Quote from: Bren;868192Assuming the targets are equally likely, the random probability of the intended target being chosen in a group of 4 is 25% not 40%.

Not for the character with 20% Archery ability.

Quote from: Lunamancer;868197Not for the character with 20% Archery ability.

Then you don't understand what the words "firing into melee calls for the target to be chosen randomly" means. Choosing the target randomly with, as I said, each target being equally likely means there is only a 25% chance to hit the target. Because you are randomly determining who gets hit, assuming anyone gets hit.

If what you meant to say was the following.

   There is a 20% chance for the crappy archer to hit his target and if he misses his intended target, then he hits some target anyway, rolling randomly among the possible targets to find out which target he hit. In that case even when he misses he still has a 25% chance to hit the intended target through dumb luck.*

Then you should have actually said that instead of ""firing into melee calls for the target to be chosen randomly".


* And piss-poor rules design.

Quote from: Bren;868202Then you don't understand what the words "firing into melee calls for the target to be chosen randomly" means.

I said what I meant and I meant what I said. I'm sorry if you have trouble following a conversation. That's really not my problem.

Quote from: JoeNuttall;868114100%   99.00%   97.00%   94%   90%   85%   78%   71%   62%   53%   44%   35%   28%   22%   16%   12%   9%   6%   5%   4%   3.30%   2.60%   2.00%   1.50%   1.20%   0.90%   0.70%   0.60%   0.50%   0.40%

Using these figures, for the sake of comparison, I ran through the example of Johnny B Bad, Joe Average, and Dick Marvel. Calibrated for Joe Average (so we're talking about that awkward +3.5 modifier for the sake of comparison), under this system Johnny B Bad would go from 22% to 49%, Joe Average from 40% to 71%, and Dick Marvel from 78% to 95/96%.

Not all that different from 2d10, which is unsurprising since yours is basically a 2d10 system with added features.

I do have to circle back, though, to the idea that once you truncated the probabilities for a totally linear system to fit a d20 system, the probabilities end up nearly identical.

Now an important difference speaks directly to what appears to have been one of your major design goals. To leave nothing impossible, instead of an arbitrary truncation, your tail end tapers off into finely patterned probabilities.

I'm just trying to communicate that the real difference between bell-curve and linear systems is NOT really substantial in the big picture. It matters for those extreme ends. Personally, I don't understand the obsession with extremes because I would imagine most of the game takes place closer to the middle. To me, it seems that's where a system or core mechanic truly needs to shine.

QuoteYou're missing what I said in my first post:

I thought I'd seen something like that earlier up-line. No worries. I knew you'd correct me.

QuoteWhat I've found out is that whether players like a mechanic or not is a combination of several things, and when writing a game you have to be prepared to chuck the coolest idea you ever had because it just didn't survive a playtest.

So this is me with my cynical hat on. The reason why I just prefer a linear mechanic over something like yours is probably the same reason why a lot of gamers prefer yours over something linear. It's pure mathurbation. Not function. The AD&D 1st Ed attack matrix produces a close approximate of what you've got, but it's got to do this thing with 6 repeating 20's to do it. As a mathematical function, it's less clean.*

A key difference and tradeoff is that under a d20 system, the hypothetical modifier is +6, vs +3.5 in your system (or a regular 2d10 system for that matter) shows that for the common range of play, your system tends to be more grainy, your mechanic having been specialized to a high degree of resolution on extremely improbable events.

This is to be expected because adding another die doesn't change the standard deviation by much. So a 2d10 system has a graininess more similar to a 1d10 system than a 1d20 system. Again, I understand that you did successfully achieve your design goal. But my preference, being d100 then d20 then d10 is in that order of preference mainly due to graininess.


* As a side note, I created a math shortcut so I wouldn't have to look up hit tables, where I calculate purely from THAC0. To do this, I simply treat a natural 20 as if it were really a 25. That simulates the 6 repeating 20's. Once I did that, though, I pondered further tinkering. Instead of natural 20 always getting a 5 point boost, why not a d10 variable? So it's a limited-depth diminished exploding d20 mechanic that gives extreme low probabilities more of a tapering off effect.

Nothing that you posted makes any sense, showing a deeply flawed understanding on every level followed up by

Quote from: Lunamancer;868213So this is me with my cynical hat on. The reason why I just prefer a linear mechanic over something like yours is probably the same reason why a lot of gamers prefer yours over something linear. It's pure mathurbation.

No that's you with your rude and foolish and blinkered hat on.

Quote from: Lunamancer;868205I said what I meant and I meant what I said. I'm sorry if you have trouble following a conversation. That's really not my problem.

What you said was self-contradictory.

Whether you intended to contradict yourself for some unknown reason or whether you just don't understand what you've said doesn't matter as in either case, there isn't any productive conversation to be had with you.

Quote from: Lunamancer;868034Well, I often get the feeling that people are caught up on the idea of the "bell curve" more than the reality of the bell curve. Let's say we're doing a 2d10 roll-under system (for ease of calculation). And then look at what, say, the effects of a +5 modifier are:

Skill 2, jumps from 1% to 21%
Skill 5, jumps from 10% to 45%
Skill 8, jumps from 28% to 72%
Skill 11, jumps from 55% to 95%
Skill 14, jumps from 79% to 99%

I'm not 100% sure if people realize this is what the effect looks like, and if it's actually what they desire. Sure, skill 14 jumps only 20% while skill 11 jumps 40%, and skill 8 jumps 44%. Diminishing returns, right? Only lowly skill 2 also jumps only 20%. I'm not saying this is wrong. I'm asking if this is really what people think they're getting when they opt for the bell curve.

As I said in an earlier post in the thread, I don't care what the actual percentages are, but, yes, in general terms, that is indeed what I'm looking for and what I expect to get.

Also, when I do think about the actual numbers, I tend to think about relative rather than absolute change - skill 2 becomes 21 times as likely, skill 5 is 4.5 times as likely, skill 8 is about 2.6 times as likely, skill 11 is 1.73 times as likely, and skill 14 is 1.25 times as likely.

Quote from: Lunamancer;868034For me, the purpose of non-linear probability modifiers is so that I can adjust the situation in a way that may make an easy task have a decent chance of success for a low-skill character while not guaranteeing success for a high-skill character. (Or make things a heck of a lot more challenging for high skill characters while still allowing low-skill ones meaningful participation.)

For me, the idea of a task being easy for an unskilled character while not guaranteeing success for a high-skill character sits somewhere in the space between "outlier" and "contrived example".  If a rookie archer has a 50/50 chance to hit a target from a given distance, then a marksman is going to hit (and probably bullseye) that target every single time under the same conditions, barring some extreme circumstance (i.e., rolling a "fumble").  Or, going the other direction, an operation which would be tricky for a skilled surgeon is going to be botched every single time if someone with only basic first aid training attempts it, barring a miracle (i.e., rolling an "automatic success").

Quote from: JoeNuttall;868218Nothing that you posted makes any sense, showing a deeply flawed understanding on every level followed up by

No that's you with your rude and foolish and blinkered hat on.

I don't expect everyone to be a genius, so if you didn't grasp something that's one thing. But given your attitude, it seems like you didn't even try. Dishonesty is less forgivable.

But because I am not the rude one here, I will give you the benefit of the doubt and attempt to recap what I wrote into something more visual. "Your way" is based on the probabilities you posted for me for your mechanic. "My way" is the AD&D 1st Ed combat matrix with the little houserule I proposed to vary up the 6 repeating 20's.

Quote from: nDervish;868253As I said in an earlier post in the thread, I don't care what the actual percentages are, but, yes, in general terms, that is indeed what I'm looking for and what I expect to get.

Your design goal is your design goal, and that's unassailable. But ignoring the actual percentages? The players will care about them. Not the exact percentages, but it's not like seeing the number "15" on the character sheet for a skill will carry equal meaning regardless of whether they're playing GURPS or CoC. Players are sensitive to "whiff factor", especially when it comes to characters' primary skill. Your opinion, as a designer or GM, doesn't change their opinions. You have to address the actual percentages at some point.

QuoteFor me, the idea of a task being easy for an unskilled character while not guaranteeing success for a high-skill character sits somewhere in the space between "outlier" and "contrived example".

Given that I've listed several organic examples (and I could have gone on forever listing more) the "contrived" argument doesn't even seem worth addressing unless you want to reference a specific example. So let's skip over to the "outlier" argument then.

I pointed out that bell-curve systems have smaller intervals on the extreme ends, larger intervals in the middle.

80% of all rolls on 2d10 will fall in between 6 and 16, or 11 possible results. Beyond which we begin to enter the realm of outliers. 80% of all rolls on 1d20 will fall in between 3 and 18, or 16 possible results. It seems the linear mechanic in this case yields over 40% more points of distinction than the curve one.

The reverse is also true. The 2d10 mechanic has 4 points of distinction to cover the highest 10% (17, 18, 19, and 20) and 4 points of distinction to cover the lowest 10% (2, 3, 4, and 5) whereas the d20 mechanic only has 2 distinctions for each (1-2 and 19-20).

My position is that I DO think outliers are important. That's why I mentioned in my first post on this thread some ways to mimic some of the benefits of  curve mechanics when using a linear one. So to come back and say, "Well, that's only outliers"? Well, duh! That's the whole point.

Quote from: Lunamancer;868304Your design goal is your design goal, and that's unassailable. But ignoring the actual percentages? The players will care about them. Not the exact percentages,  but it's not like seeing the number "15" on the character sheet for a skill will carry equal meaning regardless of whether they're playing GURPS or CoC.

When I say "actual percentages", I mean "exact numeric representations of the probability".  If I need to roll a certain number, then yes, I care about whether it's "likely" or "unlikely", but not about whether or not it's a 74.456468465% chance vs. 72.5686863%.

In GURPS, I know that needing to roll a 15 or better is very likely to succeed without having to also know that it's a... umm... (consults anydice.com)... 95.37% chance.  Not being able to express the chances as a percentage does not in any way hinder my ability to have a general sense of whether it's likely or not.

Quote from: Lunamancer;868304Given that I've listed several organic examples (and I could have gone on forever listing more) the "contrived" argument doesn't even seem worth addressing unless you want to reference a specific example.

I just did a quick scan over your contributions to this thread.  I found two specific examples, both of which are distinguished by being essentially luck-based, namely playing a game of chance and determining who gets hit by a shot fired into melee.  Given that "several" usually means more than two, I assume there must be others that I missed.  Please point me in their general direction.

As to the two examples I did find, I was talking about how likely a low-skilled character is to succeed vs. the chance of a high-skilled character to do so.  Since skill has little-to-no effect on a luck-based outcome, I don't consider luck-based situations to be germane.

Quote from: Lunamancer;868304My position is that I DO think outliers are important. That's why I mentioned in my first post on this thread some ways to mimic some of the benefits of  curve mechanics when using a linear one. So to come back and say, "Well, that's only outliers"? Well, duh! That's the whole point.

Oh, come on...  I said that I considered a set of situations (not outcomes or probabilities) to fall between "outlier" and "contrived example".  In what way is it unclear that I meant "outlier" in the sense of "something that lies outside the main body or group that it is a part of, as a cow far from the rest of the herd, or a distant island belonging to a cluster of islands" (the very first definition given for "outlier" on dictionary.com), not in the statistical sense?

So, here, let me rephrase for you:

For me, the idea of a skill-based task being easy for an unskilled character while not guaranteeing success for a high-skill character sits somewhere in the space between "extremely unusual situation which is unlikely to come up often, if at all, either in-game or in real life" and "contrived example".

Quote from: Lunamancer;868287I am not the rude one here

Err.. excuse me - you just said this about my method:

Quote from: Lunamancer;868213It's pure mathurbation.

Are you really surprised that this ended the conversation abruptly?

Seems like we've hit the point of diminishing returns on this thread. Oh well.
 
Thus far I think the highlight for me was probably discussion on implementing Luck rolls, inasmuch as the idea of needing a secondary unmodified random roll as well to keep odds consistent).
(Though it would depend on the relative scaling of the Luck attribute as well; if a normal person has an 0% Luck you can freely call for a Luck roll as an extra; whereas if it has a non-zero default for theoretically-typical luck then an additional check gives too high a chance of the right box. In that case it'd be a matter of just modifying the Luck roll by enough to raise a default % up to the expected odds. Either way works in context.)

I have a vague sense of something else in here, but nothing's quite crystallized as yet.

Quote from: JoeNuttall;868312Err.. excuse me - you just said this about my method:

Are you really surprised that this ended the conversation abruptly?

No. I said that's a potential reason why some would like it. The context of the post as a whole made that abundantly clear. Normally, I would be understanding and see how you got the wrong thing out of it, but since you were dishonest in your last post and have refused to be a gentleman (or add anything on topic) in the face of my giving you the benefit of the doubt, I have no problem with the conversation ending right here. I'm just not going to let you putting words in my mouth or claiming I'm the rude one in this go unchallenged.

Quote from: nDervish;868311When I say "actual percentages", I mean "exact numeric representations of the probability".

Right. I wouldn't expect a player to know just through experience the difference between, say, 20% and 25%. One of the figures I track in the real world related to job performance, over a long period of time, has very consistently averaged 33%. But there are certainly data clusters where it looks more like 25% or even 20%. And others where it looks like 40 or 50%. That's why I use my lab rats, Johnny, Joe, and Dick, which have substantial skill differences between them, and I want to see how the probability shapes when a substantial skill modifier is applied. This is not for testing the minutia.

QuoteI just did a quick scan over your contributions to this thread.  I found two specific examples, both of which are distinguished by being essentially luck-based, namely playing a game of chance and determining who gets hit by a shot fired into melee.  Given that "several" usually means more than two, I assume there must be others that I missed.  Please point me in their general direction.

Bloody Stupid Johnson made the same point. I respond in Post #59 and name two more examples. Probably more importantly, I describe what's happening conceptually as cases where something about the situation itself denies the opportunity for failure. (The flip side is that in some cases something about the situation itself denies the opportunity for success.)

To give yet another example, I observed in a factory setting, first-year rookie machine operators would do just as well senior level operators. As long as the machines were running smoothly and there were no changeovers. Because in such situations, their skills as machine operators are not being tested at all. In fact, sometimes, due to peripheral skills, the newbs could even out-perform the veterans. However, introduce a change over or machine malfunction, the rookies get buried.

Of course, to properly manage the maintenance department, they keep records on frequency and severity of malfunctions. So there is a knowable, probabilistic framework in which the frequency and degree to which an operators skill will be tested.

QuoteFor me, the idea of a skill-based task being easy for an unskilled character while not guaranteeing success for a high-skill character sits somewhere in the space between "extremely unusual situation which is unlikely to come up often, if at all, either in-game or in real life" and "contrived example".

To continue with my factory example, I would agree (or rather not disagree) with you here in terms of the degree a machine problem the operator faces. If a rookie can most likely handle it, then a senior operator can definitely handle it. No argument there. However, if the factory foreman is called away for a couple of hours, what are the odds he's going to come back to a mess? Well, that would depend on whether or not there is a machine malfunction at all, and if so, only then do we need to ask how bad and how skilled is the operator handling it.

Quote from: Lunamancer;868375No. I said that's a potential reason why some would like it. The context of the post as a whole made that abundantly clear. Normally, I would be understanding and see how you got the wrong thing out of it, but since you were dishonest in your last post and have refused to be a gentleman (or add anything on topic) in the face of my giving you the benefit of the doubt, I have no problem with the conversation ending right here. I'm just not going to let you putting words in my mouth or claiming I'm the rude one in this go unchallenged.

You were insulting people who liked my method, not the method itself? This means you weren't being rude?