D&D Math

[Quixotic1]

I've been hired to run a 5e horror one-shot for a group. I'm trying to figure out how this one little subsystem will work, but my math skillz just ain't what they used to be.

A quick rundown: the party has been hired to hunt a terrible Beast that lives deep within the scary dark forest. Speed is of the essence; they'll have 12 hours of darkness to travel, capture or kill the Beast and make it back to the village.

The map shows three likely paths through the wood. Every hour, they'll have to make a group skill check to make effective progress.

The first path is the longest, but it is also the easiest (lowest DC, highest number of rolls, lowest margin for error)

The second path is the shortest and the most difficult (highest DC, least number of rolls, highest margin for error).

The third path is between the two (middling DC, number of rolls and margin for error).


I would like to set up the DCs so that, if they're crafty and a little lucky, they'll have just enough time to do so.

So I need to figure out the odds that 3-5 rolls out of 5 will succeed/fail at different individual chances of successful or failure. I'm assuming an average modifier of +3 (+3+2+5=+10 being the highest likely modifier and +1-5=-4 being the lowest likely modifier, so an average of +3), though I'd take any other conditions into account if anyone had thoughts or suggestions.

What kind of calculations do I need to do here?

Thank you for your time.

[gbaji]

I guess that depends on what the rolls are for (what skill are you using)? I might suggest re-thinking the entire method of the adventure.

The beast is in the forest right? Presumably this beast has been terrorizing the locals and the party has been hired to find and kill it, right? Great one-shot concept.

What do the three paths represent? Is the beast at a known location and there are three paths to get there? Is this a roll to see if they can follow the path without getting lost? Or are they actually tracking the beast and some tracks are more difficult to follow?

What happens if they just roll badly in this phase of the adventure? Why do they have to do this during darkness? Is there something else in the forest in-between them and the beast's lair that requires this? What are the consequences if they don't find their way there and back by dawn (and why "there and back", why not just "get there before it attacks again" or something)?

I get that you're just asking about the math, but if the math results in them failing just because of some bad die rolls, it's not going to be a very fun adventure for anyone. I'd focus less on how they get there and more on what happens when they do. You can (and should) still have some rolls to determine how quickly/easily they get there, but make the results affect what happens either along the way (maybe they run into some other minor threat and have to deal with it, wasting time and resources), or how difficult the fight with the beast is when they get there (the beast is sleeping when they get there vs awake and ready, and maybe really bad rolls means the beast has woken up, noticed them coming, and is now hunting *them*).

Just making it about the math has other problems. Any math you can do, your players can do (and do you really want them spending a significant amount of the game session just sitting there discussing math problems?). If there is one mathematically best option, then you're giving them an advantage for doing out of game math rather than making in-game character decisions. If the odds all even out in the end then there's not a lot of reason for doing the exercise in the first place.

If you really want to have multiple paths and give the players a choice, then make the paths represent something other than just die rolling odds. Maybe one path requires that they climb up a steep hill/cliff. Maybe another requires that they swim across a river at a fast flowing point. Another could be swampy/muddy. Maybe each path also has some wild animal/lesser-beasts that may be a threat as well. Use your imagination, but make each path a decision about potential (and different) hazards the PCs will have to overcome on their travel. Thus, the decision will be based on the skills/abilities/items/whatever that the PCs have, and what sort of encounters they want to deal with (or feel they are best suited to handle).

This adds to player agency (lets them pick what they want to deal with), increases fun (presumably they are more likely to enjoy what happens along the way since they picked it), and then let them get on with dealing with the beast. Each path could also include outcomes that could delay them getting to the beast (with presumed consequences), but are also providing actual choices that the characters themselves would have a reason to make. I just don't think most player groups are that thrilled with a choice of "calculate the odds of X in formulas A, B, and C". Make the choices real world choices.

[Quixotic1]

I guess that depends on what the rolls are for (what skill are you using)? I might suggest re-thinking the entire method of the adventure.

Man. I mean...thanks for the very extensive reply. It's just, I asked for a very specific thing that I wanted some input on. I don't need people telling me to "re-think the entire method" when they don't even know what it is I'm doing.

I'm sorry I didn't provide many details; I was hoping to avoid it because (1) I didn't want to spend the time on what seemed unrelated to the question I'm asking and (2) I didn't want to ask people to slog through a massive WoT to give me their input. I actually felt like I gave more than was strictly needed.
But okay. Here we go.

The three paths are THREE PATHS. Literally. The first is following the river. The second is through a bog. The third is through the densest part of the forest, overgrown with bracken and brambles.
The first path will require Str (athletics) checks or just straight Con saves at a slightly lower DC.
The second path will ask for Wis (survival) or Int (nature).
The third will ask for Wis (perception) or Dex (acrobatics).

They're group checks, so they need 3 success each time to succeed. If they fail, they don't make meaningful progress and suffer another possible consequence (save vs. exhaustion/falling into the water/taking 1d4 piercing damage).

The types of encounters that can possibly occur along the way will also depend on what path they're on/what part of the forest they're in.

I feel like that's enough to get a better picture, yeah?

why "there and back", why not just "get there before it attacks again" or something?

I have my reasons. I don't want to put them all out there, in case any of them see this. But my choices have motivations behind them, I assure you. If they while away the hours until dawn, things will be harder for them in several significant ways.

I get that you're just asking about the math, but if the math results in them failing just because of some bad die rolls, it's not going to be a very fun adventure for anyone. I'd focus less on how they get there and more on what happens when they do.

I hope I've cleared this up. I've been doing this for a long while now, and I've worked very hard at improving my abilities as a gamemaster. I'm focusing on these things as a deliberate choice. You understandably don't know all about it, but it's not necessary for the question I'm asking.

Just making it about the math has other problems. Any math you can do, your players can do (and do you really want them spending a significant amount of the game session just sitting there discussing math problems?). If there is one mathematically best option, then you're giving them an advantage for doing out of game math rather than making in-game character decisions. If the odds all even out in the end then there's not a lot of reason for doing the exercise in the first place.

Again, hope it's a little clearer now. It's not a numbers game. It's a matter of them choosing which of their strengths they want to bet on.
And the actual math will of course work out much differently than my rough n' ready generalizations. So it's really not a problem. Promise.

Use your imagination, but make each path a decision about potential (and different) hazards the PCs will have to overcome on their travel. Thus, the decision will be based on the skills/abilities/items/whatever that the PCs have, and what sort of encounters they want to deal with (or feel they are best suited to handle).

Thanks for the tip. "Use my imagination". Heh. Yup.

This adds to player agency (lets them pick what they want to deal with), increases fun (presumably they are more likely to enjoy what happens along the way since they picked it), and then let them get on with dealing with the beast. Each path could also include outcomes that could delay them getting to the beast (with presumed consequences), but are also providing actual choices that the characters themselves would have a reason to make. I just don't think most player groups are that thrilled with a choice of "calculate the odds of X in formulas A, B, and C". Make the choices real world choices.

I'm sorry. I guess I'm just sort of blown away by the number of assumptions you've made. You asked me a lot of questions that don't pertain to my questions, then filled in the blanks yourself with basically the worst-case scenario, bad GM choices out there.

I thought about coming on here to throw some ideas around and springboard off of, but I decided to go with my gut and avoid the headache that usually seems to follow.
I figured this specific question was one I was struggling with, and there are probably some people on here with awesome math brains I could tap into.

I'm sorry, but I'm really not open to discuss whether or not the game will be good as-is. It will be. I'm not here for help with that. I've got it covered. Just the math--that's what I was hoping for help with.

[ReallySeamus]

Answering the "math" question in a way meaningful from a game design perspective requires understanding the context of the scenario. You could do the arithmetic on your own using a spreadsheet readily enough (it's more tedious than complicated), and considering you've been hired to do it, you probably should if the nitty-gritty of the math matters that much.

If you're not interested in sharing more details, my suggestion would be to consult the basic ability check DC table on p. 174 of the PHB:

• Task Difficulty - DC
• Very easy - 5
• Easy - 10
• Medium - 15
• Hard - 20
• Very hard - 25
• Nearly impossible - 30

If I was running this sort of scenario, I would have the Easy path be a DC 10, but require 5 successes, Medium be a DC 15, but require 4 successes, and Hard be a DC 20 requiring 3 successes.

[meschlum]

Yay! Math!

I'm not entirely clear on the rolls you're asking for, since your reply appears to add things I didn't notice from the first post...

Anyway!

Here's my take on what is involved:

- There are three possible routes
- There are C challenges on a route (3-5 have been mentioned, depends on the route)
- Each challenge has a probability P of being passed (some routes have easier challenges than other routes), and P is constant on each route (the challenge difficulty is constant once you're on the route)
- Each route has a target number T challenges which must be passed in order for the route to be successful
- (Added in latest reply) Challenges involve a number of rolls R, and require at least 3 successes to be successful. I'm guessing each party member has to roll, meaning 4 rolls?


Fortunately, the problem can be deconstructed into separate parts. We just need the equations for one route, and can use them on other routes. And we don't need to know how the probability of passing a challenge has been created to determine the probability of passing multiple challenges.


What you're asking is the probability of having T or more successes occur out of C challenges, when the each challenge is successful with probability P. Simple!

If you need C challenges, the probability is P^C (every challenge must be successful)
If you need C-1 challenges, the probability is P^C + C * P^C * (1 - P) (pass all challenges, or fail only one)
...

The general formula is: Sum(P^(C-n) * (1 - P)^n * C(C,n) ) for n = 0 to x, where you need C-x challenges

C(a,b) is the number of combinations of b items in a (equal to b! * (a-b)! / a!, where n! = 1 * 2 * ... * n)

Edit: correction: it's a! / (b! * (a-b)!)

Toss that into your spreadsheet of choice and you have the results.


A similar analysis can be made when trying to determine the probability of success for each challenge. Simply fit in the numbers and iterate.

There are 4 rolls (one per party member), and 3 successes are necessary, so if one party member succeeds with probability p, the probability of passing the challenge is p^3 * (3 - 2p) (simplified from p^4 + 3 p^3*(1-p))

If p = 0.5, then the challenge is passed with probability 0.25
If p = 0.25, then the challenge is passed with probability 5/128 (less than 1/20)
If p = 0.75, then the challenge is passed with probability 81/128 (between 12 and 13/20)

So with four rolls, unless each roll is very likely to succeed, it's difficult to get 3 or more successes.

Looking at the results, if you had 4 challenges, and need to pass three of them, and each challenge has four rolls and you need to pass three as well, you get a 25% chance of passing any individual challenge, so a less than 1/20 chance of passing overall. Not good odds.


Edit: You're specifically after results with 5 challenges, so that lets you crunch out the numbers

5 successes: P^5
4 successes: P^5 + P^4 * (1 - P) * 5
3 successes: P^5 + P^4 * (1 - P) * 5 + P^3 * (1 - P)^2 * 5 * 4 / 2

Which simplifies to:
5 successes: P^5
4 successes: P^4 * (5 - 4 P)
3 successes: P^3 * (10 - 15 P + 6 P^2)

So if P=0.5, you have 1/32 chance of getting 5 successes (3.125%), 3/16 of getting 4 or more successes (18.75%), and 1/2 of getting 3 or more successes (50%). Again, the odds of failure are fairly high even when the chance of success is moderate.

[MoiMagnus]

I've written a code that compute the probability of victory below.

For example, assuming 4 consecutive challenges for a party of five characters with modifiers +10,+6,+3,0, and -4:

1. A DC 5 challenge where 3 out of 5 characters must succeed
2. A DC 10 challenge where 3 out of 5 characters must succeed
3. A DC 12 challenge where 3 out of 5 characters must succeed
4. A DC 14 challenge where 2 out of 5 characters must succeed

Assuming the party needs to succeed at 3 out of 4 of those, they will succeed with 90% probability, which seems reasonable.

Feel free to play with this code to search for possibilities. It should be able to run in any "Python 3" interpreter or compiler that you find online (no need to install anything on your computer).

Party_modifiers = [+10,+6,+3,0,-4]
DC_of_each_check = [5,10,12,14]
Nb_character_needed_to_succeed = [3,3,3,2] #Number of characters that must succeed for the group check to be a success
Nb_checks_needed_to_win = 3 #Three out of the Four group checks must succeed for the party to win

#Now, let's compute stuff
assert(len(DC_of_each_check)==len(Nb_character_needed_to_succeed))
import random
def single_check(modifier,DC):
    die = random.randint(1,20)
    result = die+modifier
    return (result >= DC)
def group_check(DC,n):
    count = 0
    for m in Party_modifiers:
        if single_check(m,DC):
            count = count+1
    return (count >= n)
def all_checks():
    count = 0
    for i in range(len(DC_of_each_check)):
        if group_check(DC_of_each_check[i],Nb_character_needed_to_succeed[i]):
            count = count+1
    return (count >= Nb_checks_needed_to_win)
nb_victories = 0
nb_tries = 10000
for i in range(nb_tries):
    if all_checks():
        nb_victories = nb_victories+1
percent_victories = int((nb_victories/nb_tries)*100)

print("The party is composed of",len(Party_modifiers),"characters with modifiers",Party_modifiers)
print("They encounter the following obstacles:")
for i in range(len(DC_of_each_check)):
    print("DC",DC_of_each_check[i],"where",Nb_character_needed_to_succeed[i],"characters must succeed")
print("Their probability of VICTORY is",percent_victories,"%")

[Quixotic1]

Answering the "math" question in a way meaningful from a game design perspective requires understanding the context of the scenario. You could do the arithmetic on your own using a spreadsheet readily enough (it's more tedious than complicated), and considering you've been hired to do it, you probably should if the nitty-gritty of the math matters that much.

If you're not interested in sharing more details, my suggestion would be to consult the basic ability check DC table on p. 174 of the PHB...

Well for one, I disagree. To solve a mathematical equation, you just need enough information to... you know, solve the equation.
If Jimmy has 2 apples and Jane gives him 2 more, you don't need to know what the relationship is between Jimmy and Jane, what kind of apples they are or why Jimmy wants all the apples and Jane doesn't seem to care for them.

Secondly, so you think that, because I've been hired to run a game, I am somehow ethically obligated to prepare for it entirely on my own? Want to walk me through that logic?
And hey, what if I *can't* do this arthimatic? You know, because I literally don't know how?
It's not like this is required for the game; I could just slap some generic numbers on there, but I want the pacing and the tension to be really good and satisfying, so I'm trying to go above and beyond here.

And third, I shared more details. I didn't think it was necessary, I thought it was a waste of my time and would be asking others to waste theirs. But when I was basically told, "I don't know what you're doing, but it seems like maybe it's bad", I went ahead and provided the details. As you can see above. So I'm not sure what you're referring to.

[MrStabby]

I've been hired to run a 5e horror one-shot for a group. I'm trying to figure out how this one little subsystem will work, but my math skillz just ain't what they used to be.

A quick rundown: the party has been hired to hunt a terrible Beast that lives deep within the scary dark forest. Speed is of the essence; they'll have 12 hours of darkness to travel, capture or kill the Beast and make it back to the village.

The map shows three likely paths through the wood. Every hour, they'll have to make a group skill check to make effective progress.

The first path is the longest, but it is also the easiest (lowest DC, highest number of rolls, lowest margin for error)

The second path is the shortest and the most difficult (highest DC, least number of rolls, highest margin for error).

The third path is between the two (middling DC, number of rolls and margin for error).


I would like to set up the DCs so that, if they're crafty and a little lucky, they'll have just enough time to do so.

So I need to figure out the odds that 3-5 rolls out of 5 will succeed/fail at different individual chances of successful or failure. I'm assuming an average modifier of +3 (+3+2+5=+10 being the highest likely modifier and +1-5=-4 being the lowest likely modifier, so an average of +3), though I'd take any other conditions into account if anyone had thoughts or suggestions.

What kind of calculations do I need to do here?

Thank you for your time.

By the sound of it, this is wha you want:
https://en.wikipedia.org/wiki/Binomial_distribution

[Quixotic1]

Yay! Math!

I'm not entirely clear on the rolls you're asking for, since your reply appears to add things I didn't notice from the first post...Here's my take on what is involved:

- There are three possible routes
- There are C challenges on a route (3-5 have been mentioned, depends on the route)
- Each challenge has a probability P of being passed (some routes have easier challenges than other routes), and P is constant on each route (the challenge difficulty is constant once you're on the route)
- Each route has a target number T challenges which must be passed in order for the route to be successful
- (Added in latest reply) Challenges involve a number of rolls R, and require at least 3 successes to be successful. I'm guessing each party member has to roll, meaning 4 rolls?

Wow. Your maths outstripped mine by far. Thank you.
There are some misunderstandings, though. Let me see if I can clarify:

1. There are 5 PCs. So, per the group skill check rules, more than half of them need to succeed. So 3, 4, or 5 of them need to succeed out of 5.

2. There are 3 paths. Each path has a minimum number of rolls that need to be made (a) and a DC for those rolls (b). The lower (a) is, the higher (b) is.

4. Each roll represents 1 hour. If the 5 players roll 3, 4 or 5 succees, they make meaningful progress. If 0, 1 or 2 succeed, they do not.

5. I am aiming for each path to take a total of 11 hours to travel it's length twice.
So the path's length (a) cannot be 11 or more, because they need to have some room to make at least one mistake/take a short rest, etc.
And because paths with a higher (b) will result in the PCs making less progress/hour, I want to make those path's (a) lower, to give them a larger margin of error.

So, for example;

The first path is along the River Gloaming. It's the longest, so there isn't much room for mistakes. They don't have much spare time. Str (athletics) DC12, 5 rolls to get through it.
They can mess up or take a break twice total before they run out of time.

The second path is through the Pinetar Swamp. It's shorter, but harder. Say, Wis (survival) DC15, 4 rolls to find their way.
They can mess up/rest up to 3 times.

The third path is straight through the woods. It is the shortest and most difficult. Dex (acrobatics) DC18, 3 rolls.
They can mess up/rest up to five times.

Does that make sense?

[Quertus]

So, for example;

The first path is along the River Gloaming. It's the longest, so there isn't much room for mistakes. They don't have much spare time. Str (athletics) DC12, 5 rolls to get through it.
They can mess up or take a break twice total before they run out of time.

The second path is through the Pinetar Swamp. It's shorter, but harder. Say, Wis (survival) DC15, 4 rolls to find their way.
They can mess up/rest up to 3 times.

The third path is straight through the woods. It is the shortest and most difficult. Dex (acrobatics) DC18, 3 rolls.
They can mess up/rest up to five times.

Does that make sense?

I guess I’ll reply to this bit.

Are the paths only make progress / make no progress, or are there other a) consequences for failure; b) effects even with success?

I’m assuming this isn’t in the 5e forum because, in theory, anyone could help you with this math?

Lastly… although I’m… not a fan of “unnecessary secrecy”, I can appreciate the need for secrecy in a horror game. That said, two important questions: 1) will the players / PCs have any idea that they are on a time limit; 2) will answering our questions about this time limit actually give your your players (assuming they read this thread) more information to metagame in choosing their character(s) than you’ve already given. For reference, you’ve already said things like “timed adventure”, “single beast”, “certain skill rolls (like Survival or Athletics) important for group skill rolls” “time for short rest(s) before/after monster fight (and between ‘forest fights’, if applicable)”.

So, to explain my questions, if, “15 minutes in” (ie, before they choose their path), the PCs understand that they are on the clock, and why, but wouldn’t understand this when choosing / building their characters, then I’ll go on record as supporting your decision for secrecy. Otherwise, it’s hindering our ability to evaluate what we need to ask, to make sure we’re answering the correct question.

[Quixotic1]

Are the paths only make progress / make no progress, or are there other a) consequences for failure; b) effects even with success?

There are other consequences, but nothing that influences the math I'm wondering about.

I’m assuming this isn’t in the 5e forum because, in theory, anyone could help you with this math?

Precisely.

I’m… not a fan of “unnecessary secrecy”...1) will the players / PCs have any idea that they are on a time limit; 2) will answering our questions about this time limit actually give your your players (assuming they read this thread) more information to metagame in choosing their character(s) than you’ve already given.

I am not either. I share DCs and ACs and all that pretty regularly. I feel like it keeps things flowing, focuses the tension to a finer point and takes some of the mental burden off of me.
Yes, the players will know about the time limit. Before they choose a path. They will also understand the basics of what each path will ask of them (physical speed, woodcraft, awareness or nimbleness).
And I don't worry about metagaming. Like... at all. I've just never found a way to avoid the contrived situations that metagaming created that isn't equally or more contrived itself.
This is more about the narrative. I don't want to reveal too much and ruin the climax of the game.

...Otherwise, it’s hindering our ability to evaluate what we need to ask, to make sure we’re answering the correct question.

I hope that clears it up. But I don't really see how it would.

In a lot of 5d20 what is the probability that 3 or more dice result in a number of X or greater? --that's the question, as purely a simply as I can put it.

[ReallySeamus]

Well for one, I disagree. To solve a mathematical equation, you just need enough information to... you know, solve the equation.
If Jimmy has 2 apples and Jane gives him 2 more, you don't need to know what the relationship is between Jimmy and Jane, what kind of apples they are or why Jimmy wants all the apples and Jane doesn't seem to care for them.

That's true for the Jimmy and Jane example, but you're assuming you've shared every relevant variable. I don't know why we should take that as a given. For instance, if there's a risk of danger on the paths such that the number of party members in the group could realistically change, or if they might split up and take multiple paths, that changes the numbers involved. You may be able to get your specific question answered, but that answer may not factor in things that would become relevant during the actual game.

Secondly, so you think that, because I've been hired to run a game, I am somehow ethically obligated to prepare for it entirely on my own? Want to walk me through that logic?
And hey, what if I *can't* do this arthimatic? You know, because I literally don't know how?
It's not like this is required for the game; I could just slap some generic numbers on there, but I want the pacing and the tension to be really good and satisfying, so I'm trying to go above and beyond here.

I'm not saying you can't have help preparing. I'm saying if you're dead-set on this approach, you should probably kick the tires a little more such that you'd be coming to the board with "Hey, I set the DC for this scenario at X, does that seem fair?", or at least be better equipped to evaluate the feedback - the two crunchiest answers you've gotten so far seem to have very different results. The alternative would be to just set up a scenario that plays to your individual strengths if math's not your thing - there are ways to build tension and the sense of a ticking clock narratively without relying on formulas. I think it's worth taking a step back and asking if this math problem is the only way to achieve your objective, but you'd know the answer to that better than me and I'm happy to defer to your judgement.

And third, I shared more details. I didn't think it was necessary, I thought it was a waste of my time and would be asking others to waste theirs. But when I was basically told, "I don't know what you're doing, but it seems like maybe it's bad", I went ahead and provided the details. As you can see above. So I'm not sure what you're referring to.

This is a board for TTRPG fans. I really don't think many people are going to find a description of what seems like a potentially exciting scenario to be a waste of time, and I would hope you like the scenario enough that sharing it would be enjoyable rather than tedious for you. You did provide a few additional details - I just meant that I thought there were still other potential variables, but you don't seem to enjoy discussing that (which is fine).

Good luck with the game - I sincerely hope you and your players have a great time! If you're interested, I'm sure folks would love to know how it goes and how you end up handling this aspect of the adventure.

[Quixotic1]

That's true for the Jimmy and Jane example, but you're assuming you've shared every relevant variable. I don't know why we should take that as a given. For instance, if there's a risk of danger on the paths such that the number of party members in the group could realistically change, or if they might split up and take multiple paths, that changes the numbers involved. You may be able to get your specific question answered, but that answer may not factor in things that would become relevant during the actual game.

I mean. If the answer isn't helpful to me, then that's on me for not asking a good question. I'm fine with that responsibility.
To address the concerns you mentioned, I wouls assume that 3 out of 5 is similar enough to 3 out of 4 and 2 out of 3 that I wouldn't sweat it. If there is some character death along the way, I'll roll with it. And as for splitting up, I'll ask them not to. Because it's a game and it's supposed to be fun and all that, and splitting up every which way is a great way to bore everyone very quickly.

I'm saying if you're dead-set on this approach, you should probably kick the tires a little more such that you'd be coming to the board with "Hey, I set the DC for this scenario at X, does that seem fair?", or at least be better equipped to evaluate the feedback - the two crunchiest answers you've gotten so far seem to have very different results. The alternative would be to just set up a scenario that plays to your individual strengths if math's not your thing - there are ways to build tension and the sense of a ticking clock narratively without relying on formulas. I think it's worth taking a step back and asking if this math problem is the only way to achieve your objective, but you'd know the answer to that better than me and I'm happy to defer to your judgement.

I am well aware of various was to build tension and impart a sense of urgency. I will be utilizing several. This is one.

And again, it's not specifically necessary. It would just help me set the pacing of the mechanics and use them to reinforce the tone established in the narrative.

As for "kicking the tires", I mean. I gave some examples with DCs and stuff. And I don't know. Maybe math isn't my thing. But "in a lot of 5d20, what is the probability that 3 or more dice come up X or greater" is a pretty simple question, and I haven't seen an answer yet. It feels weird to me that several people seem to be saying, "sure, we could answer your question...but are you sure it's the right question?"--and then just. Not answering the question.

Granted, there's been two really awesome passes at it. But they were operating under misunderstandings, so obviously that's not quite it. And...man, I don't know. When I say "there will be five players, so 3 or more need to succeed" and I get asked, "so there's four rolls, right?"

This is a board for TTRPG fans. I really don't think many people are going to find a description of what seems like a potentially exciting scenario to be a waste of time, and I would hope you like the scenario enough that sharing it would be enjoyable rather than tedious for you. You did provide a few additional details - I just meant that I thought there were still other potential variables, but you don't seem to enjoy discussing that (which is fine).

Sure. But there's got to be a limit (no one's going to read the entirety of "The Wheel of Time" to help someone determine which weapon their character favors or whatever), and I only have so many hours in a day. At this point, I'd rather spend time working on the game itself than telling another group of people about what I've got so far.
And of course, I ran into this problem a while ago: that I've probably spent more energy explaining myself than it would have taken to lay it all out from the start. But from the start, I felt less like I was having a discussion and more like I had to defend myself from accusations. So. I guess frustration and offense are great motivators to spend time on stuff that wasn't previously worth it. More's the pity.

Good luck with the game - I sincerely hope you and your players have a great time! If you're interested, I'm sure folks would love to know how it goes and how you end up handling this aspect of the adventure.

I just might. Sorry if I've been difficult. That first response really seemed to set the tone wrong and I haven't really been able to get the conversation in the direction I wanted since then.

[Quertus]

I mean. If the answer isn't helpful to me, then that's on me for not asking a good question. I'm fine with that responsibility.

That first response really seemed to set the tone wrong and I haven't really been able to get the conversation in the direction I wanted since then.

This… might get more traction than the longer post I stated around 2.

I fully agree with the tone of the first post (if maybe not all the particulars) as a response to your opening question. It’s a matter of presentation. Given your presentation, you shouldn’t be surprised at the responses you’ve gotten so far. I hope you can learn to see that.

Similarly, I hope you can come to understand that you are almost certainly asking the wrong question, and that several of us are… well, I can only speak for myself, but I strongly suspect several of us are testing that theory / trying to help you come to that conclusion / trying to give you the tools to evaluate whether you have a valid solution to your mystery problem / trying to cram how wrong you are down your throat. Honestly not that last one!

Given what you’ve said so far, I highly doubt that answering the question you asked will help you. However, it is not impossible that the answer you seek is actually exactly the one you requested. Either way, I’ll apologize on behalf of all of us, that the Playground is just too dang helpful, and wants to make sure they’ve solved as many possible problems as they can. I, in particular, am (maybe?) known for trying to solve the general case, trying to solve the problem for the “folks at home”, who are silently watching, or who came across this thread months from now, and attempted to use the posted advice for their own seemingly similar problem.

I hope both this and other’s mathematical assistance helps!

[gbaji]

I think the reason so many posters are questioning the pure math angle is because gaming (and particularly "fun" gaming) is always from the players perspective. In RPGs (heck same in wargaming too), players most enjoy making decisions and having those decisions affect the outcome. Die rolling is a necessary random element to this, but should never outstrip that process. No one, at any table I've ever been at, actually enjoys failing purely because they rolled badly on the dice. They accept it. But they are never happy. This should be minimized as much as possible.

What you seem to be doing is the exact opposite. You're giving the players very minimal choices (one: take path A, B, or C). That's it. Then they are asked to spend the next X amount of time at the table rolling the same skills over and over, waiting to get enough successes in each set of rolls to determine advancement, and to then get enough advancements to get to the goal. Even if you lay out the entire set of skills required, numbers of players who have to succeed in each round to advance, the amount of time each attempt takes (one hour in this case), and the number of times they must succeed to get through that path, that's not really "fun" for the players. It's repetitive dice rolling. Even if you insert other encounters/events/activities in between the die rolling, that part (the die rolling) is the part the players will least enjoy. So why do it?

I'd present them with the three paths. I'd tell them what skills can be attempted to traverse that path. Then I'd have them each select which skill they are using and roll *once*. The number of successes determines how many hours it takes to get through the path. And I'd have a number of encounters/events/whatever occur along the way based on that result. To be perfectly honest, I'd also *never* make simply traversing the path(s) take so long that it causes failure of the adventure (again, not knowing the consequences if they are "late" makes it hard to assess this). Why does the math matter? Because the consequences matter. If the outcome is between "you get there with plenty of time" and "you fail. Everyone dies" then it's important to make the skill checks extremely easy so that their odds of failing just because of bad die rolls is minimized (zero even). If the outcome for failure is "you get back and now there's another problem you have to deal with that could also be fun", then by all means make the DCs super high to maximize the odds of that end encounter/whatever happening, but still giving them a chance of sailing through easily if they are abnormally lucky with the die rolls.


To be fair, you are looking for answers just on the math question. But we can't teach you math right here in this forum. We can't calculate the entire set of possible probabilities for each possible path, lay them out and create a statistical graph of likely "total hours taken" for you. We'd need to know not just the information you have provided, but also the distribution of skills on every character's sheet as well. I mean, we could, based on every possible range for every possible skill, for every possible path, but it would take a ridiculous amount of time and virtual ink to do. If your goal is to have say, a 75% overall chance of a party of 5 making it through each path in 5 or fewer hours, with scaling probabilities for each hour shorter or longer, we still don't have nearly enough information to calculate that for you (and it's not "easy" math either).

And again, we don't know if those odds are "reasonable" or not, because we don't know what the relative consequences for success and failure are. Hence, why I recommend that you should just minimize the die rolling and maximize the decision/encounter aspects of the game instead. You're spending a lot of time on a part of the gameplay that the players will least enjoy. I'd focus all of that time on adding in more scary/spooky elements, things to make the characters worry, decisions to make, etc, along the way instead. I'm not assuming you aren't doing this already, but I'd still just leave the excessive die rolling out of the game.

Yeah. Unsolicited advice. Take it or don't.

[Amidus Drexel]

Wow. Your maths outstripped mine by far. Thank you.
There are some misunderstandings, though. Let me see if I can clarify:

1. There are 5 PCs. So, per the group skill check rules, more than half of them need to succeed. So 3, 4, or 5 of them need to succeed out of 5.

2. There are 3 paths. Each path has a minimum number of rolls that need to be made (a) and a DC for those rolls (b). The lower (a) is, the higher (b) is.

4. Each roll represents 1 hour. If the 5 players roll 3, 4 or 5 succees, they make meaningful progress. If 0, 1 or 2 succeed, they do not.

5. I am aiming for each path to take a total of 11 hours to travel it's length twice.
So the path's length (a) cannot be 11 or more, because they need to have some room to make at least one mistake/take a short rest, etc.
And because paths with a higher (b) will result in the PCs making less progress/hour, I want to make those path's (a) lower, to give them a larger margin of error.

So, for example;

The first path is along the River Gloaming. It's the longest, so there isn't much room for mistakes. They don't have much spare time. Str (athletics) DC12, 5 rolls to get through it.
They can mess up or take a break twice total before they run out of time.

The second path is through the Pinetar Swamp. It's shorter, but harder. Say, Wis (survival) DC15, 4 rolls to find their way.
They can mess up/rest up to 3 times.

The third path is straight through the woods. It is the shortest and most difficult. Dex (acrobatics) DC18, 3 rolls.
They can mess up/rest up to five times.

Does that make sense?

Your lack of math savvy here may be frustrating you, as your stated problem ignores some rather important details, like the party members' respective bonuses to various checks (as well as your desired P(success)). Those make a big difference.

That said, I'm bored and am totally willing to do all of this in a spreadsheet. Assuming I've done it correctly - here's your results for a *single* challenge:

DC    (1 roll)   (3/5 rolls)
1     100.00%    100.00%
2     95.00%     99.88%
3     90.00%     99.14%
4     85.00%     97.34%
5     80.00%     94.21%
6     75.00%     89.65%
7     70.00%     83.69%
8     65.00%     76.48%
9     60.00%     68.26%
10    55.00%     59.31%
11    50.00%     50.00%
12    45.00%     40.69%
13    40.00%     31.74%
14    35.00%     23.52%
15    30.00%     16.31%
16    25.00%     10.35%
17    20.00%     5.79%
18    15.00%     2.66%
19    10.00%     0.86%
20    5.00%      0.12%

Using the math in meschlum's post and the target numbers laid out in the post I'm replying to, the three paths proposed are as follows:

required successes	5	4	3
total attempts allowed	7	7	8
prob per attempt	40.69%	16.31%	2.66%
prob path total 	10.31%	1.63%	0.10%

Things get significantly easier if your PCs have bonuses to any of their abilities, of course. If each of your players has a +5 to each relevant roll, then the probabilities look more like this:

required successes	5	4	3
total attempts allowed	7	7	8
prob per attempt	83.69%	59.31%	31.74%
prob path total  	90.92%	69.68%	49.23%

The big thing to notice here is that if a single challenge gets slightly harder, repeating a challenge of the same difficulty multiple times gets much harder. Ditto in the opposite direction, of course. Even small bonuses stack up over time if the DC is relatively low.

[Quixotic1]

I fully agree with the tone of the first post...you shouldn’t be surprised at the responses you’ve gotten so far. I hope you can learn to see that.

So if I don't give a fully detailed account of things that I don't feel the need to discuss, people will ask me a bunch of unrelated questions and then imply I have no idea what I'm doing after they assume they know the answers to the questions they've already admitted they don't know the answers to?
I mean. If you want to know stuff, ask. But going, "what's X? What's Y? What's Z? You should probably rethink your whole thing, because X, Y and Z are obviously wrong" is just...baffling. If you don't know what they are, how do you know they're wrong?

Similarly, I hope you can come to understand that you are almost certainly asking the wrong question, and that several of us are… well, I can only speak for myself, but I strongly suspect several of us are testing that theory / trying to help you come to that conclusion...

Okay, well. Thank you for your feedback. It was not asked for, sought after or needed in any way, but thanks for taking time out of your day to provide it.

I have been doing this for 22 years. It is at the core of who and what I am. I have pursued the skills necessary to improve my natural ability. Pretty hard.
I've had people throw around terms like "best GM ever" or say that I've "ruined" the hobby because their expectations are now too high.
--and I am absolutely NOT saying I'm better than anyone. There are a million ways to approach this hobby and storytelling and all similar forms of expression. I'm just mentioning this to explain why I didn't come here to discuss the game I'm planning. Online forum is a useful resource. I come to forums to get thoughts and info on things I'm not sure about. But I've also learned to trust my instincts, especially when I've backed them with sound reasoning and bounced them off a few other people.

Given what you’ve said so far, I highly doubt that answering the question you asked will help you. However, it is not impossible that the answer you seek is actually exactly the one you requested. Either way, I’ll apologize on behalf of all of us, that the Playground is just too dang helpful, and wants to make sure they’ve solved as many possible problems as they can...

Well thanks. And by all means, solve away!
It's just...really, REALLY weird to me that some of these replies seem to be attempting to answer a slew of questions I didn't ask and NOT the one I did.

I think the reason so many posters are questioning the pure math angle is because gaming (and particularly "fun" gaming) is always from the players perspective. In RPGs (heck same in wargaming too), players most enjoy making decisions and having those decisions affect the outcome. Die rolling is a necessary random element to this, but should never outstrip that process. No one, at any table I've ever been at, actually enjoys failing purely because they rolled badly on the dice. They accept it. But they are never happy. This should be minimized as much as possible.

100% agree. I strive for this, always.
That's a big part of why I asked about the math part; in most cases, I'm hoping to present challenges that, if the players are clever and make smart choices, they will scape by with a victory. So I was wondering how high the target numbers could be, on average, to present the threat of imminent failure without crossing over it (unless they make poor choices, of course).
In 3rd and Pathfinder, my understanding of the system is instinctive enough that I can do that pretty much every time. But 5e is much more streamlined and has less options on the adjudicating side of things.

What you seem to be doing is the exact opposite. You're giving the players very minimal choices (one: take path A, B, or C). That's it.

I am asking them to (1) pick between the long and easy option, the short and difficult one and the one that's somewhere in the middle and (2) to choose which sort of skills they want to bet on as a team.
It's one semi-layered choice. There will be many more choices in other aspects of the game.

Then they are asked to spend the next X amount of time at the table rolling the same skills over and over, waiting to get enough successes in each set of rolls to determine advancement, and to then get enough advancements to get to the goal. Even if you lay out the entire set of skills required, numbers of players who have to succeed in each round to advance, the amount of time each attempt takes (one hour in this case), and the number of times they must succeed to get through that path, that's not really "fun" for the players. It's repetitive dice rolling. Even if you insert other encounters/events/activities in between the die rolling, that part (the die rolling) is the part the players will least enjoy. So why do it?

U don't know what to tell you. If you don't see an ongoing struggle towards a goal with an ever-dwindling margin of error as a potential for some nice tension, then...yeah, I dunno. I've seen games that ended with a verbal debate where players were standing around the table, craning their necks to see the result of those last few die rolls.
I mean, this isn't meant to be the bulk of the game. This is one mini-system of several. I don't need it to be THE MOST EXCITING THING EVAR. It's a way to interact with the setting, establish the tone and transition between small encounters. After that, it's on to Act 2.

To be perfectly honest, I'd also *never* make simply traversing the path(s) take so long that it causes failure of the adventure (again, not knowing the consequences if they are "late" makes it hard to assess this). Why does the math matter? Because the consequences matter. If the outcome is between "you get there with plenty of time" and "you fail. Everyone dies" then it's important to make the skill checks extremely easy so that their odds of failing just because of bad die rolls is minimized (zero even). If the outcome for failure is "you get back and now there's another problem you have to deal with that could also be fun", then by all means make the DCs super high to maximize the odds of that end encounter/whatever happening.

I've run survival games where getting lost can result in death, or more typical heroic fantasy where the clock is ticking down to the end of the world or whatever, but those are fairly uncommon. This game will not be that.

To be fair, you are looking for answers just on the math question. But we can't teach you math right here in this forum.

Yeah, I've guessed as much. It feels like something that could appear on a high school statistics exam, so I thought maybe someone remembered more of that unit than I did.

We'd need to know not just the information you have provided, but also the distribution of skills on every character's sheet as well.

No. I never plan games around the exact capabilities of the characters. That's why I said I was assuming the average roll for the characters will be a +3.
But even then, it's not necessary: "what is the probability that, of 5d20, 3+d20 come up X or higher?" --that's all I'm looking for. I don't need or want anything more precise.

And again, we don't know if those odds are "reasonable" or not, because we don't know what the relative consequences for success and failure are.

Don't need to. If I see 70%, 40% and 20% that'll be enough for me.

You're spending a lot of time on a part of the gameplay that the players will least enjoy. I'd focus all of that time on adding in more scary/spooky elements, things to make the characters worry, decisions to make, etc, along the way instead. I'm not assuming you aren't doing this already, but I'd still just leave the excessive die rolling out of the game.

Excessive. Like...three dice rolls. Excessive. Hm. Okay.
And yeah, I am most certainly doing all of those things.
And I promise you, I spent very little time coming up with this subsystem. It is one part of the session. Not even an encounter in and of itself.
What has taken considerably more time is defending myself when I was all but insulted.

It's just so WEIRD. It's like I asked someone if they have the time and they started lecturing me about my time management skills. Like...yeah, thanks. Anyway. Anyone got the time?

Yeah. Unsolicited advice. Take it or don't.

Thank you.

Your lack of math savvy here may be frustrating you, as your stated problem ignores some rather important details, like the party members' respective bonuses to various checks (as well as your desired P(success)). Those make a big difference.

So okay, first: wow. That's awesome. Thank you.

Secondly, I specifically said I'm assuming an average modifier of +3. And my desired P(successes)? You mean, how many successes in each attempt are required? That's 3.

So 1d20+3, five times. Three or more of those need to be successful.

But again, I really don't get why we'd need to know the modifier for the equation. If I know the likelihood of rolling X three or more times, I'm all set. Because then I can plud whatever modifier Y I want into it and figure out the odds of rolling X-Y, right?

[meschlum]

Wow. Your maths outstripped mine by far. Thank you.
There are some misunderstandings, though. Let me see if I can clarify:

1. There are 5 PCs. So, per the group skill check rules, more than half of them need to succeed. So 3, 4, or 5 of them need to succeed out of 5.

2. There are 3 paths. Each path has a minimum number of rolls that need to be made (a) and a DC for those rolls (b). The lower (a) is, the higher (b) is.

4. Each roll represents 1 hour. If the 5 players roll 3, 4 or 5 succees, they make meaningful progress. If 0, 1 or 2 succeed, they do not.

5. I am aiming for each path to take a total of 11 hours to travel it's length twice.
So the path's length (a) cannot be 11 or more, because they need to have some room to make at least one mistake/take a short rest, etc.
And because paths with a higher (b) will result in the PCs making less progress/hour, I want to make those path's (a) lower, to give them a larger margin of error.

So, for example;

The first path is along the River Gloaming. It's the longest, so there isn't much room for mistakes. They don't have much spare time. Str (athletics) DC12, 5 rolls to get through it.
They can mess up or take a break twice total before they run out of time.

The second path is through the Pinetar Swamp. It's shorter, but harder. Say, Wis (survival) DC15, 4 rolls to find their way.
They can mess up/rest up to 3 times.

The third path is straight through the woods. It is the shortest and most difficult. Dex (acrobatics) DC18, 3 rolls.
They can mess up/rest up to five times.

Does that make sense?

Alright!

So with 5 PCs and 3 successes required, you can use the formula I provided for 5 directly: p^3*(10 - 15p + 6p^2) gives the probability of the party succeeding at a challenge, assuming they all have the same probability p of succeeding. The interesting breakpoints are:

p = 0.5: the party has a 50% chance of success (each character succeeds on an 11+)
p = 0.25: the party has a ~10% chance of success (each character succeeds on a 16+)
p = 0.75: the party has a ~90% chance of success (each character succeeds on a 6+)

You can compute the others, of course.

So the odds of the party succeeding move fairly quickly - if each party member faces a DC 5 higher (from 50% chance of success to 25%), the 'party' DC goes up by 8 (from 50% chance of success to 10%).

If your round trip total is 11 hours, the 5 hour trip allows for a single break (not two), incidentally.


The goal you describe reads to me like you need 10+ successes out of 11 challenges (hours) for the first path, 8+ out of 11 for the second, and 6+ for the third. This is entirely amenable to the standard equations, just with different numbers.

Since we're looking at 11 challenges each time, it's possible to set down the relevant equations

11 successes: p^11
10+ successes: p^10 * (11 - 10p)
9+ successes: p^9 * (55 -99p + 45p^2)
8+ successes: p^8 * (165 - 440p + 396p^2 - 120p^3)
...

As a bonus, a few computed values (very easy to do on a spreadsheet, the Excel equation for having exactly S successes is p^S * (1 - p)^(11 - S) * COMBIN(11, S), and then you just add up the odds of having the successes you want)

p = 10% (3+ party members need to roll 16+): ~1 in 700 million of 10+ successes, 1 in 600,000 of 8+ successes, 1 in 2,800 of 6+ successes. The party will fail.
p = 50% (3+ party members need to roll 11+): ~1 in 170 of 10+ successes, ~1 in 9 of 8+ successes, exactly 50% chance of 6+ successes. A gamble when 6+ successes are needed, very risky at 8+, requiring a lot of luck for 10+
p = 90% (3+ party members need to roll 6+): ~68% chance of 10+ successes, ~98% chance of 8+ successes, ~99.96% chance of 6+ successes. A likely bet if 10+ successes are needed, basically certain if fewer are required.

So the lesson from this is that when making lots of rolls, getting a failure is more likely that it feels - if you want the party to succeed you'll need to have DCs lower than you think.

Since I set up the equations, I might as well go a bit further...

10+ successes: if the required roll is 7+, 44% chance of success. With 6+, it's 68%, and with 5+ it's 87%
8+ successes: if the required roll is 10+, 28% chance of success. With 9+, it's 51%, and with 8+ it's 75%
6+ successes: if the required roll is 12+, 26% chance of success. With 11+, it's 50%, and with 10+ it's 74%

So if you want the party to have more than a coin flip chance of succeeding, you need to set the DC so that they have a fairly high chance of success from the start.


Also note that characters are different, so the 'average' modifier is deceptive. If there are two party members and the average modifier is 0, then you could have two cases at DC 11 (to simplify)

Both characters have a modifier of 0: 75% chance of one or more succeeding, 25% chance of both succeeding
One character has +10 and the other has -10: 100% chance of one succeeding, 0% chance of both succeeding

What this means is that characters with poor modifiers will make things worse more than characters with equally good modifiers will improve the odds. So in a mixed party, you'll get failures more often than the numbers I set down - and therefore I'd recommend moving the DC a bit more...

[Amidus Drexel]

So okay, first: wow. That's awesome. Thank you.

Secondly, I specifically said I'm assuming an average modifier of +3. And my desired P(successes)? You mean, how many successes in each attempt are required? That's 3.

So 1d20+3, five times. Three or more of those need to be successful.

But again, I really don't get why we'd need to know the modifier for the equation. If I know the likelihood of rolling X three or more times, I'm all set. Because then I can plud whatever modifier Y I want into it and figure out the odds of rolling X-Y, right?

Oops, totally missed that you were assuming +3. That's easily captured in the first table I gave you (and you're correct in your intuition that you can just shift up/down the table to include player bonuses), but it actually misses some nuance where bonuses higher or lower than the mean will skew results in unusual ways. That percentage will give you the probability that the party succeeds at a given skill challenge (which is what you asked for, mostly).

However, unless I've misunderstood something, the scenario is thus:

• There are 3 paths, each with a different number of skill challenges at different difficulties.
• Each path requires the party as a group to pass a certain number of skill challenges.
• Each path has some leeway where the party may make additional attempts to pass skill challenges.

The probability that the party succeeds at the scenario, therefore, is dependent on which path they take, and meschlum did this in much more detail than I was going to, so I'll just leave you with their math. I do want to reiterate a few things they said though, because probability can do unintuitive things if you don't have experience with it:

So the lesson from this is that when making lots of rolls, getting a failure is more likely that it feels - if you want the party to succeed you'll need to have DCs lower than you think.
--
Also note that characters are different, so the 'average' modifier is deceptive.

What this means is that characters with poor modifiers will make things worse more than characters with equally good modifiers will improve the odds. So in a mixed party, you'll get failures more often than the numbers I set down - and therefore I'd recommend moving the DC a bit more...

[gbaji]

I am asking them to (1) pick between the long and easy option, the short and difficult one and the one that's somewhere in the middle and (2) to choose which sort of skills they want to bet on as a team.

That's not two choices. That's one choice: Pick A, B, or C. There are multiple factors involved in that choice (long/easy, short/difficult, and the skills that may be used in each path), but it's ultimately only one decision being made by the entire party. The second "choice" you list isn't a choice at all. It's a determination by each player what the best of the two skills for each path is. Unless you are also going to introduce yet another factor that makes outcomes different based on which skill was used, then there is no choice being made.

U don't know what to tell you. If you don't see an ongoing struggle towards a goal with an ever-dwindling margin of error as a potential for some nice tension, then...yeah, I dunno. I've seen games that ended with a verbal debate where players were standing around the table, craning their necks to see the result of those last few die rolls.

I personally dislike outcomes that are strongly determined by dice rolling alone. That's just me. That doesn't build tension. It just builds frustration. Yeah. People like it when they win, but if they only won because of a lucky die roll, it's not terribly satisfying. And when they lose, they just feel frustrated because there was nothing they could do except just roll the dice.

Also, and I can't stress this enough, I don't think the methodology you're trying to use is very likely to actually result in the tension and "dwindling margin" that you think it will. You will far better achieve that through roleplaying techniques than through die rolling ones. That's just my opinion, of course.

No. I never plan games around the exact capabilities of the characters. That's why I said I was assuming the average roll for the characters will be a +3.

Again though, that's critically important. I don't think you really realize just how failure prone the methodology you're using is. Even if the "average" bonus is +3, the mechanism you're using requires a given number of characters to succeed in each round for the whole to succeed in each round. Average isn't the issue. You need X successes to make progress in each hour. The odds are rapidly dwindling even if all the characters have the same bonus and we do the math based on that. If there are variations (even a point or two makes a huge difference here) you failure rate may be 2-3 times higher than you think it might be.

Again. The method you are using has an almost impossibly small margin for error. I get that you're trying to go for dramatic tension, and even setting aside my own personal dislike for that form of drama, your odds of getting results that come even close to the "OMG. If we make this we succeed, but if we fail we're screwed" is incredibly low. Odds are the players will have a series of rolls, with a series of failures, and find themselves falling farther and farther behind with no statistical chance of ever recovering. Because the rules you are following have skewed things that way. And even a minor adjustment in the other direction will result in them sailing through with no problems.

I'd pick something else to drive tension. if you're dead set on it, then take the tables others have provided and run with it. Maybe it'll work out fine. Personally, I'd work up some method that drives odds towards success rather than drives towards failure. Maybe allow the best skill to be used and assume that character is leading/guiding the rest through the obstacles. Or allow extra die values to be applied to the outcomes of other character's rolls (so every point you succeed by in excess of that needed can be used as a modifier to another characters, perhaps poorly rolled, check). This would represent those who are having an easier time of things helping out those who are struggling, but every character has to make the skill check in this case to advance as a group.

Either of those methods is easier to calculate as the GM, thus easier to manage in terms of total odds of success/failure, and most importantly allow you as the GM to calculate things to maximize the odds of the total time taken being "close to the limit", so as to maximize that tension. The method you are trying to use is going to be wildly variable and may easily spin off into "high failure rate", and likely result in a very early determination of "no chance to win" by the players. At which point, your entire scenario falls apart.

But again, I really don't get why we'd need to know the modifier for the equation. If I know the likelihood of rolling X three or more times, I'm all set. Because then I can plud whatever modifier Y I want into it and figure out the odds of rolling X-Y, right?

Because the odds of three or more players out of five succeeding in a roll varies massively based on smallish modifiers to each roll. It's the requirement that X number must succeed or everyone fails that causes this effect on the resulting probabilities. It's an innately unstable calculation and I'd avoid trying to use it at any cost if you at all want the outcome to have significance to the overall outcome of the scenario. Doubly so since you seem to want there to be tension based on time taken. Your method will tend towards the edges of the outcome scale. They will likely either fail miserably (not even come close), or succeed easily. Getting that perfect middle point is extremely difficult and unlikely.

[Quixotic1]

...So the odds of the party succeeding move fairly quickly - if each party member faces a DC 5 higher (from 50% chance of success to 25%), the 'party' DC goes up by 8 (from 50% chance of success to 10%)...So the lesson from this is that when making lots of rolls, getting a failure is more likely that it feels - if you want the party to succeed you'll need to have DCs lower than you think...the 'average' modifier is deceptive. If there are two party members and the average modifier is 0, then you could have two cases at DC 11 (to simplify)...What this means is that characters with poor modifiers will make things worse more than characters with equally good modifiers will improve the odds...

Awesome. Thank you for breaking it down. This is exactly the kind of thing I was looking for. I figured that the numbers would crunch in ways I couldn't predict unless I understood it on a deeper level, and you've shown me that level with clarity. Thanks!

...you're correct in your intuition that you can just shift up/down the table to include player bonuses), but it actually misses some nuance where bonuses higher or lower than the mean will skew results in unusual ways...I do want to reiterate a few things they said though, because probability can do unintuitive things if you don't have experience with it...

Agreed! That's what I was concerned about.

That's not two choices.

So it's one choice with multiple factors. Yeah. Cool. That works for me.

I personally dislike outcomes that are strongly determined by dice rolling alone. That's just me.

It's me, too. But I just wanted to build a quick n' easy subsystem. The adjudication of that system in-game will (hopefully) be another thing entirely. If the players are smart and attentive, they'll make good choices to skew the odds in their favor. If they don't...I mean. That's the whole "challenge" part of play, to me. You want to win? Then listen up and be clever. Try. Get that effective +5. Get it on every roll, if you can. And they should be able to.

Also, and I can't stress this enough, I don't think the methodology you're trying to use is very likely to actually result in the tension and "dwindling margin" that you think it will. You will far better achieve that through roleplaying techniques than through die rolling ones. That's just my opinion, of course.

I roll dice when there is a chance of success, a chance of failure and consequences for either. There are literally no exceptions.
It seems like you think I'm going to sit down at this table and just go, "roll X...okay, you succeed. Roll Y...okay, you fail...roll Z..." and that is as far from my gamemastering style as you can get. The dice are one tool in the kit. Among many.
In all honesty, I am extremely, supremely confident of my ability to set a tone and create tension at the table. I am, in the deepest chamber of my secret heart, a storyteller.
But this thread was never about any of that. I just wanted to get a feel for how this rule in this unfamiliar system worked in terms of probability.

[QUOTE=gbaji;25588968]

Again though, that's critically important. I don't think you really realize just how failure prone the methodology you're using is. Even if the "average" bonus is +3, the mechanism you're using requires a given number of characters to succeed in each round for the whole to succeed in each round. Average isn't the issue. You need X successes to make progress in each hour. The odds are rapidly dwindling even if all the characters have the same bonus and we do the math based on that. If there are variations (even a point or two makes a huge difference here) you failure rate may be 2-3 times higher than you think it might be.

I get that you're trying to go for dramatic tension, and even setting aside my own personal dislike for that form of drama, your odds of getting results that come even close to the "OMG. If we make this we succeed, but if we fail we're screwed" is incredibly low. Odds are the players will have a series of rolls, with a series of failures, and find themselves falling farther and farther behind with no statistical chance of ever recovering.

Well again, you keep assuming that I'm just going to run the system without any effort put anywhere else, which is confusing. Like, when someone asks me "what do you think of this build for my character?", I don't go "I really think you're missing the point of what a character is. You're focusing too much on the numbers. I'd spend more time with who they are as a person", because that's just not what the conversation is about.

And yeah, the odds ARE what the conversation was about, from the beginning. And now that I'm getting a refresher course in statistics (and going well beyond anything I retained or was probably ever taught, honestly), I'm seeing how and why. Which is what I wanted.

I'd pick something else to drive tension. if you're dead set on it, then take the tables others have provided and run with it. Maybe it'll work out fine...They will likely either fail miserably (not even come close), or succeed easily. Getting that perfect middle point is extremely difficult and unlikely.

Thanks. I am; I would really like to use the rules set down in the system a bit before I deviate wildly from it. I'm working on making this a legit side-hustle to supplement my family's income, so it seems like it's in my best interest to get accustomed to D&D 5e.
Once I have that understanding down, I'll polish things up a bit here and there to get it to where I want it.

It's hard to heed someone's warnings when they're being so presumptuous. And on top of that, they seem unable to answer your actual question. They hint that they know the answer, but they don't offer any evidence themselves.
But when other people step forward and actually address what I'm concerned about and I can see where some problems might lie--that's when the conversation can move forward in a meaningful, constructive way. I hope you can see that.

Thank you for your help, everyone. The rest is all but done, now. Maybe I'll come back and report on how it went.

[meschlum]

Awesome. Thank you for breaking it down. This is exactly the kind of thing I was looking for. I figured that the numbers would crunch in ways I couldn't predict unless I understood it on a deeper level, and you've shown me that level with clarity. Thanks!

I got curious, and pushed things a bit further...

With the DCs you provided (12, 15, 18) and the average +3 bonus, you get success on a 9+, 12+, and 15+ for party members (each challenge is passed with probability 68%, 40%, 16%). Which is bad news - the party's chance of success overall is ~9%, ~3%, and ~0.4% along the different paths.


I also ran some experiments with different skills levels, to see how much moving away from the average changes things. Assuming the range of modifiers is +/- 7 (-4 to +10 in your example), so +/- 35%.

- If the average does not change, the overall probability of success for the party does not shift much if party members have different modifiers - the overall shift in the party chance of success is typically less than 5%. This is for a single challenge!

- One party member having an extreme modifier (35% more or less than the average) changes the overall average by 7% (35% / 5 party members), so in 'average' terms it's comparable to a change of 1 in the DC.

- If the average party member has a chance of success of 60% or more (DC 12 or less with a +3 modifier, need a 9+ or lower to succeed), more volatility between party members is good. The insight here is that a party member with a high chance of success means that the other four members only need two successes (rather than three), and still have decent odds (since the average chance of success for the four remaining members at least 53%).

- If the average party member has a chance of success of 40% or less (DC 16 or more with a +3 modifier, need a 13+ or higher to succeed), more volatility between party members is worse. This is the same point as above - the remaining party members have < 50% chance of success overall, and need three successes!

- If the average party member has a chance of success between 45% and 55% (DC 13, 14, 15 with a +3 modifier, need 10+ to 12+ to succeed), it's harder to tell. The exact distribution starts to matter more: one outlier and the rest are similar? One very high and one very low? In any case, bigger differences between characters will amplify the benefit or disadvantage, but the shift will be relatively minor.


So if you set the DCs low (per my prior email) to give a good chance of success overall, a more diverse party will typically be a bit more likely to succeed than the numbers I suggested (the experts pass, the others are competent and so likely contribute enough). If you set the DCs high (or even moderate, per your initial suggestion), any competent PC will probably be dragged down by the difficulties of the rest and the party is even more likely to fail than its already poor odds.

[gbaji]

Thanks. I am; I would really like to use the rules set down in the system a bit before I deviate wildly from it.

If there's time for one more suggestion. Maybe instead of rounds with each requiring a set number of successes, just require each path (to and from), require a number of total successes, regardless of who succeeds, and in what order or round.

Just changing the math from (3 out of 5 successes to advance, and 3 advancements required to finish the path), just say "once they get a total of 9 successes they make it through the path", dramatically changes the outcome calculation. This retains the same methodology (everyone rolls their skill against the DC each round), doesn't require any additional math with the skill successes themselves (just pass/fail for each character), but also eliminates a lot of the "trend towards failure" problems.

You can then pretty easily calculate the average number of successes per round of die rolling and then calculate the average number of rounds to travel through each path, and therefore calculate the likely total number of hours for each trip. You can then adjust the difficulty and/or number of total successes needed and get the results you are looking for. And in this case, due to the methodology, the outcome will trend towards the average result, giving you a high degree of "success" at ensuring that the outcome is "close" to what you are trying to do.

[Quixotic1]

https://forums.giantitp.com/showthre...4#post25605494

-- here's the thread where I outline how it all went, for those that are interested.