Probabilities, mechanic tweak, blathering pointlessly

[taalyn]

After reading Mike's rant again, I've decided what will happen re DL and my mechanic. Simply draw vs. skill - opposing skill (whether that's Doorness or Joe Bob Spriggan's 'Hurt People' skill). One thing that's always annoyed me about WoD and similar systems is calling them successes when they aren't. If they were really successes, I'd succeed, right? So I want to avoid successes unless they really are.

  This comes from a simple algebraic transformation similar to the one that ended up as skill-2d10. The basic draw starts as skill vs. skill. Quick switcheroo makes it simply skill - skill. If this results in a negative hand (hand=dice pool), then it's up to the player to argue for more motes to bring it into the positive realm.

  Examples:

  Jonas(STR 4) breaking down a door (Doorness 3). Jonas really needs to get thru, so he uses 3 Luck for an extra mote. He pulls his two motes, target red, gets red and amber. That's either 3 successes (adjacency) or 2 successes + 1 more if he can argue convincingly how artistically he accomplishes the task  (stacking - and I need better terms for these!). In either case, he succeeds.

    Now, Jonas (Softball R8) vs. Spriggan (Watch TV Sports G4). Jonas draws 4 motes (his 8 - Spriggan's 4), target red. Gets RGGB. Adjacency: 2 successes. Stacking: 2 + 1 for knowing how to fake out an amateur (G), +1 for focusing and concentrating (B), 4 successes.

    I like this a lot, but I am sort of worried about the one-sidedness of color. That is, only the good stuff is likely to be described. Should there be a small mote draw that may apply, to add this opposition color? I.e. draw 1 mote to subtract a success with adjacency rules, or -1 for description? Or perhaps even a range of opposing motes based on the number of motes drawn (1 opposing mote for every 3)? No answer is really necessary - I'm partly using the forum as a blog of sorts - a place to note my ideas where others, if so inclined, can say something about them.

  Now, what I do hope for an answer on: Mike, can you help me figure out formulae to calculate probabilities for various sorts of Caerns? If I figure out odds for several different kinds of caerns (where color isn't so important, but the relative amounts are - unbalanced favoring 1 trait, unbalanced favoring 2 traits, evenly balanced, etc.), I can add them all together to get some good average probability sorts of things.

 On the other hand, maybe my new method makes this a pointless number crunching exercise.

 And then I also wonder if this will introduce a necessity for different mechnics (particularly re: magic and combat), which I want to avoid entirely.  

  And I'm more than happy to have only players draw as The GM will have plenty of other stuff to do.

  Aidan

[taalyn]

Using this new system works well for magic. Weaves are normally less than 10 motes in complexity, and same goes for simple tasks (doorness over 10 is highly unuisual, for example). So the Evilness(tm) of Subtraction is not a major issue - it's subtracting small numbers.

For magic, the test was originally going to challenge the caster's technique to weave, with a DL equal to the complexity of the weave. A spell with 4 motes is DL 4 to cast successfully - now, the DL is just subtracted from the skill and get a success. This works great.

Combat, though - still thinking. Also wondering, does opposing "skill"'s color apply at all - is it relevant or intrinsically a part of the task? I think not, but....

Still cogitating the opposing color - providing detail on complication as a means to create tension. Hmmm...

A.

[Mike Holmes]

I can help, but only if you can ask the questions correctly. Too often people say that they want to just "know the odds" but don't even really know what they're asking for.

What I'm guessing you want to know is what the odds are to get a certain number of "things that aren't successes, but like successes" (matching draws), given a certain number of draws, and a caern of a certain size, with a particular number of motes of the appropriate types and adjacent types? I could do that, but only if three of the five dimensions are kept small, or just one size.

For example:
Caern: 45 (just one size I heard tossd about)
Correct Color Motes: 5
Adjacent Motes: 10
Draws: 1 to 15
Matches: 0 to 20

Would that tell you what you need to know? You could then modify some variables for a second run.

Mike

[taalyn]

Heya Mike,

 here's what I need to specify, know about:

 Caern: it's makeup (how many red motes, etc., as well as total # of motes)
 correct color motes and adjacent motes can be determined from that
 Draws: 1 to 15 (or even 10 would probably be enough)
 Matches: yeah, same stuff

  Here's what I want to do. Plug in the composition of the caern, and have it spit out the odds of getting any given number of successes. Taking a clue from a suggestion in the thread I started over in theory about probability, I got a book on probability calculation, so i think I can now work out the adjacency probabilities. I may bug you (pm wise) if I get stuck, though. Is that okay?

  The other question is if there is any way to account for / (gu)es(s)timate stacking successes? If not, I'll deal, fudge it, or some such. Maybe if I allow that, say, 25% of the hand will be used that way (2 motes of an 8 hand draw could be explained as successes), is there a way to incorporate these odds into the procedure?

 Thanks for the help, BTW.

 Aidan

[Mike Holmes]

Yer making my head spin.

Heya Mike,

 here's what I need to specify, know about:

 Caern: it's makeup (how many red motes, etc., as well as total # of motes)
 correct color motes and adjacent motes can be determined from that
 Draws: 1 to 15 (or even 10 would probably be enough)
 Matches: yeah, same stuff

  Here's what I want to do. Plug in the composition of the caern, and have it spit out the odds of getting any given number of successes.

That's not a coherent statement of intent. "Composition" only matters in terms of how many motes there are of the appropriate color (which doesn't have to be determined), and the number of adjacent color motes. Thus you'd input 5 "matching motes" and 10 "similar motes" or whatever you want to call them. Anyhow, apparently you want a formula. I usually do charts and display the odds, because I often derive the formulae non traditionally, or I just use the brute force method (using a spreadsheet to roll a jillion times). As charts it would take a lot of space. The problem with a formula is that it doesn't tell you anything until you empoloy it, and then you'll need to fill up the spreadsheet again anyhow.

Given what you're after, you're looking at potentially hundreds of charts and tens of thousands of entries. Which won't make analysis any easier.

Taking a clue from a suggestion in the thread I started over in theory about probability, I got a book on probability calculation, so i think I can now work out the adjacency probabilities. I may bug you (pm wise) if I get stuck, though. Is that okay?

Uh, sure. So you don't want the tables, I take it?

The other question is if there is any way to account for / (gu)es(s)timate stacking successes? If not, I'll deal, fudge it, or some such. Maybe if I allow that, say, 25% of the hand will be used that way (2 motes of an 8 hand draw could be explained as successes), is there a way to incorporate these odds into the procedure?

No idea what you're talking about here. I must have missed a post. What's the difference between "stacking" and "successes", etc. You need to define these terms before we can look at it.

 

Thanks for the help, BTW.

I'm feeling less of a help to you by the minute. :-)

Mike

 Aidan[/quote]

[taalyn]

Okay, yeah, I don't need tables. Here's what I'm going to do, and you can tell me if I'm missing something. The goal is to find out the average chances of getting X successes with a given effective hand (EH = skill - skill), as regards certain kinds of caerns (#1), as well as across all varieties of caern (#2):

 1) have a set of composed caerns: one that's exactly balanced, one that's extremely biased to one color, one that's biased to two colors, and so on. Each caern's make-up will be specidied. Then I'll calculate the odds/tables for these 10 (or whatever) caerns, using adjacency rules (adjacent motes = 1 success), specifically to have some baselines to understand the next part.

 2) randomly create a gajillion caerns (1-10 of each color, frex.), calculate the odds by adjacency, and add them all together, to get average results independent of caern makeup.

 3) do both parts above for "stacking" rules.

  "Stacking" is an alternative success-generating method. I don't like the term "stacking", but here's how it works: you get 2 successes for each appropriate color. But that's it - no adjacency successes. Instead, if you can argue that a particular mote represents some aspect of the task that you do well and that contributes to success, it counts as 1 success. For example:

  Our favorite guy Jonas is trying to slip some magic dust into his boss' coffe, so that she'll hallucinate him at work while he's off beating up spriggans. His dex is 5, her Bossness is 3. Skill-skill, so he draws 2 motes, aiming for cyan. He gets a red and a magenta, no success. Derek, Jonas' player, argues that the magenta (social skills) is his getting the boss involved in a conversation, distracting her while he puts the dust in her coffee. The GM allows it, Derek got 1 success, and Jonas succeeded.

   That's stacking - as I said, I hate the name, but don't know what else to call it at the moment.

    And you may not feel it, but you are helping!

   Aidan

[taalyn]

I just realized, that's huge amounts more than I need to do. All I need to do is calculate odds for a balanced caern, since over a gajillion random caerns, the odds will settle around the results for a balnced one. Now I just need to figure out how to guesstimate how to deal with stacking - if at all. It might be a non-issue as well, given the grittiness of the game in general. Anyway, I think can figure out the probabilities fairly easy now.

Aidan

[Twinsoul]

effective hand (EH = skill - skill)

Hmm just a question, what if your skill is lower than your opponents skill. Does that mean that you can have a negative hand?

[taalyn]

You've posed 2 questions, one here and one on the the other thread. I'm going to answer them separately in each place.

Anyhoo, yeah, you can have a negative hand, meaning that without extraordinary measures, you just can't do it.  Jonas has Latin G1 - he sucks. He needs to read a text in Latin (Latinness 3). His effective hand is -2, no way he can do it, unless he spends Luck and/or Boons (and even that might not be allowed), or casts a spell, or finds some other way to rapidly improve his Latin.

  Aidan

[Brian Leybourne]

You've posed 2 questions, one here and one on the the other thread. I'm going to answer them separately in each place.

Anyhoo, yeah, you can have a negative hand, meaning that without extraordinary measures, you just can't do it.  Jonas has Latin G1 - he sucks. He needs to read a text in Latin (Latinness 3). His effective hand is -2, no way he can do it, unless he spends Luck and/or Boons (and even that might not be allowed), or casts a spell, or finds some other way to rapidly improve his Latin.

  Aidan

Uhh.. doesn't that lead to some serious problems though? I'm up there with the worlds best fencers (say), with Fencing 6. Geralt, the guy I hate, is also up there, he's slightly better than me with fencing 7.

I have zero chance of hitting him unless I spend SIX luck points and that only gives me a single mote...?

No sir, I don't like it at all. As soon as someone is better than you at something (even slightly), you're screwed. Surely a draw-off is better because it gives everyone chance (but the higher skilled person still has the better chance because they're drawing more motes), even though it means the GM having to draw motes as well? The GM would of course have a balanced composition at all times for all NPC's to save having to rearrange every time he's drawing for a new NPC.

Brian.

[taalyn]

Uhh.. doesn't that lead to some serious problems though? I'm up there with the worlds best fencers (say), with Fencing 6. Geralt, the guy I hate, is also up there, he's slightly better than me with fencing 7.

I have zero chance of hitting him unless I spend SIX luck points and that only gives me a single mote...?

No sir, I don't like it at all. As soon as someone is better than you at something (even slightly), you're screwed. Surely a draw-off is better because it gives everyone chance (but the higher skilled person still has the better chance because they're drawing more motes), even though it means the GM having to draw motes as well? The GM would of course have a balanced composition at all times for all NPC's to save having to rearrange every time he's drawing for a new NPC.

Brian.

  Ahh, see, I knew there was a good reason why this was bugging me. And why I was here (I spent time at RPGnet and got tired of the high noise ration). People who will actually point out the problems.

  Okay, first - your effective hand would be -1, costing only 2 Luck to get you back to positive, not six.

  Second - you have a good point. That hadn't occurred to me, though something was nagging in the back of my brain. This is why I'm so keen on my probabilities.

  Difficulty Level (DL) will correlate to a skill level: DL basically equal to the mean number of successes for that skill. This will counter the problem you point out above, as well as my generic DL issue.  Basically, a return to DLs proper, with the DLs removed from the end and stuck on the beginning of the draw. As I've said, calling them successes bugs me if they're not actually successes.

  Better? You can still add a mote to the draw with luck, still add an autosuccess/Boon, and it's still possible to get negative hands (but only if your skill is pretty terrible).

  Aidan, thinking he needs to finalize this stuff better before he blathers on about it

[Brian Leybourne]

Okay, first - your effective hand would be -1, costing only 2 Luck to get you back to positive, not six.

Sorry.. I thought it was 3 luck per mote. My bad.

Difficulty Level (DL) will correlate to a skill level: DL basically equal to the mean number of successes for that skill. This will counter the problem you point out above, as well as my generic DL issue.  Basically, a return to DLs proper, with the DLs removed from the end and stuck on the beginning of the draw. As I've said, calling them successes bugs me if they're not actually successes.

  Better? You can still add a mote to the draw with luck, still add an autosuccess/Boon, and it's still possible to get negative hands (but only if your skill is pretty terrible).

Hulk brain hurt. Can you repeat that in English? I'm not quite sure I follow you (actually, I'm very sure I don't follow you).

Brian.

[taalyn]

Brian, it's not your fault. Too many years writing obscure philological papers. Plus, I've changed some of the details but haven't explained them here - partly because I keep changing them. I thought I should keep them to myself as much as I can, until I'm sure of stuff. Of course, then people point out glaring mistakes, so...

The system is still all-opposed draws. The opposing skill, instead of being subtracted directly, corresponds to a number N. N is the average number of successes for a hand the size of the opposing skill. Frex, with a hand of 8 the average number of successes is (say) 5. Jonas with Hittite 7, against a text of Hittiteness 8, would draw 2 motes (his skill 7 - 5, the DL corresponding to a skill of 8). Any successes he gets are actual successes. This is :
skill >= DL becoming skill - DL >= 0.

 Did I explain it better that time, Hulk? :)

 Aidan

[Shreyas Sampat]

Aidan,

Why not simply allow the entity with the higher relevant skill draw stones?  Then you don't need to bog yourself down with this weird transformation of numbers for less-skilled opposition.

Maybe you could have a system where stones get drawn from the bag of the "active character", while the number of motes drawn is the difference of skills, and the character with the advantage gets first claim to motes, and then the disadvanaged character gets t pick out of the leavings.  This way, you can even have partial success of both parties.  With mutually exclusive success, you can just say that after motes are claimed, only the character with the greater number of motes can actually succeed, but the other can still lookcool while failing.  The idea behind this is that it should bias the outcomes (over time) toward the active character, while still giving the advantaged person an opportunity to excel.  Also, you can save yourself the trouble of having a GM stone bag by basing NPC draws on player bags.

Hm.  That confused me, so let me try to come up with an example:

Yamina the shamaness is asking her totemstaff, Headstick, a question about the future.  Headstick responds in his accustomed cryptic manner, and Yamina has to decipher it.

This is Headstick's Enigmatic Prophecies-6(Blue) against Yamina's Decipher Looney Ravings-4(Green).  We determine that it's Yamina's performance that will actually determine the outcome of the event, so we draw out of her stone bag.  Two stones, for the difference between skills.  Cyan and Amber.  Headstick claims the Cyan as an adjacent success, observing that his prophecy was very elegantly crafted - in perfect heroic hexameter.  In Greek.
Fortunately for Yamina, she can claim the Amber stone as an adjacent success, and does.  She mentions that she learned some Greek from an actor she loved while studying occult glassworking in Venice.  She deciphers one line of the poem, but it doesn't tell her anything useful.

[Brian Leybourne]

4WW - I quite like that idea. The concept would be that each side picks one at a time, so if there's an odd number the higher skill always gets one extra? This also introduces a little strategy into what you pick, I could (for example) pick a color that is only adjacent, instead of another color that would give me 2 successes, because the color that is adjacent for me is 2 successes for my opponent and I want to deprive them of those 2 successes, etc. Tactical thinking. Nice.

Aidan - I understand now, the only problem I can see is how to work out the average pull for a skill level X given that the composition is variable. The GM would be stuck working out that average on the fly each time.

And, it still means that if someone is twice as good as you at something you're back to relying on using luck points to draw at all. Surely it's better to get both parties to draw and compare successes? (Not trying to tell you what do do, it's your game, just being devils advocate and making you think *grin*). 4WW's idea wasn't bad either.

Brian.