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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2
votes
3answers
67 views

How to make Anydice see if two values are the same among 3 dice and keep them?

Is there a way to calculate/simulate rolling 3d20 and spit the middle one (that is easily done with middle function), or if its value is the same as the high or the low one, spit that one too? Here it ...
7
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2answers
601 views

Is it possible to model these probabilities in AnyDice?

I was asked by a pal to help him model a dice mechanic in AnyDice. I must admit I am an absolute neophyte with it, and I offered to solve it using software I'm better versed in. I'd like to be able to ...
26
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11answers
5k views

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, ...
12
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2answers
333 views

How can I ensure my dice roll fairly if they appear to have a bias?

I have purchased several sets of dice from different online retailers. I did some salt-float tests on them recently and I'm concerned a good amount of my d20s are favoring a specific corner (all 3 ...
4
votes
1answer
58 views

How do I graph the chance of success with a range of dice pools against a range of target numbers?

I'm having a hard time coding an anydice script to show what I want. Let me contextualize the mechanic I'm trying to simulate: You roll a POOL of d10 against a TARGET number. If at least one die from ...
3
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2answers
76 views

What target numbers would be a certain level of difficulty under this system?

I’m writing a homebrew game system, and I found that I have an action resolution mechanic but not a good system for target numbers (I call them Success Thresholds, or STs, in this game, and from now ...
4
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3answers
258 views

Which modifier added to a 1D20 has the closest outcome probability as rolling 2D20 with advantage with no modifier? [closed]

I'm trying to determine the probability of every modifier to a 1D20: 1D20 +1 1D20 +2 1D20 +3 1D20 +4 1D20 +5 vs flat 2D20s with advantage ...
3
votes
1answer
221 views

At what point is a Lifedrinker Warlock's expected damage reduced by Sharpshooter/GWM?

At Level 12, a Pact of the Blade Warlock can take the Lifedrinker Eldritch Invocation, which states the following: When you hit a creature with your pact weapon, the creature takes extra necrotic ...
10
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2answers
865 views

What is the formula for Unarmored Movement's bonus?

I'm trying to plug in an equation for a monk's unarmored movement in DiceCloud, so that I don't have to change the bonus value whenever it changes. I had a formula, but lost it. Does anyone know what ...
15
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5answers
6k views

A player rolls several 20-sided dice, takes the lowest value, ignores the rest. What is the probability of this value being at least 7?

I'm designing a tabletop game, and I need to figure out how to calculate a few probabilities: Roll 3 20-sided dice, take the highest value. What is the probability of it being 7 or higher? 15 or ...
5
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3answers
384 views

How to calculate the probabilities for eliminative dice pools (dice cancelling mechanic) in Neon City Overdrive?

The game Neon City Overdrive uses the following resolution mechanic for checks: create a pool of Action Dice and (possibly) another pool of differently-colored Danger Dice (all d6, generally up to 5 ...
1
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2answers
188 views

What is the formula for damage per round?

I'm creating a web app to learn JS that will calculate damage per round but I'm stuck on adding criticals. I have successfully created variables for: diceNumber, diceSides, bonuses, attacksPerRound, ...
6
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1answer
533 views

What is the percentage of possibly hitting something that has stacked Blur, Blink, Mirror Image, and Armor of Hexes?

This question is mostly for hypothetical fun because setting all of these up isn't super practical (unless it's a 1-on-1 campaign perhaps?) But with all of these stacking, how likely are you to be ...
3
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1answer
166 views

How do I calculate d20 success probability using the Halfling 'lucky' trait with advantage?

Here is a comprehensive DPR calculator, and here is the mathematics behind it. I'm trying to follow along with the equations. At the bottom of the second page are formulas for success probability \$L\...
15
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3answers
2k views

What's worse, -2 or disadvantage?

So, I'm building a system that adds an extra level of flavor, with some minor mechanics as an optional side system for a 5e campaign. The basic function is, you collect points, then collect a deficit. ...
3
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5answers
148 views

For anydice.com, is there a way to set a total number for three rolls?

I am very, very new to writing code and working on designing a RPG. As part of that, I am trying to do a simulation of three weighted dice rolls, ranging from 1-12 where I set the limit of how much ...
9
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3answers
2k views

How do I mathematically find this distribution?

I roll 10d6. I can then reroll any ones or twos. Then, I can reroll any ones. What is the distribution of the number of sixes I will have?
0
votes
1answer
300 views

Between the half-orc's Savage Attacks trait and the Elven Accuracy racial feat, which is better?

In a mathematical comparison of the Half-Orc Savage Attacks trait and the Elf/Half-Elf feat Elven Accuracy (XGtE, p. 74), which one increases average damage more at level 10 for a Fighter-Champion 5 / ...
4
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1answer
176 views

AnyDice: How to calculate opposed roll probabilities for an unusual mechanic

I'm currently playing with a dice mechanic that is basically: Roll 2d10, compare each dice to a target number. If one rolls equal to or below the TN, it's a weak success. If both roll equal to or ...
8
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3answers
2k views

How many times can the Psionic Talent Die be rolled before becoming unusable?

In the Psionic Options UA all the subclasses get access to a Psionic Talent Die that works as follows: Changing the Die’s Size. If you roll the highest number on your Psionic Talent die, it ...
6
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2answers
651 views

How can I calculate the distribution of “Roll 3D6, reroll any dice once, treat all 1's as a 2” in AnyDice?

I'm wondering how to use Anydice to calculate the following: Roll 3d6, treating all 1's as 2's, you may reroll each die once, so we do this if the roll is below the average. So 3d6, can reroll each ...
27
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10answers
6k views

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 ...
7
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2answers
415 views

Is probability of succeeding an opposed check the same when the second check is passive?

An "opposed check" is a well-known kind of check in many games, when two opponents roll dice, add modifier and compare results. It differs from a convenient dice roll when you compare your result ...
8
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2answers
277 views

Roll and Keep in Anydice

I want to check out the probabilities of the Roll and Keep system (as known from L5R 1-4th Edition) in Anydice. We luckily have boundaries: We roll Skill + Stat + Modifier initial dice. 10 explodes;...
0
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3answers
679 views

Are attack rolls or saving throws more consistent or predictable?

In D&D 5e, spellcasters often have to choose between spells which can affect a target on a successful melee attack. The fire bolt cantrip (1d10 to 4d10 damage depending on character level), for ...
2
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0answers
101 views

How do attack rolls and criticals affect a 2d6 vs 1d12 damage roll? [duplicate]

For example, given the probability distribution between two similar weapons: D&D 5E Weapons - Basic Rules pg.48: Damage Discrete Distribution - AnyDice: Its evident that Greatsword is more ...
2
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0answers
96 views

Balance implications of these output to input luck change house rules? [closed]

What classes and approaches are helped and/or hindered by this set of house rules? For an upcoming DnD 5e campaign I am considering two house rules, both of which substantially effect one another. ...
24
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8answers
3k views

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 ...
11
votes
2answers
2k views

What are my odds of a critical hit with my level 20 Champion?

I'm trying to calculate what my odds are as a level 20 Champion to score at least one critical hit on my turn, and how many I can expect. I make four attacks per attack action I take, and can Action ...
4
votes
1answer
218 views

How do I find the outcomes of Ironsworn rolls in Anydice?

Ironsworn generally has two kinds of dice rolls in play: action rolls and progress rolls. Progress rolls are static, and use the number of progress boxes you've filled in through play (ranging from 0 ...
1
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0answers
90 views

What is the odds of rolling specific numbers on 4 d20s? [closed]

If I roll 1d20, then 1d20, then 1d20, then 1d20 (effectively 4d20), what are the odds that I'll roll specific numbers? For example, all 20's, or a combination of numbers such as (1, 16, 16, 1)?
11
votes
5answers
3k views

Odds of rolling the same results twice on advantage rolls

I know that this has probably been answered before, but I couldn't find any specific threads on it. This happened in a tabletop game recently, where all dice rolls are rolled with advantage anyways ...
7
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3answers
1k views

Does bounded accuracy effectively increase randomness in D&D 5e, compared to previous editions?

I have been reading D&D 5e for a forthcoming campaign and I have a small concern with bounded accuracy: Proficiency bonus growth at a low rate (a level 20 character has only a +6 proficiency bonus....
0
votes
0answers
118 views

Is there any way to improve ability score without items, only with spells or class features? [closed]

I found a few, but they are all bad, like true polymorph to improve ability scores (but I lose class features), does someone know any way to improve ability scores without losing class features, and ...
34
votes
24answers
7k views

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 ...
4
votes
1answer
209 views

Has anyone done research on average RPG probabilities?

I've been looking at designing an RPG system lately and I'm currently considering where to set the "difficulty" of a roll at to get some satisfying results. I'm wondering - has anyone researched some ...
6
votes
3answers
4k views

How does the double-bladed scimitar compare to using two weapons with the Dual Wielder feat and Two-Weapon Fighting fighting style?

I've often felt that having a consistent bonus-action attack (or other mechanic) is 'optimal' in builds during combat. The more actions/options you have, the 'better' you are able to handle different ...
6
votes
1answer
1k views

With the Great Weapon Fighting fighting style, how does the double-bladed scimitar's damage evolve?

Traditionally, the Greatsword, Maul and Greataxe are considered the strongest two-handed weapons (unless you take the Polearm Master feat, where Glaives and Halberds rock out). Barbarians and Half-...
5
votes
2answers
379 views

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 ...
-4
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5answers
351 views

How does one convert disadvantage on the attack of a attacker, into a bonus to AC for a target, in particular for a Cloak of Displacement?

Question: How does one convert disadvantage on the attack of a attacker, into a bonus to AC for a target Assume a monster is attacking with disadvantage, the target is a level 12 PC with an AC of 16. ...
5
votes
3answers
410 views

Function to calculate “Nd6 take highest 2, sort descending” probabilities in AnyDice

I'm creating an injury-table where the player has to roll a d66 to see how severe the injury her character sustains is. The players roll up to ...
4
votes
1answer
215 views

How does the Impervious Modifier apply to Defenses other than Toughness?

It's been about a Month since i started playing Mutants and Masterminds 3e with my friends, and we absolutely LOVE the system (particularly the one-shot modules), but something in the Impervious ...
6
votes
2answers
246 views

To what extent is a lower DC skill check with disadvantage harder than a higher skill check without?

I'm wondering how mechanically I could calculate a lower DC challenge with disadvantage as a middle-ground between a higher skill DC and that same DC with disadvantage. I'd like to describe a ...
10
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2answers
1k views

Which spell is the better use of concentration for a ranged Valor bard with the Elven Accuracy feat: Greater Invisibility or Swift Quiver?

Assumptions: ranged College of Valor bard the bard has 20 Dex the bard is shooting with a longbow another player can consistently provide the Help action for 1 attack with advantage every turn the ...
4
votes
3answers
660 views

How do I model a fudge dice roll with re-rolls in Anydice?

I need a little help with a probability calculation in Anydice. We are making a fudge based game using 4 fudge dice, so basically a d3 system: -1,0,1 We are allowing your attribute or stats in the ...
1
vote
0answers
127 views

Given an array of probabilities, can AnyDice output the number of specific die type (d6) combinations to best fit? [closed]

Given an array of probabilities: 5% 5% 4% 2% 1% 12% 12% 10% 6% 4% 42% 41% 38% 23% 11% 53% 51% 45% 21% 9% 87% 86% 80% 54% 31% Can AnyDice generate a list ...
5
votes
1answer
285 views

How would this House Rule for combined Advantage/Disadvantage Impact Rolls?

According to the rules for Advantage/Disadvantage: If circumstances cause a roll to have both advantage and disadvantage, you are considered to have neither of them, and you roll one d20. This ...
27
votes
4answers
5k views

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 ...
14
votes
1answer
785 views

What is the statistical difference between “choose either total” or “choose new total” when rerolling damage die?

I am reworking a homebrew class I made a while ago where one class feature stated: when making a melee attack you can choose to reroll the damage die. The new total must be used. I wanted to make ...
6
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2answers
1k views

How much on average does the Durable feat increase the number of Hit Points gained when spending Hit Dice?

There are other similarly mathy questions on this site such as "How much damage does Great Weapon Fighting add on average?" and "Are features that allow −5 to attack to get +10 to damage ...

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