# Tagged Questions

Statistics deals with the mathematics of probability-based games.

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### Does the chance of rolling a 1 in a pool of d10s increase as the number of dice increases?

Just a question about probability. If I roll one d10 there is a 10% chance of rolling a 1. Assuming that receiving any 1s among the results of a pool of dice is a failure, what are the chances of ...
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### What is the average roll of a die with an expanded explosion threshold as compared to one with an expanded success threshold?

This is going to be a bit of a weird question, but I'm figuring dice pool probabilities for a homebrew system and I want to know how certain abilities should be priced regarding their use. The basic ...
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### Considering Complex Dice Roll Probabilities

Hoping someone more math and excel/troll/anydice competent than I can help me out. I've long been considering implementing some Dungeon World style die roll mechanics into D&D. With Next about ...
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### What is your chance to win in a contest where you have advantage and your opponent has disadvantage?

I'm trying to think of the answer to a certain problem, but I'm finding it hard to calculate. How much of a statistical edge do you have in a scenario where all of the following are true? You ...
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### Dice pool success probability with one exploding die

I'm looking for the math behind the following: Players have a pool of 3–11 d6s, and have to get from 1–4 successes, "success" being a roll of 5+. One of these dice is special (represented ...
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### How do I approach the probability of a d100, using 2 d100's?

We're running an almost 100% homebrew system, which uses skills in order to craft objects during play. Allow me to first formulate an example to explain my question better: Jack is quite the mason ...
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### When rolling percentages, do 1d100 and two d10s (percentiles) share the same probabilities?

I know d100s are shunned because they take too much time to roll, and 1d10+1percentile is really fun, but do they share the same probabilities? Is it better to use a (digital) d100? Also, do d100s ...
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### What is the probability of surviving my death saves?

If my character drops to 0HP but is not killed instantly by massive damage, what is the probability that I will stabilize via death saves unassisted/unhindered? As a refresher, here are some of the ...
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### How many rolls does it take to get to six coins?

I'm designing a microRPG and need some help calculating probabilities so I can make an informed decision about how many coins to start with (controlling session duration and early-game frustration). ...
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### Improving “fumbles” when using pools of d10s in TROS

The original rules in TROS use varying pools of d10s to attempt rolling one or more successes against a varying Target Number (e.g., commonly a TN=7). Roll the pool of dice, count up the successes ...
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### What is the formula for average damage for an Avenger against an Oath target?

I am creating a spreadsheet to compute average damage for my party. One of the issues that I am having is calculating average damage for the target of our Hybrid Avenger-Assassin's Avenger attacks ...
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### How do you calculate an average damage when damage is conditional on circumstances?

I'm trying to compare two rogue builds to each other. The first rogue is easy. It's a wood elf with a long bow in a wilderness campaign, doing 1d8+mod damage and always being hidden with SA damage. ...
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### Does a roleplaying game that uses continuous probability exist? [closed]

I have an idea for a roleplaying game that uses continuous probability distributions (like the normal distribution) to decide random outcomes (instead of discrete distributions that comes from using ...
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### What is the statistically superior character creation method, twelve 3d6 or six 4d6?

The D&D 3.5 Player's Handbook gives (among others) two preferred methods to roll ability scores for a new character: a) roll 3d6 twelve times and keep the preferred six results, or b) roll 4d6 and ...
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### Are Earthdawn's dice mechanics as unfair and wonky as my player claims?

After an Earthdawn one-off running Misguided Ambitions with my regular D&D 4E group — because one guy was MIA — I had a discussion with one of the players about Earthdawn's dice mechanics. The ...
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### How much damage does Great Weapon Fighting add on average?

The Great Weapon Fighting Fighting style states the following: When you roll a 1 or 2 on a damage die for an attack you make with a melee weapon that you are wielding with two hands, you can ...
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### How to calculate the expected damage increase from Empowered Spell?

In D&D 5th Edition the Sorcerer Metamagic ability Empowered Spell states the following: "When you roll damage for a spell, you can spend 1 sorcery point to reroll a number of the damage dice up ...
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### How do I calculate the chance of hits?

(I do not know if I should post this in math.stackexchange.com, so I try to phrase it in a way that it makes sense for non-roleplayers. Just in case it gets moved) In the latest two editions of ...
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### Calculating 6D6 similar to poker dice [closed]

I keep coming back to the idea of building a game system around a 6D6 roll, taking matching sets of numbers and 'straights' as measures of effect. This guarantees that something always turns up (as ...
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### What's the probability curve of the D10 Storytelling System?

Recently a friend commented that he thought the dice pool in the d10 Storytelling System actually gave mediocre results, and that by increasing the number of dice thrown you were actually decreasing ...
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### How do you calculate the odds of success for an ability contest

I'm having a hard time understanding how to figure out the odds of success from an ability contest. I originally thought that each +1 would be 5% but anydice suggests 4% but only after a +1 ...
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### How does rolling two dice and taking the highest affect the average outcome?

D&D 5E has an "advantage" concept where instead of rolling 1d20, you roll 2d20 and take the highest. Likewise, disadvantage means rolling 2d20 and taking the lowest. How does this affect the ...
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### Is there a subtle difference between increasing DC and adding detrimental modifiers?

Modifying difficulty works in various ways within and between various roleplaying systems. But generally speaking, it seems added difficulty either modifies the target number (altering the check) or ...
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### Improving “fumbles” when using pools dice in TROS, part 2

(Thank you all so much for your help on my last post! I appreciate the explanations, graphs and suggestions given. As I continue to experiment with my homebrew variant, I do a lot of probability ...
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### How does replacing Advantage with a flat +2 affect Champion critical hit damage output?

My DM does not like Advantage/Disadvantage. While I disagree with his reasons on this, he has decided to replace it with a +2/-2 rule and I respect him (mostly) enough to follow his rules. I recently ...
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### Are Half-Elves immune to the paralyzing property of a Ghoul's Claw action?

The Ghoul's Claw attack in the Monster Manual (p.148) has the rider of forcing a save or paralyzing a creature if the target: ... is a creature other than an elf or undead ... My question is ...
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### Can you roll a dice pool or multiple dice rolls with only one die?

Say I'm playing Vampire: The Requiem and I need to roll 5 d10's. Can I roll a d10 5 times instead of having 5 d10's? Can I split it up if I must, so if I only had 4 d10's could I roll the 4, then roll ...
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### How can I get the highest or lowest values of an irregular dice pool in AnyDice?

I want to calculate irregular dice pools, such as (2d10, 1d8) in AnyDice, but I'm having difficulties. What I mean to do is out of a roll of 2d10 and a 1d8, take the highest (or lowest) two values ...
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### What are the statistical implications of doubling damage on crit instead of doubling the dice rolled?

I've been playing with a group that frequently allows players to double the value of dice rolled for crits (and other things) rather than rolling double the dice. Example, someone crits with 2d6 and ...
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### How I figure what dice I need to attain a certain curve? [closed]

I want to make character stats that fit within certain bell curves depending on choices during character creation (for example race, gender, class, sprokets amount, whatever). And I am wondering how ...
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### What is the Expected Damage Gain from this Part of my Homebrewed Gunslinger Feat?

Preamble: One of the players in a campaign I will be DM’ing for will be playing a fighter archetype called the Gunslinger (made by Matthew Mercer for the RPG show Critical Role). Since the player ...
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### Are class features, Abilities, and feats that allow −5 to attack to get +10 to damage mathematically sound?

Some class features, abilities of monsters, and feats allow you to take a −5 to your attack roll in order to gain a +10 to your damage roll. At first glance this looks really good, but when will it ...
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### How can I simplify a series of rolls without changing probability too heavily?

Ok, I'm working on a combat system converted from a video game to a tabletop game, and I'd appreciate some feedback on how I can make my combat defense system work. Currently attacking is handled as ...
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### Can I substitute a d3 with a d6?

I don't have a lot of dice yet, just a basic set of polyhedral dice: 1d4 1d6 1d8 2d10 1d12 1d20 Sometimes an ability or save calls for a die that I don't have. Strike, Unarmed [...] ...
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### How to compare hit % and damage between 1 attack vs 4 attacks with disadvantage?

Quite a few scenarios here, wish my AnyDice fu were up to par—if it's too much, no need to cover all of them, just the most representative, so I can figure out the rest. For the given character ...
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### How do I calculate the chance to hit a given AC?

My current level 2 variant Ranger has the Sharpshooter Feat. His hit modifier is normally +7, but with Sharpshooter it's +2 (due to the −5). I am wondering what the % based chance to hit is ...
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### What circumstances make Heighten Turning worthwhile?

The feat Heighten Turning has the following as part of its benefit: When you turn or rebuke undead, you may choose a number no higher than your cleric level. Add that number to your turning check, ...
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### Is giving one side advantage always equivalent to giving disadvantage to the opponent?

Sometimes, players get advantage; sometimes, monsters get disadvantage. Sometimes it's not clear whether to give someone advantage or his opponent disadvantage, especially in improvised contests (PHB ...
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### 3d6 vs a d20: What is the effect of a different probability curve?

What is the effect on game play of replacing d20 rolls with 3d6 rolls in a D&D 4e campaign? I started thinking about this after reading this question where the example was given of playing a d20 ...
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### Bulldogs! Gear damage vs. accuracy

I'm looking at ways to model weapons for my setting, and I like quite a few things what the Bulldogs! system does. Basically, it's a system that has Fate's Damage Floor (+Damage) combined with a ...
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### How can I model Burning Wheel probabilities in AnyDice?

I have a basic intuition about dice in Burning Wheel, but it's handy to be able to look at actual probability distributions to hone your intuition. Especially since important rolls can involve ...
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### Help calculating opposing dice pool in AnyDice

I need to calculate the probability of A winning against B. Both A and B throw 1-15 d6s, the one with more successful dice (SD) wins. There are actually 5 possibles outcomes: ...
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### Concerns about a dice-pool system [closed]

I'm writing "yet another rpg system" and I'm choosing a way to determine success. I'd like a dice pool mechanic, and I've come up with this. PCs have characteristics and abilities. Char. Mods will ...
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### Multiclassing in 3.5e (epic level)

I've started making a character for my first epic level campaign, and I need to know how to add up your BAB in higher levels. I understand that (for example) a +6/+1 BAB and a +2 BAB make a total of +...
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### What's the probability formula for succeeding at a Complex Skill Check? [closed]

The SRD page for Complex Skill Checks gives percentage numbers for a number of different scenarios. For example, if the required roll on a 1d20 is 2, the chance of success on a simple check is 95% (...
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### How to address Damage/Toughness bias in M&M Tradeoffs

The Basic Problem Right, Mutants and Masterminds is a True20 system where everything is resolved via rolling a d20. Attacks are made by rolling a d20 and adding the attack bonus, trying to match or ...
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### Are there any RPGs with an insane amount of stats? [closed]

Are there any RPGs with a ridiculous amount of stats? I'm not looking for an enjoyable play experience, just a game with many stats to see how crazy and complicated it is. (The reason being I want ...
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### How Do You Determine Static Statistics of Creatures?

I am writing stat blocks for creatures in a D&D module that I am working on with a friend. I am the designer, not the DM and I need to determine static stats for some creatures. Exempli gratia, a ...