[DEADWORLD] Help With the Math

edited January 2013 in Game Design Help
Hey folks,

I'm working on this thing. It's going to be a mashup of World of Dungeons and Deadlands: Hell on Earth. I'm creating on a core mechanic that I'm hoping functions similar to WoDu/DW/AW in effect, but with an added dimension to allow for a few more mechanical modifiers to come into play. Mechanically, it's inspired by NYC2123 RPG, *World games, Danger Patrol, The Bureau, and my old APEX system.

Here's the primer so you see what's I'm doing.

Can anyone help me make sure the math is good here? I'm pretty savvy when it comes to figuring dice probabilities with anydice.com, but the way I designed the mechanic is throwing me off and I'm unsure. Basically just wondering if I have a good sweet spot here or what the problem (if any) might be.

Comments

  • Honestly, my initial response to having 10 different stats plus a number of skills is "you gotta be kidding me."
  • P.S. Math-wise, failure seems astonishingly unlikely, compared to AW hacks.
  • edited January 2013
    Honestly, my initial response to having 10 different stats plus a number of skills is "you gotta be kidding me."
    There is quite a few terms listed there, but they're culled straight from Deadlands so I was kinda hoping to keep them. It doesn't seem too overwhelming to me. *shrug*
    P.S. Math-wise, failure seems astonishingly unlikely, compared to AW hacks.
    Hmm...
  • edited January 2013
    So, if we look at what you can roll on one die, it goes, 1, 2, 3, 4, ... n, where n is the number of sides that die has.

    The odds of rolling 3 or less on one die are 3/n, where n is the number of faces on that die. That's because it happens in 3 cases (1, 2, 3) no matter how many other cases there may be. So the odds of rolling 3 or less on 1d4 is 3/4, on 1d6 it's 3/6, and so on.

    The odds of rolling 3 or less on two dice, 1dx and 1dy, are (3/x)(3/y), or 9/xy. (Let's call this formula F for failure.)

    So, if you're rolling two poor (d4) scores, your likelihood of failure is 9/16. If you're rolling a poor (d4) and an average (d6), your odds improve to 9/24. One poor (d4) and one amazing (d10), it's 9/40. Two amazing (d10), it's 9/100.

    The odds of rolling 4 or greater on 1dx is (x-3)/x. In other words, it's all the rest of the faces. Okay, so the odds of rolling 4 or greater on 1dx and 1dy are [(x-3)/x)][(y-3)/y)], or (x-3)(y-3)/xy. (Let's call this formula S for success.)

    So, with two poor scores, your likelihood of success is (4-3)(4-3)/(4)(4), which is 1/16. With a poor (d4) and an average (d6), it's 3/24. One poor (d4) and one amazing (d10), it's 7/40. Two amazing (d10), it's 49/100.

    Everything that's not a failure or a success is a qualified success (ie., one die 4+, one die 3-). So the formula for the likelihood of qualified success is 1-(F+S). For ease, convert 1 to xy/xy, and then you can just subtract the numerators (the first number for each expression).

    For two poor (d4) scores, you get (16-9-1)/16, which is 6/16. For a poor (d4) and an average (d6), it's 12/24. And so on.

    Here's an example of a probability table, using d4 and d4:

    2 sorry scores
    1234
    1FFFQ
    2FFFQ
    3FFFQ
    4QQQS
    Success: 1/16
    Qualified success: 6/16
    Failure: 9/16

    Here's d4 and d6:

    1 sorry and 1 average score
    1234
    1FFFQ
    2FFFQ
    3FFFQ
    4QQQS
    5QQQS
    6QQQS
    Success: 3/24
    Qualified success: 12/24
    Failure: 9/24

    Here's d6 and d6:

    2 average scores
    123456
    1FFFQQQ
    2FFFQQQ
    3FFFQQQ
    4QQQSSS
    5QQQSSS
    6QQQSSS
    Success: 9/36
    Qualified success: 18/36
    Failure: 9/36

    See the patterns? The F square doesn't get any bigger as the rectangle gets bigger, so it forms a smaller part of the rectangle. The Q and S areas become bigger.

    You can figure out the odds for each combination of dice. There are 10 combinations (d4+d4, d4+d6, d4+d8, d4+d10, d6+d6, d6+d8, d6+d10, d8+d8, d8+d10, d10+d10).

    Here are some trends:

    Using only poor scores, you're more likely to fail (9/16) than to achieve a qualified success or better (7/16).

    The better your dice get, the less likely failure becomes, and the more likely both qualified and pure success become, but the likelihood of qualified success grows faster than that of pure success.

    I wouldn't call failure "astonishingly unlikely", although it does become pretty minimal when you're rolling only bigger dice. 9/100 ain't nothing, though, that's for sure, and that's the smallest it becomes.

    (ETA: For comparison, in AW, if you're rolling with +3 to your roll, you only fail if you roll 2 or 3. That means your odds of failure are 3/36, which is about 8.3%. I think that compares favourably. You're somewhat more likely to get a complicated success rolling two amazing scores on your system, though, than rolling 2d6+3 in AW. It's 42/100 in your system, which is 42%, and in Apocalypse World it's 12/36, which is 33.3%.)

    I think that's probably your intended effect! But you should run the numbers and maybe playtest it and see if things are quite where you want them.

    Hope this helps!
  • You know I hate to be that guy but...have you thought of just using Apocalypse World with some custom moves and maybe a playbook? Hell on Earth but less camp and more honest to god weird is basically what Apocalypse World is.
  • Hope this helps!
    Dude. That was awesome. Seriously, thank you.

    I think it definitely needs play testing, but if your calculations are correct, it might be fun!
    You know I hate to be that guy but...have you thought of just using Apocalypse World with some custom moves and maybe a playbook? Hell on Earth but less camp and more honest to god weird is basically what Apocalypse World is.
    Kinda. I thought about an Apocalypse World hack for Hell on Earth with the camp. But, that's not really what I want to do.
  • My pleasure!

    Another formula to figure out the odds of qualified success is (3x+3y-18)/xy.

    I think in general, rolling 2d4 in your system is roughly comparable to rolling -1 in AW, and rolling 2d10 is comparable to rolling +3. But your system is more finely grained, since there are 10 die combinations, versus AW's five-point interval from -1 to +3.

    Best of luck testing it!
  • edited January 2013
    I agree with creases on the math, and I think the concept is sound.

    I feel like there could be a more interesting implementation, though I'm not sure exactly why I have that feeling just yet.
  • edited January 2013
    http://anydice.com/program/1bc3

    I do agree with the above statement: if you want to combine trait + aptitude, you need a lot less traits. Otherwise you will - in my experience - use the same trait almost every time. In Feng Shui, you got three ways in how you use a skill: practical, knowledge and contacts. That gives three easy-to-apply traits to combine with each aptitude.

    On a similar note: I got the same issues with Vampire. Nine "traits" are to many. Three is enough.

    EDIT: it's weird, but when you roll a d6, my program says it's always 50% chance to roll one success. Can it really be so?
  • If you want to keep that many traits for PCs, I guess that's youre call, but I worry, like some other folks, that people will just default to their better scores all the time in those cases, when there's less obvious restrictions on what stat you use for what. More stats means it's more open to interpretation.

    My real worry is that you said EVERYTHING in the setting (people, monsters, etc.) has these stats. Including NPCs? That sounds like a nightmare. Or are you assuming that the GM side of things will be much simpler, like it is in AW?
  • I feel like there could be a more interesting implementation, though I'm not sure exactly why I have that feeling just yet.
    I kind of feel the same way. I mean, the dice resolution mechanic seems really cool to me and with crease's math it seems like it's producing a sweet spot that I like, but I think with some more updates/ideas, it could be more interesting. This is preliminary of course, but I agree with you.

    Now, Rickard and J, you worry about people using the same traits over and over. I guess I don't follow. With more Traits (10 vs. standard 5), each one has a narrower, more specific focus so that would lead me to believe players are less likely to be able to continually use the same Trait. Less Traits that cover more ground seem more open to interpretation, especially AW-style Traits.

    For a simple example, compare a single Dexterity Trait against Quickness, Nimbleness, and Deftness. A thief character darting past a distracted guard, then leaping over a balcony, then picking a lock on a door would engage either Dexterity (alone), or Quickness, Nimbleness, and Deftness (all three). Or maybe we use more new-school 'attitude based' Traits, like maybe "Slick"? Again, I think the above scenario would engage a single Trait vs. three.

    Can you elaborate a little if you don't mind? More than one person mentioned it so I must be missing something.
  • Quickness, Nimbleness, and Deftness all mean essentially the same thing in many RPG contexts. If I'm jumping out of the way of an oncoming rolling boulder, do I do it because I'm quick? Or because I'm nimble? Or because I'm just really good at this kind of thing (really deft, one might say)? If one of those stats is better than the others, I'll maneuver myself socially with the GM to let me roll that one.
  • edited January 2013
    Yeah, exactly. (Agreeing with Jonathan.)

    Although when I was designing the Bureau, I thought about it as a point of the design. Since I expect players to wrangle the rules a bit so they can use their better dice, I can set the odds of success (in this case, the die values of the traits) a little lower to compensate, and I think it should work out fine. I hope that makes sense!
  • edited January 2013

    EDIT: it's weird, but when you roll a d6, my program says it's always 50% chance to roll one success. Can it really be so?
    That does seem a little odd. But it actually makes sense mathematically: you're multiplying two fractions that add up to 1 by 0.5 and then adding them together to get the odds of a "partial hit" when one of the dice is a d6.

    Can you explain how you put together that code, and what each line does? I'd like to be able to replicate it with some different dice.

    Do you know how to do "roll a bunch of different dice and keep the two best results" with anydice?

  • The definitions of Quickness, Nimbleness, and Deftness are fairly straight forward and each makes a clear distinction to me, personally. I didn't come up with the list so I don't have a special designer advantage or anything.

    Per the doc:
    Deftness (hand-eye coordination, aim, and manual dexterity)
    Nimbleness (physical agility, grace, balance, and flexibility)
    Quickness (reaction, reflexes, speed, staying calm in stressful situations)


    If there is a doubt about what Trait to use, then we probably need to look closer at the fiction and figure out what the stakes are. So, given your example boulder situation, I would say the stakes of the threat is getting out of the way before you get squished (reacting quickly to the incoming danger - Quickness is the obvious choice). If I had plenty of time to react but the question was whether or not I could get to the catwalk above to avoid the danger, then Nimbleness would make most sense. If it's about reacting quickly AND/OR being agile enough to get out of the way, then I don't see a problem with the players choosing whichever thing they're better at. If it's not about reacting quickly or being agile enough to maneuver out of the way, then I don't see why you'd roll at all.

    Deftness really never comes into play as a viable argument since the situation doesn't have anything to do with hand-eye coordination or manual dexterity.

    I mean, of course there is the possibly of the fiction being a little muddy and the players wanting to use their best Trait. If the fictional risk can be interpreted in multiple ways, then it's okay for the player to try to frame their action into their better Traits (a Quick character is more likely to behave quickly).

    There is certainly a chance that players might try to exploit the system ("I Quickly talk the guard into letting me past"), but that's just dysfunctional play. The group needs to approach that on a social level. That seems to be very similar to saying "I want to push past Rourke but I don't want to Go Aggro". In this case it's, "I want to manipulate someone socially, but I don't want to roll Mien."

    All of this is at the risk of sounding like I'm just getting defensive. I'm very grateful that you guys are pointing out the potential issues. And, the more I work on the project, the more I want to do something completely new instead of porting Deadlands. I've also considered doing more AW style Traits, but I still enjoy the discussion.
  • edited January 2013
    EDIT: it's weird, but when you roll a d6, my program says it's always 50% chance to roll one success. Can it really be so?
    Well, I'm no math whizz but you roll 4+ 50% on a d6. So if you roll two dice but are only looking for 1 success, then you should get that 50% of the time (50+50=100/2=50). That's probably wrong but it seems to make sense to me.
  • edited January 2013
    Rolling 2d6, you should get a qualified success (one or the other die shows 4+ but not both) 50% of the time, and a full success (both 4+) 25% of the time. And a failure 25% of the time.
  • You shouldn't be rolling 2d6. You should be rolling better dice, or else why would you have chosen those as your stats to have good dice in? 2d6 shouldn't be the baseline, really. I'd say about a 5 feels right.
  • edited January 2013
    You're talking TN, UC?

    NYC2123 had it like this.

    Roll...
    If two dice show 5+, full success.
    If at least one die shows 4+, partial success.
    If no dice show 4+, failure.
  • The 50% thing is simple, really (although certainly not intuitive!). To get a "partial hit" in this system, you need to roll a miss on one die and a hit on the other.

    Whenever one die is a d6, there's a 50% chance of a hit and a 50% chance of a miss. But, in the case of a miss, the other die must roll a hit for the result to be a partial success. And in the case of a hit, the other die must roll a miss for the result to be a partial success.

    Add those two together, and you always get 50%, no matter what the other die type is.

    For instance, if you're rolling a d4 and a d6. If the d6 misses, the d4 must roll a hit (1/4 chance). If the d6 hits, the d4 must roll a miss (3/4 chance).

    1/4+3/4, divided by two (for the 50% chance of the d6 going either way), is 50%. It would be the same if you had a d10 (3/10+7/10, divided by two), or any other die type.

    So, yeah, any time one of the dice is a d6 in this system, the odds of a partial success will ALWAYS be 50%.

    I hope that makes sense.
  • Oh, cool! I see it on my example tables, too.
  • Paul, that's some beautiful maths right there. Really interesting!
  • edited January 2013
    Me and @J_Walton aren't talking about the same thing, as I understand. He worries about the players using their highest score all the time, while I worry about using the default score all the time. I did that in Deadlands and Feng Shui and I've seen other GM's do it in Vampire where all games specifically states that different traits (or whatever they are called) should be combined with different skills depending on the situation.
    Now, Rickard and J, you worry about people using the same traits over and over. I guess I don't follow. With more Traits (10 vs. standard 5), each one has a narrower, more specific focus so that would lead me to believe players are less likely to be able to continually use the same Trait. Less Traits that cover more ground seem more open to interpretation, especially AW-style Traits.
    More traits creates more work in decide which trait to be used in a given time. If you got one million traits with a really specific areas, you will probably go with the one that you used the last time you used that skill. It's just to much time and effort to decide which of the million traits you got. I noticed how I was more enable to change the base trait for each roll when I narrowed down from Feng Shui's twelve(?) attributes down to four.

    That said, I would go with ten traits if all of them wasn't used with skills. If Strength only was used to give damage, if Quickness only was used to determine initiative, or if Spirit only was used to resist horror, but you should in that case differentiate those with the ones who are combined with skills. Perhaps not in how you categorize them, but in placement in the game text and character sheet.
  • I agree with creases on the math, and I think the concept is sound. I feel like there could be a more interesting implementation, though I'm not sure exactly why I have that feeling just yet.
    Still beating my head against the wall on this one. I totally agree that the probabilities of the system are hitting a sweet spot and I want to harness it. But also agree that Attribute+Skill is not the most interesting implementation. I think the pairing of two sources to get the pair of dice is a solid method - intuitive at least.

    In an effort to keep it simple, I'd say maybe...

    "When you do something risky, roll 1d6 and the Attribute Die that makes the most sense for the action you're taking. If both dice show a 4+, you get a Full Success. If one die shows a 4+, you get a Partial Success. If no dice show a 4+, you get a Failure."

    With that approach, it's pretty quick and easy to figure out what to roll, and it provides a consistent 50% chance to get a Partial Success, which I dig. Still feels a little uninspired though.

    Then I thought, why not make that core D6 variable? Maybe you select your core die from a pool of dice based off of what you're doing? Like...

    The Peril Die (d4) - Roll this when you're acting despite having a condition that would make this action difficult.

    The Risk Die (d6) - Roll this when you're acting under normal circumstances.

    The Skill Die (d8) - Roll this when you have a Skill that applies to the action.

    The Hero Die (d10) - Roll this when you're really hoping to succeed. If you get a Partial Success or a Full Success, discard this die for the rest of the session after you roll it.

    The Legend Die (d12) - Roll this when you're really, really hoping to succeed. If you get a Partial Success or a Full Success, discard this die for the rest of the session after you roll it.

    Which lead me to thinking about designing the character sheet to have printed "slots" where you actually place the physical die on your character sheet (for ease of reference). So you would have your attribute list with slots next to each attribute large enough for you to actually place the die for that attribute in the slot (as well as pencil in the die type in the slot for reference). Then you'd have your Dice Pool at the top of the character sheet with slots for each type of Dice Pool die. I did a quick hand-drawn mockup and it seems kinda novel, albeit a little gimmicky.

    What do you guys think?
  • This is definitely moving in a more interesting direction now.
  • Maybe this will inspire you in some way?

    Dice discussion from barf forth
  • Random idea: you could mix the die selection with player agency type stuff (i.e. choosing a "bad" die when you could choose a "good" die gives you a benny to spend later or whatever, but also adds a narrative complication, yadda yadda).
  • In the Dungeon Girls thread, there is a magic sword which can "store" a die result, and you can use it to swap in and out of rolls you make when using the sword. This generally means having to take a failure or a worse result in exchange for a bonus later, which is a neat effect.
  • edited February 2013
    Nice!

    The link to Barf Forth is interesting. Thanks for the link, Paul! Different approach, but interesting none the less.

    The "Scourge" approach of storing a value is interesting. I'd have to play with that one a bit to make sure I have a good idea of how it works.

    I like the idea of player agency-based dice. I'm intrigued by mechanics that encourage players to volunteer their characters for mishap and complication. Like, there was a couple times in the DungeonGirls thread where a kid decided to have their character put into danger or get knocked out of the action, which I thought was awesome.

    I need to ponder on this more, but feel free to fire your brain storms at me.
  • Okay, so I put some further thought into this one.

    Scourge won't work here as far as I can tell. Scourge works with World of Dungeons because each die's total is being added to a sum, whereas in the system we're working on in this thread, each individual die is essentially a binary yes/no. Maybe it can be applied in a different way?

    I really like the idea of incorporating player agency. I'm thinking about bringing it in through another pathway though. Players can opt to forfeit a roll (choose to accept a Failure and eat the consequences voluntarily in the name of good story) in exchange for a benny. One of the things I planned to do is have players mark XP when they fail a roll, and also when they spend a benny. So, when you forfeit a roll, you mark XP for the failure and get a benny, and you mark xp again when you spend that benny. I feel like this is quite a bit of incentive to occasionally let your character get slammed.

    What a bout a sliding dice-type scale. Start at D6. If you have a Condition or otherwise there is something making this action really tough beyond the norm, downgrade. If the action fits your background, upgrade. If the action fits your alignment, upgrade. If you have a skill that applies, upgrade. Spend a benny to upgrade.

    I wonder if that would be bad on the handling-time...
  • Ohhhh! Hey what about Dogs style Traits? Like, you might have:

    "I spent the formative years of my childhood on the streets" d8
    or
    "I'm very comfortable dealing with people on the street and finding my way around" d8
    or
    "I'm a city slicker" d8
    or
    "Street Savvy" d8

    So, you write your Trait however you want and assign a die type to it. When that Trait applies to the situation, you roll that along with your Attribute die. Otherwise, if you don't have a Trait that applies, you roll a d4.

    That would be an interesting take...
  • That's basically like The Bureau, right?

    You'll face all the challenges you normally face with freeform traits: how limited can they be? How often can they apply? Etc.
  • edited February 2013
    Yeah, you're right. The Bureau does have that kind of thing. I love The Bureau, so that's not a bad thing at all, but you're right about the limitations. There would be nothing stopping someone from saying:

    "I'm an excellent combatant" d12.

    Now they're roll a d12 for anything that has to do with combat, which I don't want.

    Good call Paul.

    This would be an interesting approach: http://dailyosr.blogspot.com/2013/02/capabilities-and-heroic-actions-osr.html

    Not much different from the normal Skill system though.
  • edited February 2013
    There are lots of interesting ways to design around freeform traits being a problem! Let's talk about those.

    For instance:

    1. Pay to succeed/earn to fail. This is like Fate Aspects: you decide when they apply, but it costs you. If the "trait" is a bad thing, maybe you get a reward every time it comes into play, instead. Then you don't need to worry about how broadly traits apply.

    I have a game ("The Camel's Egg") where you assign dice to your equipment. For instance, you can choose to assign three dice to your sword. They act as a resource: three dice means your sword is really important. Each time you use the sword, you can spend any number of those dice, but they disappear when you spend them, so choose carefully.

    2. Traits are defined in some more specific way, appropriate to the genre. For example, My Life with Master's "more than human/less than human". If you have a conceptual framework which tells you how a trait works, you can make a design system which feels fair, because it gives you both advantages and disadvantages to work with.

    3. The game is designed so that the more traits you pull in, the better. Dogs and the Bureau both do this. You're *supposed* to use your best traits, or as many of your best traits as possible, all the time. It's built in, in one way or another.

    Danger Patrol has this sort of effect with Danger dice. In some other games, whatever traits you use in a game action are at risk somehow: maybe if you lose, the opponent gets to lower one of them, or you ante them in conflict, and they are "exhausted" or reduced on failure, that kind of thing.

    In the Pool, using Pool dice works like this: sure, use as many as you want, but if you fail, you lose all the ones you used, so be careful.

    4. The game has defined arenas or types of actions. While the traits may be freeform, we know how and where they apply; that's set.

    For example:

    * Weapons in Old School Hack/Red Box Hack. You can make up any kind of weapon you want, but we assign it a category (e.g. "heavy", or "ranged"), and that determines its strengths and weaknesses.

    * Particular Strengths in IaWA. You can describe whatever the hell you like for your PS, but the system tells us that it only applies in certain contests (depending on the options you choose).

    * Apocalypse World does this, too. Your stats are pretty vague: you could make an argument for why being "sharp" could help you spot a danger and avoid it. However, the game tells us that, no, sharp has nothing to do with acting under fire: it's linked to the reading moves. You could do this with freeform traits, too: make up a stat, and we decide which basic moves it affects. So you can say your character is "Fucking Metal", and write down that it adds to going aggro and manipulate/seduce.

    * I've been thinking of doing this in Dogs, too. As written, you can write a Trait which applies to almost any conflict. One player had a "piercing stare" Trait, which of course came into play in pretty much every conflict every rolled. So what if we made a rule to balance Traits: when you write your Trait, you pick two arenas of conflict where it can apply. Your stare? It's only good when talking or gunfighting. Can't use it in a physical or fighting conflict. Your memories of your father only help you in a fight or while talking. And so on.

    5. There is a counter-balance to these wide-open abilities. This can fictional: in World of Dungeons, you can do pretty much anything with magic, but there will be a price or a twist based on your bargain with the demon(s). Or it can be at-the-table: like in Mortal Coil, where you can use magic to do anything you want, but another player gets to determine what the cost or limitation of that thing you're doing is.

    Can we think of some other options?
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