Unusual dice systems you likeNo d20 or 3d6 + modifiers here.Post dice systems you like and why.For me, although the game itself is not my favorite, I really like The One Ring's d12+xd6 system. It doesn't have such an extreme differential between increments of d6 as straight d6 dice pools have, since all rolls start with a flat d12 that mellows out the difference, yet each additional d6 still feels significant. in d20 dnd terms, each additional d6 averages out to the equivalent of roughly +2.5.
I like this, it gives me a median of 0.In a dice pool system like the d6 system, this makes it easier to visualize how hard is a check, since if I roll 4 d6s, I know a difficulty of 4 is a 50% chance.
OVA's dice pool (roll 2+bonus d6, add matches, pick largest) is pretty neat, though the probability curves look shit and have "gaps". Minimum rolls increase very slowly, typical rolls get better faster, and a long tail gives occasional spectacular results without the extra rolls or unbounded nature of exploding dice.
>>93413373There is something to be said for die systems with tiers of impossible rolls. Say 5e's d20 vs d12+nd6, n up to 3With 5e's DC system (6 DC up to 30) there are only 2 DC an unskilled player cannot achieve. With the alternative, there are 4.Only issue is each roll takes more time to calculate. This can be solved with a die ladder rather than increasing number of dice. Or a roll and keep system.Let's say all players combine a base die, attribute die, and skill die and keep the highest two. Base is d8. You could have d6-d12 for the att/skill. Six DC if 4-24 would give an average unskilled person (2d8) access to 4 DC like 5e, but with much lower chances to succeed high while highly skilled can achieve all, but the most impossible tasks are incredibly unlikely.Issue with that is the probabilities are far more nebulas.
Ok, so question, even if for a board game.I'm a mathlet, so please be patient with meYou roll 2d100. Each die acts separately, but they still are going to create a curve (right?) and they can be applied at once, so they really are a 2d100 roll, even if each die graded separately1 and 100 are crits, so let's exclude them for a moment, as they aren't important here2-5 penalties eroding success (-1 at 5, -2 at 4 etc)6-19 fuck all20-30 + 1 success31-45 + 2 success46-59 + 3 success60-75 + 4 success76-90 + 5 success91-99 + 6 successSo on roll of 2d100 (remember, each die operate separately), what is going to be your average success from such roll? Remember, there are values eroding and for the sake of argument, it's really 2d98, since neither 1 nor 100 are to be accounted.I have no fucking clue how to calculate it, since it has three different ranges: penalties (2-5), nothing (6-19) and successes (20-99)
>>93413373I am a 2d6+1d10-2 Aryan giga uberchad
>>93416295A combined +6 at 13.1%.And you've got a 50.98% chance of at least 6 combined successes.97.06% to stay non-negative.Excluding 1 and 100 is fucking with the numbers though.
>>93416295By the way, as an addendum to >>93417691>6-19 fuck all>20-30 + 1 success>31-45 + 2 success>46-59 + 3 success>60-75 + 4 success>76-90 + 5 success>91-99 + 6 success>0; 14>1; 11>2; 15>3; 14>4; 16>5; 15>6; 9That's hella ugly and inconsistent.
>>93417691Ok, so theoretically, an average outcome of 200d100 with such set up would be 582 successes (97% out of 100*6)?>>93417824It's intentionally uneven
>>93417898>an average outcome of 200d100 with such set up600.>(97% out of 100*6)?What?>intentionally unevenWhy?And how are crits supposed to work? And what about the four different crit&crit combinations?
>>93413373It might be just because it's what I got used to, but like WoD's dice system. In WoD, you roll d10s equal to your stat+skill for checks, anything above a 7 is considered a success. That means things you're untrained in have a low but possible chance of getting a at least one success, and better skilled actions have a fairly reasonable chance of getting one or more successes. Getting 5+ successes though is very rare mostly because dice pools don't get that big, though possible if you roll 10s as rolling a 10 gives you a success and lets you roll again (exploding dice).The storyteller can modify a roll in various ways beyond just adding or subtracting dice from the pool like increasing or decreasing the target number for a success or making 9 or even 8 explode if you roll it, but pretty much no matter how its modified, a player still has a reasonable chance of failure on any action, so someone who min-maxes will still have to deal with poor rolls on occasion. There's never a point where your skills are so high that you're basically safe from things going wrong.
>>93417944The general idea is a rapid catch-up to allow people just ignore having to roll for 50 or 100 turns they are behind, but also account for the penalty outcomes. Crits are excluded, because their outcomes are pretty drastic.>What97.06% to stay non-negative.You see, if this was all about just having average outcome of rolling 2d600 hundred times, I know how to get the value.I need to account in those the fact a penalty outcome might come up.In reality, a 1d100 outcomes are>rare-4-3-2-10+1+2+3+4+5+6But they aren't spread evenly - the penalties have each just 1% chance of happening, and the 0 outcome is the largest bracket of them all.Hence: I need to know what's the average outcome of rolling 2d100 for 100 times in accordance with potential penalties and null outcomes, too, rather than "it's going to be just 6*100">WhyBecause those values are adjustable as the game plays on
>>93418062*ignore the>rare
>>93417945Try Ubiquity for comparison. It's very WoD-like, but 1) it works and 2) they did their math
>>93418062>Crits are excluded, because their outcomes are pretty drastic.Only more reason to include them. Explain what they're supposed to do and how they work. Is the outcome of a 1 identical to that of a 100? What about a double 1? 1+x? x+1? 100+100, 100+x, x+100? How do they affect the range of possible outcomes of a roll (which is currently all integers from -8 to 12)?>In reality, a 1d100 outcomes areYou forgot about the second "rare" for 100. And in the end the individual results don't really matter, as the sum of both is the relevant aspect, is it not?>they aren't spread evenly>I need to know what's the average outcomeDo you mean the expected value? That's roughly 5.429 per roll, or about 543 in total. But not for "rolling 2d100 for 100 times", but for "rolling 2d98 for 100 times", with the numbers you provided.
>>93416295>I have no fucking clue how to calculate itGrab your favourite spreadsheet software (which should be LibreCalc).Create a 2-99 column listing the results of your gimped d100. Slap their mapped results (-4 to +6) next to them.Use that to turn your d98 into a weighted d11. Use COUNTIF() with the mapped results as variables (or count them manually like a peasant), and then some basic division (count of individual mapped result divided by 98) to do so. Each in their own column. Voilà, you've got the probability for each face of your weighted d11.Since you're summing two weighted dice and are a self-admitted mathlet (time to change that if you're serious about what you're doing), don't bother with combinatorics and do it exhaustively, spreadsheets are good at that.d11 #1 into a column, 11 cells -4, followed by 11 cells -3, etc. Skip one column. Third column: next d11. Cycle through -4 to +6, 11 times. Bam, all 121 possible combinations. Skip one column. Sum both colums into the fifth to get the actual result (-8 to +12). Grab the previously calculated relevant d11 face probabilities (LOOKUP() is your friend) and slap them into the second and fourth colums. Multiply those into the sixth.You'll end up with something like this:>-4 || 1.02% || 3 || 14.29% || -1 || 0.15%>result of -4 on the first d11 || probability of that result || result of 3 on the second d11 || probability of that result || sum of both results || probability of that sum (product of the involved probabilities)Now all you have to do is sum up the probabilities of the sums (i.e. those of the actual results, -8 to 12) in your huge list. One column with the values (-8 to +12) used as the variable for the second, the next one for the final probabilities (via SUMIFS() for example). That's basically it. Sum the probabilities to go from "exact" to "at least". Or sum the 21 products of probability and result to get the overall expected value.And now you can fiddle with your numbers.
>>93416295>>93419546That said, all of this is pretty much worthless without including the crits and their effects, and moving on to the actual d100s.
>>93416295>Each die acts separately, but they still are going to create a curve (right?)No.I'm not sure you even know enough to describe your problem properly, because you keep jumping between results for a d100 (but ignoring 2 values and invalidating the whole thing anyway), 2d100, 200d100, and 2d600. None of which are the same thing.
>>93419905>No.If you do the math and look at the final number of successes, they are definitely not uniformly distributed, and the probs are indeed "curvy". Not at all surprising, since you're adding two inputs together.
>>93418147>Do you mean the expected value? That's roughly 5.429 per roll, or about 543 in total. But not for "rolling 2d100 for 100 times", but for "rolling 2d98 for 100 times", with the numbers you provided.Ok, so a mathlet question is: how does this value comes up? In details, and slowly.Even if >>93419546 got it covered in his method.>>93419546>time to change that if you're serious about what you're doingThis is literally the most complex piece of math of the whole ruleset, and stands out, too. Everything else is the most basic and regular adding and subtracting to 100. And so far, this wasn't even a thing, people just had to roll dice in quantity to catch up - precisely because I don't know how to turn it into an automated procedure.>>93419551The crits are excluded, because the goal of this method is to not have them. As in - you get fixed amount of successes for the turns you are not rolling, which is the average possible outcome for the amount of turns. But because you aren't rolling:- you don't get crits (of either kind)- you don't get your faction bonus applied- you don't get regular, build-up bonuses that would affect dice outcomes along the gameplay.To put that into some context:You can keep rolling your dice to build farm fields, and along the way, the bonus from improving your agriculture will apply, which will change the value ot the dice outcome in your favourORYou just use fixed amount of successes (the average amount, including penalties and null outcomes) as a raw value, umodified by anything. In other words - eventually you get significantly LESS than if you were rolling, because the bonus can grow big enough to make even a penalty into a succcess. And you don't get this if using the fixed valueThe goal of this is allowing a quick and effective catch up of players not present for some duration or joining late to the game, so they can safely and securely get basic stuff done, save themselves time and then switch to regular rolling
>>93419905Maybe it's just a matter of me explaining the problem poorly - >>93419546 seemed to get everything I'm doing, other than the confusion why I'm so incompetent about it.
>>93420080>how does this value comes up?>https://en.wikipedia.org/wiki/Expected_valueWhat you've most likely been doing to derive the expected value of fair "standard dice" is adding the lowest and highest faces together and dividing by two. (1+6)/2 = 3.5 for a d6 and so on. That doesn't work for weighted dice. For more general cases you multiply each face with its probability and then add up all the products. Works for fair "standard dice" as well.>1*(1/6) + 2*(1/6) + 3*(1/6) + 4*(1/6) + 5*(1/6) + 6*(1/6) = 21/6 = 3.5In your case that looks something like this>(-8)*P(-8) + (-7)*P(-7) + ... + 11*P(11) + 12*P(12) = 5.4285714286with the added complication that P(-7) is equal to P(-4)*P(-3) + P(-3)*P(-4), that P(-6) is equal P(-4)*P(-2) + P(-2)*P(-4) + P(-3)*P(-3), and so on.>This is literally the most complex piece of math of the whole rulesetYou're nonetheless attempting to design a ruleset, thus "I'm a mathlet" is not something you should be saying proudly, but something you should be trying to fix.>which is the average possible outcome for the amount of turnsBut the "average possible outcome" is affected by those crits, since you stated that "their outcomes are pretty drastic". So, what are those outcomes? Excluding them from this calculation will very likely invalidate it.
>>93420261>You're nonetheless attempting to design a ruleset, thus "I'm a mathlet" is not something you should be saying proudlyExcept I'm not proud of it. But I'm more than aware of my limitations. Ask me to do geometry, we can do that, since I'm a land surveyor and a certified helmsman. Probabilities? Tough fucking luck, as last time it was of any use to me was in high school, 20+ years agoWhich is also why the ruleset so far is:"Roll 2d100, compare with outcome table, add results from table".This isn't rocket science.But counting weighted probabilities of dice roll is - or at least it is for me. So far, I didn't even need it for anything at all, precisely because I can't do the computation and don't even know where to start, but people are complaining that it's a chore to catch-up by rolling loads and loads of dice. If I'm to provide an automated option, I need to do the math that I'm clueless about (on top of it being explained to me in English, which means I have to check in dictionary what is what and then check in different dictionary to grasp what that is after translation)>But the "average possible outcome" is affected by those critsWhich part of "crits are deliberately removed from the pool to entirely and deliberately remove high-risk element" I need to repeat for the n-th time for it to finally sink in?Ok, let's simplify it to the most basic stuff (since I can't make it work in excel as described by >>93419546, it just throws errors):Is - in the described circumstances of weighted dice - the average sum of successes from a 200d100 roll 543 (rounded up from 542.85714286)? And does it also mean that - again, same circumstances - 20d100 gives 54 successes (rounded down from 54.285714286)?
>>93419933>If you do the math and look at the final number of successesThen you're not looking at a d100.You are not describing your problem properly at all.
>>93416295Custom dice in Anydice can do that. The syntax for your case is "successes:outcome weight", so if you wanted a d100 with 1 success on 97-100 and 0 on everything else then the die would be 1d{1:4,0:96}.https://anydice.com/>output 2d{-4:1,-3:1,-2:1,-1:1,0:14,1:11,2:15,3:14,4:16,5:15,6:9} named "weird">output 3d6-5 named "3d6-5"Also, I have to agree with the other anons that the distribution and outcomes are both really fucky. I don't know what the rules of the system are, but if this combined roll is going to be done repeatedly (especially if you're modifying the ranges) then it's going to end up even more convoluted and you should really consider whether you actually need that much granularity. 3d6-5 is statistically almost identical, and -2 and 13 could be reserved for whatever crits do.>>93420508>Is - in the described circumstances of weighted dice - the average sum of successes from a 200d100 roll 543 (rounded up from 542.85714286)? And does it also mean that - again, same circumstances - 20d100 gives 54 successes (rounded down from 54.285714286)?Yes. I don't know how you'd count crits though, unless you're either rolling that separately or checking each die individually.>output 100d(2d{-4:1,-3:1,-2:1,-1:1,0:14,1:11,2:15,3:14,4:16,5:15,6:9}) named "100x weird">output 100d(3d6-5) named "100x 3d6-5"
>>93420786Again, I DON'T WANT crits in this, consciously so.>>93419546>>93420261>>93420786Many, many thanks for solving a catch-up problem in a builder game.Feel free to join (especially since now you DON'T have to roll all the catch-up dice) or at least see how this stuff works here:>>>/qst/6041566
>>93420786Also:>you should really consider whether you actually need that much granularity. 3d6-5 is statistically almost identical, and -2 and 13 could be reserved for whatever crits do.With actual dice that would be an argument. With 4chan's dice generator, it gets kooky at any dice below d100. Not to mention actual dice commands with modifiers.So yeah, germanium transistors might be the best, but the silicon ones are just so much cheaper and easier to make.
>>93413373Legends of the Wulin and Weapons of the Gods' set-counting d10 system. You roll xd10 dice, and then group them by number rolled. So far very similar to ORE. However, once you've grouped them together, you combine the height and width to create a base-10 number again, which you can then apply regular modifiers to. So for example, if you roll two 8s with your dice, you get a result of 28 (two 8s). If you add a +5 modifier, it's the exact same as if you rolled three 3s (33). Not to mention, you get to preserve some of these dice to use for creating future sets. All this makes for a really interesting resource allocation feel to the dice mechanic. As beautiful as it is funky. I mean, just look at this
>>93420786Also also>granularityIt is absolutely needed. When things give (intentionally so) +1 modifiers to dice outcome and the whole gameplay loop is to to pile them up, it's kind of a biggy to have things granular>3d6-5... and then you have to account for the fact that players gain additional dice as the game progresses (up to 5d100), so not a long-term solutionMan, I really need to brush back the probabiliy textbook. I remember fuck-all about it.
>>93420508>Which part of "crits are deliberately removed from the pool to entirely and deliberately remove high-risk element" I need to repeat for the n-th time for it to finally sink in?You've made your point. But it's also obvious that you do not understand the repercussions of this decision, nor the fact that this is not how you "remove crits from the pool". The current calculation does NOT represent "the average possible outcome".>it just throws errorsThen do it again, learn something. You do understand the steps and what you're supposed to be doing, right? Where do the first errors pop up?>Is - in the described circumstances of weighted dice - the average sum of successes from a 200d100 roll 543 (rounded up from 542.85714286)?No. That's the expected value of 100 2d98 rolls with the numbers you listed. This 2d98 roll is NOT equivalent to the 2d100 roll used in your game.>again, same circumstances - 20d100 gives 54 successesAgain, same objection as above.>>93420605>Then you're not looking at a d100.You don't have to tell me. But even anon's 2d98 rolls do "create a curve", which is what you disagreed with.>>93420786>Yes.No. See above.>>93421305>I DON'T WANT crits in thisIf you tell us what they do we might be able to remove them, properly.
>>93423055>But it's also obvious that you do not understand the repercussions of this decision,Chance wise, you've got a d98 dice, instead of d100, since both 1 and 100 do nothing in this mental exercise and aren't part of the actual diceSo for all purposes intended, it does represent it properly.Crits are non-numerical effects. A permanent or timed modifier to your pace that is completely beyond the scope, especially since it doesn't affect the dice itself.I mean seriously mate, what's your problem? Think of the dice as an exercise in weighted d98 and move on. If that affects the final outcomes from the final line of >>93420508 - great, then say so. If no - then what's the problem? Other, than, of course, obsession?
>>93423923>confused stare>what's your problem?Several anons have given you the mathematically correct answer to the question you asked, yet all of us have told you that you're asking the wrong question.>If that affects the final outcomes>then say soWe did.>it does represent it properlyIt doesn't. What it does represent is the expected value of your modified 2d98 or weighted 2d11 roll, but that's not the expected value of the actual roll that you apparently want to replace. And to answer your actual question (not the one you asked) we need more information. Like, do 1s and 100s do the same or is one a crit fail and the other a crit success? How do they interact with the other dice and with each other? If you roll 2d100, do you need just one 1 to trigger the effect? Does the second result matter? Is a double 1 worse than a single one? Do 1s and 100s cancel each other out (assuming they do different things) or do they apply both? Are the positive effects comparable in impact to the negative ones?Not to mention that none of this actually helps you when you go from 2d100 to 3, 4, or even 5, as mentioned here >>93421467, or when you change the mapping as mentioned here >>93418062.
>>93425694>Several anons have given you the mathematically correct answer to the question you asked, yet all of us have told you that you're asking the wrong question.... meaning you are useless? But thanks for your concernUnless you have something that's gonna drastically alter outcomes from >>93420508 (and by drastically I mean more than 20 on the 543), I've got everything that I needed
>>93425980>meaning you are useless?You got the answer to your question, you just don't want to hear that you've been asking the wrong question from the getgo.>something that's gonna drastically alter outcomesWe can tell you how the outcomes are being altered once you provide the necessary information.Have you by now figured out how to work the spreadsheet (or AnyDice if you have to), so that you can at least correctly assess on your own which effect fiddling with the mapping will have?Have you understood it well enough so you can implement how rolling more than 2 dice per round will affect things?>I've got everything that I neededYou have what you think you need, and you have several people telling you that what you think you need is not what you actually need.>Can you guys help me?>Sure, here you go!>Thanks, but I'd rather be wrong!
>>93426363Oh no, you've detected a minute difference that's a rounding error! The horror! Now the whole thing is wrong, because people should get 542, instead of 543 successes from this method!Look mate, I'll make it quick to you: the error doesn't matter. Any approximation below 50 is fucking ok for the purpose it is doing. As as it's not actually 600 and it's around 550, that's all that's needed.But I guess you're the Babbage type, so you're gonna write an angry letter informing everyone that the actual ratio should be 11/16 instead.
>>93413373>absolute difference between a pair of thirty-sided dice>functionally identical to roll 2d30 take low>exception: doubles count as the doubled number (e.g.: 30 & 30 = 30) and count as "critical" (success or failure)>target number 10 = 50% (*almost*) chance conveniently>chance of 1 = 1/300>chance of 30 = 1/900>finally a use for those 2d30 (You) already have
>>93426877https://anydice.com/program/31a29
>>93426877>>93426888Checked & checked again... sure signs that this project must be pursued to production & publication.I call it the Absolute Thirty System, or A30 RPG.>not sure why this picture is for ants
>>93420508>certified helmsmankek>>93421305>Many, many thanksYeah, as if...>>93421451So someone turned the basis of the look-and-say sequence into a dice mechanic? Funky indeed. You sure that graph's correct though?>>93426363He hasn't learned a thing and never intended to, he only wanted to be spoonfed. And he still hasn't answered the ship question.
>>93426950>kekNever question or laugh at man's credentials when he's giving them to you, bitch. And especially not when he's drunk.
>>93426877>chance of 1 = 1/30059/900, off by a factor of almost 20. In both cases by the way, since they are indeed functionally identical.
>>93427201I laughed because you're clearly an angry/salty seaman, if only a sporting one. You've proved that at least twice now. Is the Baltic Sea very salty?
>>93427252Not really. North one is much better. Except for Norwegian prices - fuck that shit. It was bad pre-covid, and now I'd have to give away my kidney to just fucking anchor there..
>>93416381Basado
>>93427201>The old Polish seaman's book>Writing in cursiveGo to sleep, grandpa. Especially if you're drunkAre you even aware they've switched the pattern almost a decade ago and are going to retire the whole thing next year? Only the plastic card from then on.
>>93427211>checked & mathpilled; however:Chance of rolling 30 thusly is still only 1/900 (but your other adjustment for 1 being 59/900 is correct afaik).
>>93429761>Chance of rolling 30 thusly is still only 1/900I can't see where I said it wasn't.30 is 1/900, and it steadily increases in 2/900 steps until it reaches 59/900 for 1.
>>93429787Ah, yes, I misunderstood your previous post. How do you like that stepping?
What even is this thread?It's just autism about dice systems that are completely impractical and superfluous. Is this just for people to wank about math?
>>93435438... is that why you bumped it from page 10 for the... 3rd time?
>>93436098I bumped it one time.What's your excuse?
>>93436227>Implying I bumped any thread in the past 5 years
