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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How does rolling two d20 and taking the higher affect the average outcome?
D&D 5E has an "advantage" concept where instead of rolling 1d20, you roll 2d20 and take the higher. Likewise, disadvantage means rolling 2d20 and taking the lower.
How does this affect ...
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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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My DM insists on rolling a single save for groups affected by AoE save spells. How does this affect my odds of successfully affecting the enemy?
As the title question, my DM rolls a single d20 save for groups affected by my area of effect spells that require a save, in order to save time. I can't help but feel like I'm being ripped off by ...
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Does microwaving a die significantly alter its balance?
I saw a rumor online a long time ago that stated by microwaving a die on a specific face it would be more likely to land on said face and have been looking for science by which to either prove or ...
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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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What dice mechanic gives a bell curve distribution that narrows and increases mean as skill increases?
I'm looking for a dice mechanic that produces a bell curve at all skill levels. I also want it to increase accuracy and precision as a character's skill increases — this basically means better average ...
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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 reroll ...
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Is it better to take the array and be Joe Average, or to roll for the odds of getting on average better scores?
I am new to D&D. I was looking at character creation for D&D 5th edition. There were a few ways one could generate ability scores. I assumed the optional method of taking the numbers 15, 14, ...
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Are features that allow −5 to attack to get +10 to damage mathematically sound?
Some class features, monster traits, 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 deal more ...
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How to approximate rolls for potions of healing using only d6's?
I want to make tabletop potions of healing out of corked vials (test tubes) filled with dice. Each vial would be labeled and filled based on the potion it represents. For example, a vial for a potion ...
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Is it possible to produce a bowl-shaped probability curve with dice rolls?
In D&D's basic D20 system, you roll one d20 and add in some modifiers, then compare the result to a target number. Each modifier effectively adds or removes a 5% chance of success with the roll.
...
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Is GameScience's non-cylindrical seven-sided die a balanced/fair die?
You might have come across GameScience's seven-sided die before:
There's mixed discussion of whether it might be biased toward the 6 and 7 faces (the 6 being on the opposite side of the 7 you can see ...
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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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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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Which feat, Resilient (Con) or War Caster, improves the chances of maintaining concentration more?
The Resilient feat (PHB, p. 168) allows you to increase one ability score by 1 and gain proficiency in saving throws using the corresponding ability. In essence, taking the Resilient feat and picking ...
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Mathematically, is a +2 bonus to AC better than attackers having disadvantage?
Mathematically speaking, I'm trying to determine if Bracers of Defense (AC+2) is better than a Cloak of Displacement, which causes all attackers to have disadvantage on attack rolls against you.
If ...
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Simulating these special dice on more regular dice
I've got a game that uses special dice for its resolution. Basically when making an opposed check, each side rolls a bunch of them based on the relevant trait, and whoever rolls most points wins. The ...
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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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What is the difference between giving advantage on a roll and reducing the DC?
I run a 5e campaign, and I like rewarding my players for thinking outside the box, roleplaying well, etc. Suppose we have the following scenario:
Violet is a bard, and is attempting to intimidate a ...
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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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Is it possible to emulate common polyhedral dice rolls using just a d6, and if so, how?
This is a question that I've asked myself numerous times, but I've never gotten a really satisfying result.
The issue is this: let's assume we only have one or multiple d6 dice (arguably the most ...
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How does Halfling Luck (re-rolling my Nat 1's) affect my dice outcome?
The Halfling Luck racial trait lets you reroll natural 1's on checks, saves, and attack rolls, but you must keep the second result. With Advantage or Disadvantage, it lets you re-roll only one of the ...
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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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Are these two methods of handling Elven Accuracy "Double Advantage" mathematically equivalent?
For context, part of the Elven Accuracy feat (Xanathar's Guide to Everything, p. 74) states:
Whenever you have advantage on an attack roll using Dexterity, Intelligence, Wisdom, or Charisma, you can ...
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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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Is "1d10 rerolling 1&2" equivalent to "1d8+2"?
Good old Cyberpunk 2020, 2nd edition, 2nd printing, offers two versions of rolling for statistics to players because point-Buy without rolling is for referees only. They read:
Random: Roll 9d10 and ...
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How does one calculate the distribution of the Matt Colville way of rolling stats?
Specifically, the Matt Colville way of rolling stats is:
Roll 4d6, drop the lowest value die for 1 stat;
If this roll is lower than 8, reroll it;
Repeat steps 1 and 2 until you have a set of 6 stats ...
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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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What are my chances of rolling a natural 19/20 critical if I roll 3d20?
The Oath of Vengeance paladin gains the Channel Divinity option "Vow of Enmity" at 3rd level (PHB, p. 88):
As a bonus action, you can utter a vow of enmity against a creature you can see within 10 ...
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How can the probability of a fumble decrease linearly with more dice?
I'm working on a simplified RPG system that uses only D6s, and I want a mechanic for fumbles/critical fails.
Depending on how good the player character is, they have 1-5 dice to roll and they have to ...
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What is the ideal way of emulating a full dice set using a single d20?
Imagine you are trapped in a post-apocalyptic world and only have a single d20 at your disposal, nothing else whatsoever. What is the ideal way of emulating all other common dice types (d4, d6, d8, ...
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Dice Rolling Method Fairness
Recently, in D&D sessions I have been rolling poorly (nothing over 10), and thus tried ways to improve my rolling. I was using a plastic solo cup last session, and got really good results compared ...
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How do I calculate my probability of success in Vampire the Masquerade?
How can I calculate my chance of success given my ability + skill vs a difficulty? How is this complicated when the difficulty is rolled as well?
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Roll For Shoes - Does the advancement system work for longer campaigns?
I'm about to start in on a new campaign with the Roll For Shoes system, but I'm concerned that the characters will swiftly outstrip basic and intermediate challenges as they grow in dice.
In the title ...
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How to approximate decaying probability distributions with few dice?
I am looking for ways to generate a probability distribution using dice which produces results that are skewed towards lower numbers, ideally as some kind of smooth decay.
For example, imagine a ...
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How do I compare the result of "1d20+x, with advantage" to "1d20+y, without advantage", assuming x < y?
I roll a d20.
If I have a choice between d20+x with advantage, or d20+y without advantage, what choice do I make to maximise the result? What are the values of x and y where the choice changes (if it ...
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Is it okay to roll multiple attacks that all have advantage in one cluster?
I am planning to make my first Ranger and going Hunter to eventually get Volley. If I get the preemptive strike from an unseen position, then RAW I get advantage on attack rolls.
Let's say I am ...
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What are the odds of rolling high all the time?
So, I have a suspicion that a player in an online game is... being creative in the way they call their dice rolls. I play with them in several games, and in 2 games I have convinced the DM to enforce ...
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Expected damage of a moonblade with 𝑛 runes?
As noted in David Coffron’s answer to another question, the moonblade (Dungeon Master’s Guide, pg. 217) has no fixed limit on how much damage it can do: there is no stated limit to the number of runes ...
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What is the difference between rolling more dice versus fewer dice?
Let's say there are two attacks: one rolls a 10d10 and the other rolls a 5d20. Assuming the modifier was the same, which rolls would have better chances of rolling average, and which would have ...
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Is there a subtle mathematical difference between increasing the target number 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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Is there an accepted likelihood of hitting that is consistent across tiers, and how has it been determined?
One can easily calculate DPR given a specific build (knowing proficiency bonus, ability scores, other relevant factors) and the AC of opponents, leading to spreadsheets with a matrix of customizable ...
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Roll Xd6, keeping highest value and adding +1 for each duplicate of that value?
I'm making a card/dice game and I'm trying to set something up on Anydice to compare the odds of the dice rolls, but I'm having some trouble wrapping my mind around some of the language Anydice uses.
...
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What is the chance of rolling at least 10 before a 1 on a d20?
I need at least a 10 on a d20. I can roll until I get it, or I get a 1. What is the chance I succeed? I would like to have the general formula, not just for 10.
The chance of success on the first try ...
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What deals more damage on a weapon, +1 to hit or +1 to damage?
Background: I'm introducing masterwork items for 5e as a homebrew rule, both to help players spend surplus gold on something useful when they cannot buy magic items, and to make shopping a bit more ...
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What is the average benefit of this particular stats rolling scheme?
In one D&D campaign I played years ago, we had to roll our stats with the usual "roll 4D6 and drop lowest" rule, however with a special exception, that is, if all four dice had the same result, ...
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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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What are the odds of rolling specific ability score totals in D&D?
I am about to start running a new game in 5e and I hate all of the ways of determining ability scores.
I have always felt that we play RPGs at least in part for the opportunity to pretend to be more ...
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How do I determine the probability of rolling various ranges of numbers on 4d10, 5d10, etc.?
After realizing that my knowledge of how probabilities function has waned significantly, I'm wondering what the probability of rolling multiple 6's or higher (6-10) on four 10-sided dice, five 10-...
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How can I implement a "passive stealth" that is mathematically equivalent to rolling stealth vs. passive perception?
I think the metagaming problem with rolling for stealth is fairly well-known: once the player rolls for stealth at the start of their sneaking, they know how high they rolled and might, consciously or ...
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