trying to explain what I mean.

Edit: I guess I was trying to say a storyteller dice pool system has a leveling effect. A 1D10 vs a target number doesn't have that and a 2D6 vs a target number has a deleveling effect.

Edit 2: I seem to have miscalculated. Storyteller has a leveling effect. 1D10 or a percentile system has a straight line. But 2D6 seems to be deleveling at first and then leveling later on. That's what you get when you try to talk about something you never had any interest in. Well, dumb me. I guess storyteller doesn't have a bell curve then either. It's just a curve.

Quote from: deadDMwalking;1082300On a d10 the chance of rolling a 9 or 10 is 20%.  Even if you explode on a 10, it won't matter if you need a 9 or 10.  

On 2d6, the chance of rolling an 11 or better is 25% assuming independent exploding on a 6.    

On 2d6, the chance of rolling a 10 or better is 30% with exploding.

If you remove exploding, the chance of rolling an 11 or 12 is only 8%; a 10+ is only 17%.  If you make success happen on a 9, the odds go up to 28%.

Effectively, 2d6 does not correlate well to a d10.  If you opt for 2d6, you should consider what you're trying to do and why.  Effectively, you make a median result more likely compared to extreme results; if median results do not equate to success, you're not really helping anyone.  

If you choose independently exploding d8s, 2d8 against a target of 14 is roughly equivalent to 1d10 against a target of 9+ (21.09%).

No I wouldn't let them explode independently. I would say it's 8,333% chance of exploding on 11-12. And I think medians help characters with high stats asked for the roll. See me other huge post.

Quote from: Alexander Kalinowski;1082333I was pointing out above that this is not the case. Let's think through it logically: a bell-curve means diminishing returns at the upper end - does this induce greater specialization or does it dissuade investments into having an even higher stat level... higher by a slight margin? It clearly is the latter. When you have reached a 75% skill, it becomes harder and harder to make any significant improvements and you're probably better off using your resources to improve other, lower skills by greater amounts.

I don't think think this is correct. On a high skill plus stat of let's say 4 and 4 making 8 to a target number of 9 with 1D10 in Unisystem you only fail if you roll a 1. So that's 10% chance. If you do that with 2D6 vs 11 you only fail if you roll 2 which has 1/36 = 99,977% chance. So 2D6 rewards being skillful in that system. Which makes sense. You only need a small roll on higher skills/stats and the chance you roll them is bigger, because you have a bigger chance of rolling a median.

Quote from: jan paparazzi;1082489I don't think think this is correct. On a high skill plus stat of let's say 4 and 4 making 8 to a target number of 9 with 1D10 in Unisystem you only fail if you roll a 1. So that's 10% chance. If you do that with 2D6 vs 11 you only fail if you roll 2 which has 1/36 = 99,977% chance. So 2D6 rewards being skillful in that system. Which makes sense. You only need a small roll on higher skills/stats and the chance you roll them is bigger, because you have a bigger chance of rolling a median.

Yeah, sorry, you're right - if you change the dice but maintain the same stat/skill levels. I was, as mentioned, talking in a vaccuum. In your scenario a combined 8 represents a higher skill level ("success chance") when adding 2d6 versus 11 as opposed to adding 1d10 versus 9.

You could also use 1d8+1d4 instead of 2d6 because the differing die size might allow for some nice shenanigans, like, idk, rolling only 1d8 or only 1d4 under particularly unfavorable circumstances. Or to make only one or the other die explode.

Quote from: Alexander Kalinowski;1082353Sure. But there is still merit to comparing linear versus bell-curve basic task resolution mechanics in a vaccuum.

Not when you are considering the behavior of the players as to whether they will specialize or spread out their skills. This can't be answered on the basis of the dice mechanics alone. One has to consider the context in which the roll used to take even a educated guess to how players will develop their character.

Quote from: Alexander Kalinowski;1082353But if it's only a binary success versus fail test

This is an example  of the context I am talking about. Which wasn't stated in the post I quoted. The "if" says it all. X conclusion is only true/false/relevant if the roll is made in that context.

In addition the examples I gave about GURPS Magic and Runequest were not address. In general I found systems that do what GURPS Magic and Runequest do, give benefit for higher skill level beyond pass/fail or even degree of success tend to have more players specialize their characters to gain those benefits. System that just rely on degrees of success or pass/fail tend to have the players spread their skills once they start hitting the level "I am successful a deal of the time" level which is about when the odds get to be 80% to 90% in favor of success.

Quote from: estar;1082525Not when you are considering the behavior of the players as to whether they will specialize or spread out their skills. This can't be answered on the basis of the dice mechanics alone. One has to consider the context in which the roll used to take even a educated guess to how players will develop their character.

Are you unironically claiming that there is in general no merit to comparing linear vs bell-curve in a vacuum with regards to player behaviour? If so, I would like you to reconsider - this wouldn't be a wise position to adopt, not by a long shot.

There is, by definition, no context to consider when comparing in a vacuum. Still, general(!!!) observations can be made regarding diminishing returns and the impact on player incentivization. No context is necessary for these general (!!!, we're not talking about hard numbers here) observations either. Any context in which this happens is only an after-thought which modifies this basic (dis)incentivization.

If you still insist, you might want to read up on this here. So, yeah, my claim remains that in a vacuum, ceteris paribus, players will tend to spread out more than with linear distribution basic resolution mechanics. The reason for this remain as stated and continues to be unchallenged: diminishing returns regarding basic success chances.

Quote from: estar;1082525This is an example  of the context I am talking about. Which wasn't stated in the post I quoted. The "if" says it all. X conclusion is only true/false/relevant if the roll is made in that context.

No, but it was implied in that post since it made reference to success chances, just the one prior to it, and included a graph that gave a rough outline how the progression of success chances looks like under a bell curve to demonstrate the diminishing returns of a bell curve. Which has merit even if you're dealing with a system that has various levels of success as part of its core mechanics. Or additional actions or modified spell use. It merely means that the above is the first step of analysis instead of a complete examination. But it's still a valuable analysis step. Considering the impact of levels of success (or anything else, really) is a subsequent step - which is exactly why I referred to it as after-thought above.

Quote from: estar;1082525In addition the examples I gave about GURPS Magic and Runequest were not address.

Because you have left the vaccuum by doing so and stepped into a context which isn't applicable.

Quote from: estar;1082525In general I found systems that do what GURPS Magic and Runequest do, give benefit for higher skill level beyond pass/fail or even degree of success tend to have more players specialize their characters to gain those benefits. System that just rely on degrees of success or pass/fail tend to have the players spread their skills once they start hitting the level "I am successful a deal of the time" level which is about when the odds get to be 80% to 90% in favor of success.

I don't want to address the above specific advantages now either as neither is applicable to jan's scenario, as far as I understand it. The progression of success chances viewed in a vaccuum, however, is still of merit to considerations of using 2d6 instead of 1d10 in Unisystem. It becomes applicable the moment modifiers arise in that modified system: a +1 under 2d6 behaves differently from a +1 under 1d10 - just as having a combined skill level of 8 is different under 1d10 vs 9 from its directly converted value under 2d6 vs 11. Under 1d10 I need to stack modifiers to reach effective skill level 8 if I only want to have a 10% failure rate. Under 2d6 vs 11 I only need to stack modifiers to reach final skill level 7 to achieve roughly the same success rate.

Only after having considered basic success chances we can begin to analyze other, system-specific, mechanics that further impact gameplay.

Quote from: Alexander Kalinowski;1082527Only after having considered basic success chances we can begin to analyze other, system-specific, mechanics that further impact gameplay.

And I am telling you are wrong (see I can bold too) not to consider the system.

I responded to you talking about the behavior (see the bold part again) of people designing their character. Specifically,  whether in a skill based system do they go for specialization or spread their choices (see doing italics as well).

My point (bold, bold, bold) is that players don't based their design on the dice mechanic they base their choice on what benefits the system confers.

So discuss the impact of dice mechanics all you want on how player choose skills. Any conclusion you and other draw will be incorrect unless you talk about the skill system as a whole.

And keep in mind I have not offered, in my replies to you, any opinion on any other point in this discussion except the one above in regard to how players pick their skills.

This is speaking as a person who been refereeing and writing rpg campaigns for 40 years using two dozens or so system with skills. Observed not just a handful of friend but players from all walks of life in what they pick for their character's skills. My observation of these players is that if there is a benefit beyond a higher odds of success then it likely some will continue specialize. But if the only thing is a bump in success then they lose interest in advancing the skill with they are able to succeed 80% to 90%. of time. Irregardless of the dice mechanic used.

One might ask well what about system that rely on opposed rolls? It doesn't matter, if the opposition keeps pace with the player's character then they will keep specializing until they get a high chance of success. If the opposition doesn't keep then they will switch to buying other skills around the 80% to 90% success rate.

Quote from: estar;1082536My point (bold, bold, bold) is that players don't based their design on the dice mechanic they base their choice on what benefits the system confers.

Just as customers in an economy don't just base their decisions solely on the price of a product? That multiple factors enter such a decision is a trivial observation. Still it merits to hold all factors constant except for one ("in a vacuum") to assess the impact of that factor, which is exactly why that is done in economics all the time. I, once more, strongly recommend to familiarize yourself with the wikipedia entry on ceteris paribus.

Quote from: estar;1082536But if the only thing is a bump in success then they lose interest in advancing the skill with they are able to succeed 80% to 90%. of time. Irregardless of the dice mechanic used.

Yes and if there is a sufficiently increasing cost to raising the skill above, say, 50% then their interest tends to peter out before that. None of that invalidates anything of what I have said though.

Quote from: estar;1082536One might ask well what about system that rely on opposed rolls?

It doesn't change the equation if at constant prices of skill upgrades there are expected (or actual) diminishing returns regarding success chances. Note: having diminishing returns regarding success chance at constant prices for skill upgrades and having constant returns regarding success chances at increasing upgrade costs are functionally the same thing.

However, if there are no diminishing returns, you have changed the scenario.