# Questions tagged [statistics]

Statistics deals with the mathematics of probability-based games. This tag should be used for questions about tabletop game mathematics that relate to mechanics rather than game elements such as skills or attributes, and have relevance to RPGs in particular.

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### Help with AnyDice for custom system

Can someone please provide guidance on how to make my system work within AnyDice? The gist is: player stats dictate how many dice in a pool of d8s are rolled, if they have gear or skills proficiencies,...
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### Is a Superficial wound actually worse than a Light wound?

An interesting detail of Burning Wheel (Gold Revised) tests is that (unlike some other TTRPG systems) the exponent and the obstacle number are not "symmetric", in the sense that (say) a B4 ...
131 views

### Anydice help with irregular dice pool [duplicate]

Here's the gist of it: I roll a number of different size die like 2d6, 2d8 and 1d12, looking for the highest die. I found a nifty Anydice program that helped me understand the probabilities like this. ...
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### How can you calculate the likelihood of getting a set of stats or better when rolling 4d6 drop lowest?

If I have a given set of character stats from rolling with "4d6, drop lowest", how can I calculate the probability of getting that specific result, or better values for each of them? For ...
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### Anydice: Number of successes when dice can be boosted

Trying to run some statistics on anydice and I'm getting an odd result. Figure something must be wrong with my code but I can't find it. My situation is this: Player rolls 4d6 and drops lowest. They ...
775 views

### Recursive combined probability for triggering a bonus attack?

I'm trying to determine the average damage per round for a homebrew fighting style, so that I can compare it to other types of combat choices, and see if thing will remain balanced, when we introduce ...
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### How do I calculate the probability for a critical hit, with an expanded critical range, and advantage/disadvantage?

I know the critical hit probability for normal critical range (natural 20) is: normal: 0.05 advantage: 0.0975 disadvantage: 0.0025 But I don't know how to actually calculate this, and consequently, ...
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1 vote
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### How to include pushed roll chances in anydice?

D6 dice pool from 0 to 6 where resolving 0 is rolling 2 dice and counting the lower result only. Rolling 5 or 6 means a hit. Rolling 1 is a mishap. Degrees of Success: Failure: no hits at all Mixed ...
1 vote
69 views

### How does success chance change when a certain die result counts as multiple partial successes?

Dice mechanism: count wins (> 4) of [Mod]d6 (AnyDice). Mod ranges from 1 to 10. Difficulty ranges from 1-10, 1 being trivial, 3 being moderate, 5 being difficult, and 6-10 being ever increasingly ...
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### How can I simulate decreasing randomness even though randomness is increasing?

I am seeking a way to decrease variance as character skill advances. I've considered various mechanisms for dice tests. I have one in particular that does not accomplish this by default, but I like ...
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### Over time, how does doubling dice on a crit compare vs having another action? [closed]

Basic 5e rules for crits say that you double the values rolled on dice. I'm playing with a homebrew idea where instead of doubling the damage dice you instead get another action, which can also crit. ...
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### Part II of a probability problem I am working on for a mechanism to move tokens on a chart. Part I was two D4 dice. Part II is much different! [closed]

For Part I of this discussion, see this thread: Probability help on rolling two D4 with all doubles counting as zero except double 4s, which count as 4 That dealt with probabilities using two D4 dice, ...
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### Probability help on rolling two D4 with all doubles counting as zero except double 4s, which count as 4

So I have devised a game system involving two D4 being rolled to determine movement on a chart. It works by tabulating the difference between the dice pips on each die, e.g., Die 1=rolls '1' vs Die 2=...
1 vote
767 views

### How does this 2D6 probability math make sense?

I have a question about understanding the math to a previous question I had posed (answered successfully). Link at the bottom. The question is how does it make sense that rolling a 2D6 Die consisting ...
175 views

### Using AnyDice.com to calculate Non traditional dice combinations

I am not learned enough to figure this out alone. Not yet at least. I am trying to figure out how to use anydice.com to get probabilities of two different situations with dice. The main question is ...
1 vote
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### Producing a similar distribution to 4d6k3 but for the range [-4, 4]

I'm making a fork of D&D 5e (based on the SRD but then customized) and one of the changes I'm making is removing the whole score/modifier distinction and just going with a simple "score == ...
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### Help With Trophy Dark and Trophy Dark Risk Roll Probabilities

Has anyone done some basic probabilities on the Risk Roll from Trophy Dark or Trophy Gold? This level of statistics is well beyond my knowledge. Risk Roll A player will build two D6 dice pools. One ...
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### Anydice - Roll a d20 under target number but beat an opposed die

Curious about the following Anydice formula. I’d like to know how to calculate what it would look like to roll a d20 UNDER a specific target number (lets say 14 or 10), but also have that d20 still ...
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### Is it possible to combine multiple outputs in AnyDice?

I have a situation where I will be making four attacks that do different amounts of damage over the course of a round. I have the average damage of each of them(including the likelihood of missing ...
860 views

### How do I calculate probability for the dice mechanic in my custom indie ttrpg?

I am currently working on writing an indie TTRPG based on the "press your luck" style games instead of being based around miniature war games. I am struggling to understand the probabilities ...
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### AnyDice: Limited exploding dice

I'm trying to write a custom explode function, which has a limit on the number of rerolls available. A basic limit of limiting the number of rerolls per die is easy enough. The problem is trying to ...
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### How to calculate the probability to roll a specific pattern with Y dice and Z rerolls?

I'm working on a dice-heavy RPG, and trying to model a generic AnyDice function to calculate the probability of rolling a specific desired result for dice faces, such as "At least 3 dice with ...
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### AnyDice function to reroll one die if any die rolls X

I’m by no stretch of the imagination any sort of programming type, but I’ve been trying to use AnyDice to rank all the possible ways the die rolls can be modified in the board game HeroQuest. The ...
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### How can I map a single d20 to a number of hits? (use case: Animate Objects)

The Problem Suppose we have a character using Animate Objects (D&D 5e) to animate 10 Tiny objects, and is attacking the same enemy with all of them. According to RAW, you'd make a separate attack ...
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### Calculating probabilities from d6 dice pool (Degenesis rules for botches and triggers)

I'm trying to generate a complex probability table for a dice pool with between 1--14 D6. The table will contain the probability of success and of critical failure, given a number of D6 rolled and a ...
802 views

### How does one Calculate Dual Variable Probability?

Or asked another way: How do we determine the probability of given grapple to succeed? In DnD 3.5 the grapple mechanic relies on double variable randomness in order to determine success or failure. ...
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239 views

### What is the average difference between AC and Touch AC for monsters?

Or asked another way - How much easier is it (typically) for a player to hit touch AC rather than regular AC? This is a supporting question for: Is it a viable tactic to use a flurry of blows monk to ...
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### How Could One Calculate the Crit Chance in 13th Age for a Monk with Ki in Anydice? (If It Is At All Possible)

In 13th Age a critical is achieved when you roll a natural 20 on a d20. The Monk class has a few features that can fundamentally change its potential to crit. First off, a Monk using bare hands to ...
2k views

### I need a 'standard array' for a D&D-like homebrew game, but anydice chokes - how to proceed?

So, I'm working on a homebrew RPG that is similar to several FRPs that use 3d6 sorts of starting values for attributes/characteristics. I know how to calculate the standard D&D (5E or other) '...
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### When does Polearm Master deal more damage than an ASI?

Would a fighter deal more expected damage by picking the Polearm Master feat at any point before they maxed their Strength, or is it better to first always increase your Strength in terms of damage? ...
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### AnyDice: Count successes plus a limited number of easier successes

I've been searching around but haven't yet found how to get this average out of AnyDice. Players roll a pool of d6s. Normally, a success is counted on a 4, 5, or 6. However, there's a condition a ...
3k views

### How many rolls of a D20 would you expect to equal or beat (20 - number of tries)?

I have what is chiefly a probability / game-design query, but one with a clear RPG gaming purpose behind it. Assume I have a check in some game system, using a single 20-sided dice, that requires ...
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### In Unearthed Arcana: Expert Classes, changes were made to the Great Weapon Master feat. How does this affect the damage output of Great Weapon Users?

On September 29th, 2022, Playtest material for OneD&D was released for the Expert Class Groups, and included in this unearthed arcana were some planned feats for the new version of Dungeons and ...
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### Statistically, when should you wait to use Sneak Attack on a second attack with advantage?

Assume you have a Fighter/Rogue with one Extra Attack and attack advantage. Your first attack hits, but doesn't crit. Should you apply Sneak Attack, or save it for the second attack which may crit but ...
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### How often do I need to sing Happy Birthday to myself to survive Space Junk Cyberpunk?

In Space Junk Cyberpunk I can sing Happy Birthday after every third roll to remove one loneliness. Here are the rules: You have three scores: BREAKDOWN (which starts at 0) LONELINESS (which starts ...
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### What is the average total ability score bonus for the best of 4 DCC Characters?

I need some math help to determine what an average character that survived a DCC funnel is like. When playing a funnel in Dungeon Crawl Classics, players get 4 characters each. Should they survive, ...
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### Rerolling or taking +2

In Fate Core, the game rules for skill resolution involve rolling four six sided dice, and counting faces 1,2 as -1, face 3,4 as 0, faces 5,6 as +1. You then sum up the resulting numbers and add a ...
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812 views

### Dice odds of Doubles on 2D6 + D4/D6/D8/D10/D12 and Odds of 1

I have this odd idea for a resolution system and it goes like this. For every roll you will be rolling 2D6 + D*, depending on attributes, etc. against a fixed DC of 11. Rolling an 11 or better gets ...
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### How to calculate the added expected damage from critical hits?

When optimizing character builds, it is common to use the average expected damage to estimate damage output. Calculating the average of a single die is simple, fixed modifiers are then added to it to ...
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### Ironsworn meets BitD dice mechanic (with a twist)

I'd like to find the probabilities of a mechanic inspired mainly by Ironsworn. The basic premise is pretty simple and I have a working anydice program that gives me the right results but there's an ...
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### How to make a good height and weight table? [closed]

I am wondering how I would make a good height and weight table that has balanced ranges across a range of around 6-8 feet. When I have tried making a table, it always ended up being too light for ...
10k views

### Is there any estimate of average damage output per turn for PCs by level?

For monsters, we have the guidance of how much damage they are expected to deal in a round based on their CR from the DMG on page 274. In contrast, there is no such explicit guidance for expected PC ...
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### How can you map the probability of 2d6 onto a standard poker deck?

One of the projects I'm working on in my free time is the adaptation of the Urban Shadows milieu to a live-action environment. (In 2022, this is what one might charitably call a long-term goal.) One ...
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### As Nemesis Chi increases, how do the odds of player victory decrease?

Let's assume for the sake of argument that I am not out to TPK my players when we sit down to play a narrative game based on martial arts movies. That said, it would be nice to be able to engage in ...
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### Is there a probabilistic difference in player success between the two methods of fighting a Nemesis?

The Wushu rulebook: Mono-A-Mono Speaking of diverted dice, it’s not fair for groups of players to gang up on a single Nemesis. Rolling more dice than the other guy is a serious advantage, so your ...
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### How long can my character survive without sleep?

I got into a discussion over Discord this morning about whether the Dream spell could be used to kill someone. The claim was, if I remember correctly, that it would only take 6 days/nights because ...
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### What's the closest I can get to simulating critical hits with a dice pool, without relying on the total sum?

I'm making a game that uses a dice pool rolling system (for my purpose it's always a d12 and no other dice), and I wanted to figure out if making a 'critical hit' mechanic was possible, that is ...
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### Counterspelling with a lower-level spell

I'm curious about the utility of counterspelling with low level spells, if one chooses to feat for it. Particularly the feasibility of keeping low-level spells prepared specifically for use as ...
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