@faraday Yeah. Running samples and looking at the data is the 'Monte Carlo' method for generating probability curves. It's good for a quick and dirty way to draw your image but occasionally you'll get hiccups like that. However, calculating the exact probabilities can be a massive headache. I'm just lucky because I've got a really good head for probability mathematics.
Twin Peaks: The Return. It's like going to your 25th annual class reunion and meeting that incredibly bizarre person that you haven't thought about since graduation and finding out that they are as strange as ever, but in a good, happy and healthy kind of way (and I realize most of us probably -are- that incredibly bizarre person for a lot of our classmates).
@ThatOneDude said in CofD and Professional Training:
When games have no PK, why does PT benefits matter? Everything at that point is just story/RP. Why is it a bad thing if a PC that has a back story as a soldier is able to roll 9-again with any firearm (due to year and years of training and experience) and then if he really focuses on the shot, he can do exceptionally well (rote)? What does it hurt other than furthering the story?
Why make the person roll at all in such a case? Why not say he just hits? Or give him an extra 10 dice because he was a solider?
And no, I don't actually think what you were asking was a bad question and I'm just giving you a snarky answer. I'm using what is called Reductio ad Absurdum which is a method for illustrating a logical flaw by carrying it to an extreme conclusion. In essence it matters because combat is a significant part of any game. Giving significant bonuses in combat for extremely low prices, even if that combat does not ever occur between PCs, is unbalancing.
Now I'm not going to debate whether or not the bonuses from PT are significant or not since everyone's mileage may vary but I will point out that the argument is being made that as the rules sit it is practically a requirement which would seem to prove that the bonuses are significant.
But what about allowing those bonuses for non-combat skills? Well, I don't think anyone would argue that a game becomes imbalanced because someone is able to sing really well or paint very nice pictures. Even in the case of skills likes Athletics the fact that a character has a significant advantage in climbing might help someone really shine during a 'Cliffhanger' storyline but unless your entire campaign is going to be based around a Sylvester Stallone movie the bonus probably isn't going to unbalance anything.
So I dug down a little bit more into the probabilities of FS3 and found something that I think exemplifies what happens when you design a challenge resolution system using a semi-arbitrary 'this sort of feels good' mechanism.
Before I go on I would like the say that I still feel that the probabilities in FS3 work out pretty well and my comment about how it is designed isn't meant to come off as dismissive. It is just that at the moment I've been grinding through some math and my language centers are a little out of whack so I can't think of a better term to use that would be a clear and concise summary for how the probability system was derived without making it so that some people might perceive me as being dismissive.
The flaw I've spotted is essentially one of 'countering modifiers'. To explain the term in most games if you take an action to get a +1 to attack and then someone takes an action that gives them a +1 to defense then you end up back where you started. They take some form of action that counters your modifier (although usually in doing so they have to take some other form of penalty themselves).
In FS3 this doesn't happen. If you've got 6 dice to attack someone and you attack a person with 6 dice to defend then your chance of hitting is 61.69%. If both people get a 3 die boost (from spending Luck) the odds drop to 59.60%. So even though relative positions remain completely the same (both people are equally skillful, both people catch lucky breaks) the attacker loses 2% on their possibility to hit. While this isn't a whole lot it is still awkward and this is compounded by the fact that it isn't a consistent change. If both people only have 2 dice to begin with the odds shift from 69.60% to 62.76%, nearly a 7% change. Even more inconsistent if someone with 2 dice attacks someone with 6 dice they go from a 23.56% chance to hit to a 29.25% chance to hit, so they in fact gained nearly 6%.
Now again, I'm really not trying to say that FS3 is a horrible system or anything. Honestly, if I didn't think you were looking for data like this and you weren't able to use it constructively (and in this case 'constructive' even includes saying 'you know what? I -like- that this happens') I wouldn't bother. Kind of how we were talking earlier about aspects of realism and different people having different thresholds people will interpret these 'hiccups' differently. I'm just making sure you know they are there.
Now in a tabletop game I would be a lot more accepting of these small aberrations in the probability curves. It's more important to keep things moving along quickly and so you want to avoid complex calculations. That means there's lots of mechanisms that get used to generate probability curves and character progression schemes that are 'good enough'.
We're not playing on a tabletop, however and a lot of the things that would give us a headache the computer can handle very, very easily. As an example I would never try to play a game in which I'm told that the odds of success are 1/(1+2.718281828^((level difference)*-0.183102))*100. I mean what the Hell is that? On the other hand having the computer look at the two characters and say 'Oh! There's a 6 level difference. That means the odds of success is 75%' is something a computer is -really- good at doing. Computers are so good at it that they don't even need to round the result to 75% but can actually have the 'real' probability of 74.99999458% because they don't need to roll 2 10-sided dice to generate a probability.
Even better than that, because you are using mathematics to calculate probabilities you can avoid another pitfall that is left over from tabletop games; the Hell a character goes through to increase a skill they are really good at. You're a Great pilot and you want to increase your skill another point? That's going to take you 3 months during which absolutely nothing changes because you can't roll 2/3 of an 8-sided die. Using math, however, there's not anything wrong with being partway between Great and Expert. The computer has no more difficulty calculating the chance of success between characters of equal level and characters who are 2.1 levels apart.
Now in a lot of settings players might have some difficulty wrapping their heads around some of these aspects and I can completely understand that. One of the nice things about FS3, however, is that a lot of these mechanics are already hidden under the hood and you could change the system with the players barely noticing. Just allow the players to put XP straight into a stat like Pilot. If they put 4 or 5 XP in the skill they get feedback on their sheet that shows that their skill is 'Fair'. As soon as they add the 6th point of XP to Pilot the stat now reads 'Good'. However, a pilot who has put in 5 XP has a small advantage over a pilot who puts in 4 XP. When they shoot the computer looks at their stats, compares them to the stat of the defender, and tells them whether they hit or not. Practically nothing has changed for them (and that's assuming you let them buy partial levels. While I'm all in favor of that it is hardly a requirement. It's an advantage of the system buy hardly mandated).
The biggest problem you would have with such a system is dialing in the initial values. I actually had created a spreadsheet a few years back that did the math for me so I could concentrate on shaping the curve however I wanted.
I've gone ahead and cleaned it up and added some stuff that allow you to sort of 'mock up' tests using attributes that are roughly the same scale as what FS3 is doing. I did make one cheat, however, in the mockup and rather than using the XP chart that FS3 uses I change the calculations for the levels of skills and attributes to a pair of formulas.
@Ganymede Missing on an 85% isn't that big a surprise. You should still be missing about 1 in 6.
@ThatGuyThere Actually, the average number of successes for someone rolling 9 dice 4 times is around 15 because of exploding contributing more than you think (http://anydice.com/program/bd0a. Thanks to Misadventure for pointing me to the site).
And while things like 9-again may not contribute too much to a roll by the time all is said and done they contribute a great deal more than you might think. After all, someone with 6 points in combined skill and attribute will roll 54 dice (assuming a +3 equipment bonus) so at the end of the day an extra 10% here and an extra 5% there adds up to a lot of successes.
But the real point of this thread wasn't to quibble about how much ability A helps or how many extra successes ability B will generate. It's just to figure out what the theoretical pools (and any roll modifiers) should be.
At present I think I'm more or less in line with your estimates. I'm actually ranging from 4-8 dice with the 4 dice being the skill level of your average entry level professional. These are the guys on the construction crew that do the real simple jobs. You have them handle the framing and drywall when the job is easy but in the spots where those tasks get tricky you have someone who's been doing the job for a couple of years now come in and handle it. 6 dice are your true 'average professionals' who are fully trained. They've been doing the job and 95% of the time if you want the job done you call these guys in. 8 dice are the true experts. Not necessarily world-leaders in their field but they are they guys who get called in to do jobs that even your normal professional would consider to be difficult.
Then what I did was I figured out the average number of successes for 1 to 6 rolls as an extended action using a rote action for 7 dice, 9 dice, and 11 dice. I assume that the vast number of extended roll activities your average professional does are rote actions. Sure, the tailor needs to modify the pattern for the custom fit jacket they are making and everyone's body if a slightly different shape but they've done so many jacket alterations, plus they have the time to sit down and work out any tricky areas that might exist, that it is still a rote action for them.
Then I figured out how many rolls you would expect someone normally doing that job to take. If your 'average professional' would take 1-2 rolls I used the average number of successes for 7 dice because the average person doing that job is a bit less skilled. If it was 3-4 rolls I used the average successes for 9 dice and if it was 5-6 rolls I used the average number of successes for 11 dice.
This seemed to work really well because the guys with the 4 die pool could nearly always accomplish the '2 roll' task (99.96% of the time). It might take them twice as long to get it done (because they had to make four rolls) but they would nearly always be able to, much like you would expect in real life. Meanwhile the odds of that person pulling off a '3 roll' tasks is about 50/50 (meaning that they were around 75% likely to succeed if they took 3 times as long as the 'fully trained' professional. Meanwhile the 'fully trained' pro with their 9 die pool would nearly always accomplish a '4 roll' task (99.21% of the time) but dropped to around 50% odds of succeeded at a '5 roll' task.