Statistics Help

[Xeviat]

The d20 system, and those based on it, are my favorites probably for one simple reason: I understand the statistics involved in it. If I'm shooting for a 60% success rate, or success on a roll of 9 or higher, I know that I want the DCs to clump around 9 + whatever the bonus my players have. Now, though, I am looking into other systems in an effort to broaden my gaming experience. I am looking into L5R right now, but I am very curious of the statistics involved in their Roll/Keep system.

L5R uses Target Numbers, which are just like DCs, but rolling is different. A standard roll could look like 5k2, which means roll 5 d10s and keep 2 of the dice. I know on each roll of a d10, 5.5 is the average, but when you get into rolling multiples and only typically keeping the highest roll, I don't know how that will play out at all.

I figured odds are that one smart individual could explain it to me here.

[sparkletwist]

www.anydice.com will probably be a helpful resource.
You can type in something like "output 2d6" and it will show you the chances of any outcome.

For roll-and-keep stuff like this, you specify the number of the die (from highest to lowest) that you want to keep and then an @.
For example: "output 1@3d10" is how you tell anydice you want to roll 3d10 and take the one highest die from the roll.
Multiple dice are specified with braces and commas. Like, your 5k2 example would be written on anydice as "output {1,2}@5d10"

I hope that helps. :D

[Ninja D!]

Statistics for GURPS are very well-known and easy to find. I can't remember for sure but they may even be in the core books. That's a very good systems for that, as is anything based around a D10, D20, or a D100 for obvious reasons.

EDIT : I know this isn't what you were asking but I figured I would throw it out there for when you want to look at other systems. On that note, I'm starting to feel like "percentiles FTW".

[Xeviat]

Thanks sparkle, that resource will really help with the XkY system.

I have no idea about anything GURPs, though, and I have been told that for my social life and career path, I should never pick up a GURPS book (or I will be lost to the void).

[Ninja D!]

I think you'd like it.

[LordVreeg]

Statistics for GURPS are very well-known and easy to find. I can't remember for sure but they may even be in the core books. That's a very good systems for that, as is anything based around a D10, D20, or a D100 for obvious reasons.

EDIT : I know this isn't what you were asking but I figured I would throw it out there for when you want to look at other systems. On that note, I'm starting to feel like "percentiles FTW".

yOU, AS WELL? 
No wonder we do so well...

[Lmns Crn]

Dissenting for a moment, I've always thought clear probabilities in games are overrated as long as the system consistently bears out what it describes, and there are other things besides clear probabilities I'd sometimes rather have.

By this I mean that if I'm playing a character who is a World-Class Expert Rocket Scientist (or whatever), and I'm tackling rocket-science problems int he game, I need to have a certain level of confidence and trust in the game system (whichever it is) that this information about my character-- that he's a World-Class Expert Rocket Scientist-- is a meaningful trait with appropriate impact on the world and the events in the game. I need to know that, for this character, simple issues about rocket-science are going to be trivial, difficult issues about rocket-science are going to pose a challenge but not an insurmountable one, and that any issues involving rocket-science are going to be easier for me than for other characters who are not World-Class Expert Rocket Scientists.

If I can trust that those sorts of things are true-- that is, that the game's mechanics support the game's descriptions, so that calling myself a "World-Class Expert Rocket Science" isn't just so much fraud-- I don't care whether I have a 61% chance to solve Rocket Science Problem A and a 13% chance to solve Rocket Science Problem B (or whatever). I actually think that in a lot of cases, such specific information is a distraction from the events at hand.

I think there are a lot of interesting options, in terms of game mechanics, that you can begin to explore only after you've set aside clear assessment of probability as a top priority.

In Lady Blackbird (a simple, dice-pool system where each player has as their sole resource a small stockpile of extra dice that can be added to any roll) one character assists another character in an action by passing dice across the table to add to another player's dice pool, reinforcing the "character helps character" action with a literal, physical "player helps player" action that is being acted out in front of you. This may seem simple, but it's visceral-- and you can look at the odd, extra die's result and easily tell whether the assistance helped or not.

In Deadlands, you'd resolve the effects of magic by having your magic-using "huckster" play a quick hand of poker against the devil (the GM). If you replaced this with a d20 roll to beat a specific difficulty, you could do a much better job nailing down the probability that magic's going to work, and you could probably run it a lot faster as well-- but you miss out on a lot of the things that says (and silently reinforces) about the setting, magic, and the tone of the supernatural (not to mention the role of the GM).

I'm rambling, so I'm going to wrap this up now. I'm just not sold on the importance of systems with clear probabilities, particularly when I can use the same system design energy to go after other (sometimes conflicting) things instead. You may disagree I guess.

[LordVreeg]

Dissenting for a moment, I've always thought clear probabilities in games are overrated as long as the system consistently bears out what it describes, and there are other things besides clear probabilities I'd sometimes rather have.

By this I mean that if I'm playing a character who is a World-Class Expert Rocket Scientist (or whatever), and I'm tackling rocket-science problems int he game, I need to have a certain level of confidence and trust in the game system (whichever it is) that this information about my character-- that he's a World-Class Expert Rocket Scientist-- is a meaningful trait with appropriate impact on the world and the events in the game. I need to know that, for this character, simple issues about rocket-science are going to be trivial, difficult issues about rocket-science are going to pose a challenge but not an insurmountable one, and that any issues involving rocket-science are going to be easier for me than for other characters who are not World-Class Expert Rocket Scientists.

If I can trust that those sorts of things are true-- that is, that the game's mechanics support the game's descriptions, so that calling myself a "World-Class Expert Rocket Science" isn't just so much fraud-- I don't care whether I have a 61% chance to solve Rocket Science Problem A and a 13% chance to solve Rocket Science Problem B (or whatever). I actually think that in a lot of cases, such specific information is a distraction from the events at hand.

I think there are a lot of interesting options, in terms of game mechanics, that you can begin to explore only after you've set aside clear assessment of probability as a top priority.

In Lady Blackbird (a simple, dice-pool system where each player has as their sole resource a small stockpile of extra dice that can be added to any roll) one character assists another character in an action by passing dice across the table to add to another player's dice pool, reinforcing the "character helps character" action with a literal, physical "player helps player" action that is being acted out in front of you. This may seem simple, but it's visceral-- and you can look at the odd, extra die's result and easily tell whether the assistance helped or not.

In Deadlands, you'd resolve the effects of magic by having your magic-using "huckster" play a quick hand of poker against the devil (the GM). If you replaced this with a d20 roll to beat a specific difficulty, you could do a much better job nailing down the probability that magic's going to work, and you could probably run it a lot faster as well-- but you miss out on a lot of the things that says (and silently reinforces) about the setting, magic, and the tone of the supernatural (not to mention the role of the GM).

I'm rambling, so I'm going to wrap this up now. I'm just not sold on the importance of systems with clear probabilities, particularly when I can use the same system design energy to go after other (sometimes conflicting) things instead. You may disagree I guess.

well, no.
And yes.

But you are talking about playing in a game, and i kind of agreee that one wants to have faith in the system.  So in play, sure.

But in terms of game design, understanding probabilities is critical.  When the dice pool mechanic first came out, I read a whole dissertation on how it really worked and afected a game ([urlhttp://www.wikihow.com/Calculate-Multiple-Dice-Probabilities=]here[/url]) befre deciding it was not what I wanted.   Not in terms of the easy probabilities of a d100 system, but more in terms of how success was judged and what levels of expertise mean what.

But I like your comments about how in game ritaul mechanics reinforce tone.  Much ignored.

[Elemental_Elf]

There's far more variability in L5R than D&D simply due to the fact that L5R relies on more rolled dice than on static bonuses. There are very few ways to add "+1" to your roll in L5R but there are plenty of ways to get extra dice on each roll. This variability makes the math much harder to work out since you could, on one attack be rolling 5k2 but on the next 7k2 just by switching combat stances. I have a character that can actually roll 10k3 on a regular basis! And we haven't even begun talking about Exploding dice!

What I'm getting at is that L5R is far more imprecise and thus relies far more on the DM to make the game work than D&D (especially 4E).

[sparkletwist]

I'm just not sold on the importance of systems with clear probabilities, particularly when I can use the same system design energy to go after other (sometimes conflicting) things instead. You may disagree I guess.

Oh, I do disagree.

Here's the thing:

By this I mean that if I'm playing a character who is a World-Class Expert Rocket Scientist (or whatever), and I'm tackling rocket-science problems int he game, I need to have a certain level of confidence and trust in the game system (whichever it is) that this information about my character-- that he's a World-Class Expert Rocket Scientist-- is a meaningful trait with appropriate impact on the world and the events in the game. I need to know that, for this character, simple issues about rocket-science are going to be trivial, difficult issues about rocket-science are going to pose a challenge but not an insurmountable one, and that any issues involving rocket-science are going to be easier for me than for other characters who are not World-Class Expert Rocket Scientists.

I actually agree with this statement as a player. If we're just talking about systems where the probabilities may not be entirely clear to the players, then, fine.

However, your comment about using "system design energy" on other things suggested to me that this isn't particularly important to you in general, and that's where I disagree. Knowing the probabilities as a GM, as an adventure planner, or as a system designer is quite important, for the very reasons that you explained. The GM (or whoever it is that is designing the adventure) has to ensure that your World-Class Expert Rocket Scientist is able to solve trivial rocketry issues without a second thought, whereas it would take some doing for players without such expertise-- and the GM must also ensure that world-class rocket-science problems that other characters would fall quite short on are within the realm of doing for him. It would also help, for balance's sake, to ensure that brain surgery, computer hacking, basket weaving, and other pursuits do not come as easily to the WCERS as world-class expert rocket science.

So, my question is, what happens if nobody along the line-- not just the players, but the GM, the system designers, and whoever else had a hand in creating things-- thought about the probabilities and has a firm grasp about the meaning of the different skill levels and difficulty numbers and dice rolls and whatever other crunchy mechanic the game uses? How is the player ever supposed to be able to have confidence and trust in the game system, that the things you specified (and that I agree with) are going to work out properly, if, at some point, someone didn't think long and hard about how to make them work out properly?

It just can't work. It's fine if the player doesn't know the probabilities, but if the GM doesn't, then the difficulty levels and whatnot are likely to be all out of whack, and there is no cause for putting any confidence and trust in the game system, because, without anyone having thought through the probabilities, your rocket scientist might only have a 1% higher chance of solving world class expert rocketry problems than Joe Average, or maybe it goes the other way and your average person in this game's world would fail at a roll to even determine that a conical object with fins on it might be a rocket, or... well, you get it. Without thinking through the probabilities, nobody knows, and I think the whole thing just breaks down.

[Xeviat]

If you're a world-class scientist with X in your "science" skill, then the DM better know what DCs (TNs, or whatever) are out of your range, and which are trivial to you.

The first time I played L5R, my GM didn't have the slightest idea as to what was an appropriate challenge. Our first fight we owned. Our second fight almost killed us. Trouble was, story wise, the first fight was supposed to be the hard one and the second was supposed to be mooks.

[Ninja D!]

The solution; Percentile!

[Lmns Crn]

You may disagree I guess.

Oh, I do disagree.

Hoo boy, did I ever see this one coming. :yumm:

So, my question is, what happens if nobody along the line-- not just the players, but the GM, the system designers, and whoever else had a hand in creating things-- thought about the probabilities and has a firm grasp about the meaning of the different skill levels and difficulty numbers and dice rolls and whatever other crunchy mechanic the game uses? How is the player ever supposed to be able to have confidence and trust in the game system, that the things you specified (and that I agree with) are going to work out properly, if, at some point, someone didn't think long and hard about how to make them work out properly?

It just can't work. It's fine if the player doesn't know the probabilities, but if the GM doesn't, then the difficulty levels and whatnot are likely to be all out of whack, and there is no cause for putting any confidence and trust in the game system.... Without thinking through the probabilities, nobody knows, and I think the whole thing just breaks down.

Maybe I've misrepresented my position, but it'd be a mistake to think that just because I don't prioritize probabilistically transparent systems, that I don't work things out.

I've described the virtues of a "system you can trust" and suggested that if you have such a system, you don't need to be able to crunch numbers all the time within it, because you already trust it. That shouldn't be taken to mean that I think trustworthy systems spring up by magic. As a compulsive tinkerer, I typically do a shitload of tinkering to any system I even think about running, whether it's my original system or someone else's. I just do a lot of this by trial and error, or by thought experiments, and not by raw probability math (because I think the latter is boring and often encourages boring system mechanics).

There's a lot of behind-the-scenes thought that goes into making a system that feels right, and there are many ways to achieve that result-- I absolutely disagree that you have to be able to run probability tests on actions within the system to write a sound system as a writer, or to get a feel for running a system as a GM. So I really have no incentive to prefer a system that makes it easy to check the probability of an action; I get to prioritize different things.

The solution; Percentile!

Oh, hell no.

Seriously: what's the one unique thing percentile brings to the table? What's the one thing I've just said I don't care about? (hint: two questions, one answer)

Occasionally there will be a really exceptional game that I will enjoy in spite of the fact that it insists on using a percentile system (hi, Vreeg!), but on the whole I think percentile is pretty awful and it takes a lot of persuasion to get me to try a percentile-based game nowadays. I can't think of a single percentile-based game that I don't think would be improved by conversion to a system less granular, fiddly, and generally odious.

[LordVreeg]

I don't need a game to have percentiles to be fun...I think it often makes more logical sense to people, since most people think in base 10 and use percentages easily.  It is merely one step less mystifying...

But as I said earlier...in terms of system design, knowing the exact percentages of everything is basically the same asr understanding context, parameters and experimental design in terms of designing an experiment.   If you haven't understood all of these while designing the game...you've half-assed it.

Now, playing is different.  Because more goes into the play experience than strict understanding...sometimes not understanding the probability is more immersive....

[sparkletwist]

As a compulsive tinkerer, I typically do a shitload of tinkering to any system I even think about running, whether it's my original system or someone else's. I just do a lot of this by trial and error, or by thought experiments, and not by raw probability math (because I think the latter is boring and often encourages boring system mechanics).

Right... but, here's the thing. If you are rolling dice a bunch of times, and seeing how they usually come up, what are you doing? You're figuring out the probabilities. The entire point I was trying to make was that it was important to have a feel for how the probabilities worked. Nowhere did I say that you had to sit there doing a lot of math; that's one way to do it, and, depending on how much you have to sort out, may be the most efficient way, but if you'd rather brute-force it and just run a bunch of tests, that's cool too. You're doing the same thing in the end. You're figuring out how the probabilities work so you can create a "trustworthy" system and design encounters intelligently, and that's all I ever meant that was essential to do.