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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.

16
votes
2answers
2k views

How much attack damage does the AC boost from a shield prevent on average?

Statistically, how much attack damage does the AC boost from a shield prevent on average? I've seen claims it results in a 10% reduction in damage taken, is that accurate?
50
votes
8answers
4k views

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 ...
16
votes
1answer
484 views

Which Armor Class values should be used as controls when making damage calculations?

It is known that occasionally questions will pop up that are about attempts to optimize a character's damage output (sometimes shorthanded as DPR, or Damage-per-Round), and veterans of this game know ...
21
votes
6answers
5k views

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 ...
16
votes
9answers
3k views

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 ...
2
votes
0answers
77 views

How to calculate Yahtzee-like probability without too much by-hand work [closed]

So I'm working on a game that's got (to my knowledge) a novel mechanic; at least as far as tabletop roleplaying goes. So the central game mechanic is essentially lifted from Yahtzee: characters want ...
8
votes
2answers
241 views

How can I use AnyDice to simulate rolling 6d6, and dropping the 2 lowest and 1 highest dice?

I'm running a new D&D 5e campaign soon and I'd like to try rolling for stats with some guardrails. Doing some test throws at the table, I liked the look of rolling 6d6, then dropping the highest ...
10
votes
2answers
488 views

Is upcasting the Chromatic Orb spell (for fire damage) at 2nd level ever better than casting Scorching Ray?

Is upcasting the chromatic orb spell (PHB, p. 221) for fire damage at 2nd level ever better than casting scorching ray (PHB, p. 273)? I am mainly asking this since both are attack roll based fire ...
2
votes
1answer
409 views

Drawing as many cards as possible, what are the odds of drawing a beneficial order of cards from the Deck of Many Things?

I just "won" at the Deck of Many Things. I'm legit curious. Beyond that actually. What are the odds of what just happened, happening? (Also, the DM reading my character flaws and letting me find this ...
4
votes
2answers
76 views

How do I use the encounter chance tables in the AD&D 1e DMG?

I'm trying to set up a campaign and I'm not great at math. We play old school 1e AD&D. The 1e DMG gives two tables on page 47 for chance of an encounter. The base chance of encounter depending on ...
5
votes
2answers
426 views

How effective in combat regarding damage output could a Dexterity-based Barbarian be?

The Barbarian is a MAD (Multiple Ability Dependent) class. They require a good Strength stat for their attacks, good Constitution due to their need for a large amount of HP, and good Constitution and ...
-1
votes
2answers
582 views

How do you calculate average damage for DPR comparisons?

I have asked a few questions about optimization and DPR (damage per round) and I don't understand how those numbers are reached. Take, for example, a monster with 15 AC and a level 1 fighter with a ...
19
votes
6answers
2k views

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-...
11
votes
4answers
2k views

What is the probability of the Maze Engine from Out of the Abyss activating this effect?

In Out of the Abyss, there is something called the Maze Engine which, once activated, requires the DM to roll on a d100 table for random possible effects (pp. 186-188). One of these entries is: The ...
5
votes
1answer
161 views

How can I use AnyDice to get the odds of a specific number sequence from rolling 3d10 and dropping the lowest die?

I'm not very experienced with the program, or programming in general, and so I'm stuck. I managed to figure out how to get the probability of different sums of highest 2 of 3d10: ...
5
votes
1answer
147 views

Chances to roll a number of results greater than 5 on a number of d10s

I'm trying to figure out how to implement a dice roller function. I would like to know the chance in % to get [1 to X] results of 6+ on [1 to 10] 10-sided dice. So, for example, I would like to know ...
3
votes
2answers
170 views

Which of these scenarios involving advantage/disadvantage results in higher damage per round?

Considering a character is using the same weapon in both of the following scenarios, which would result in a higher damage per round? The character makes a single attack with advantage. The character ...
2
votes
1answer
250 views

Can you help me with the math on Great Weapon Fighting style on Greatswords?

I know there is already a question regarding the average damage impact on this style and I have been successful to calculate this damage increase myself. Yet I was more interested in knowing the ...
30
votes
6answers
4k views

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 ...
10
votes
4answers
749 views

How much does “Defender Wins Ties” affect challenge rating math?

In my group, we couldn't be bothered in session 1 to look up whether the attacker needed to score equal to or greater than the defender's AC in order to hit. We decided to live in a "defensive" world, ...
1
vote
2answers
2k views

Ability score increase or feat? [closed]

I rolled up a character for the new campaign using 3d6 in order method, so now I'm playing as lvl.3 human rogue (Str 6, Dex 12, Con 8, Int 10, Wis 8, Cha 6). How do I maximize my efficiency? Is it ...
-3
votes
1answer
198 views

What would be a Ritual Caster High level Wild Mage's average daily growth?

One of the possibilities on the Surge table is the following : 11-12 Roll a d10. Your height changes by a number of inches equal to the roll. If the roll is odd, you shrink. If the roll is even, ...
24
votes
1answer
4k views

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 ...
23
votes
5answers
11k views

Does the Resilient (Con) feat or the War Caster feat most improve the chances of maintaining concentration?

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 ...
26
votes
6answers
5k views

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 ...
7
votes
3answers
570 views

By asking my players to match my roll, am I making their checks harder?

Sometimes I ask my players to make a roll to see if something random happens (winning a game of chance, for instance, or a wilderness encounter). These rolls won't involve adding any modifiers, they'...
2
votes
1answer
168 views

What would the distribution curve of a 2d6 + card(s) look like?

I'm developing a new RPG and was wanting to use things readily available in most homes so as not to create a burden to play. The solution I came up with was 2d6, which the max is 12, and a deck of ...
3
votes
2answers
74 views

Converting this action resolution mechanic from total rolled to highest die rolled

Under a standard action resolution mechanic, a player rolls 3d6 and compares the total rolled to a Target Number (TN) assigned by the gamemaster, succeeding if the total meets or exceeds the TN. For ...
18
votes
1answer
784 views

Does switching all contests to Roll vs Passive DC change the odds?

Does switching all contests from Roll vs Roll to Roll vs Passive DC change the odds? Example: Player tries to grapple a medium opponent, let's say both the grappler and target have a Strength ...
2
votes
1answer
363 views

I need a dice system with a unique behavior and rate of growth (preferably in ANYDICE to verify) [closed]

I am looking for a defense system where the probability of hitting is proportional to the inverse of a quadratic polynomial with respect to defense. I don't care about attack scaling yet. If you ...
29
votes
3answers
2k views

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 ...
14
votes
2answers
2k views

Using 3d6 versus d20 for skill checks vis-à-vis advantage and Lucky

As a follow on to this question, now that people have gotten into the weeds and into the math on D&D's 5th edition, I am interested in seeing the impact on skill checks (only) of using 3d6 rather ...
11
votes
3answers
345 views

Probability of a d10 matching any faces on another Nd10

I am trying to figure out the probability for one separate d10 to have a matching face with a pool of d10 comprised by up to 5 other d10s. So just to make myself clear, the player rolls 5 d10s and a ...
1
vote
1answer
449 views

Is there an online tool that can calculate advantage/disadvantage versus arbitrary dice probability? [closed]

A variety of questions on RPG StackExchange fit the pattern of asking questions around the probabilities of advantage or disadvantage with or without a bonus versus x number of dice with or without a ...
32
votes
6answers
7k views

Mathematically, is an AC+2 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 ...
1
vote
1answer
346 views

How likely is to roll elite array or better with 3d6 in order?

Pathfinder elite array is 15, 14, 13, 12, 10 and 8. When rolling stats with 3d6, what is the probability of getting an equal or better set of ability scores than the elite array? For a definition of ...
1
vote
3answers
209 views

TWF or increased threat range: What's more likely to deliver a critical hit?

In Pathfinder, what is more likely to deliver a critical hit: Attacking once per round with an Elven Curve Blade (critical threat range 18-20) or Attacking twice per round with Two Weapon Fighting (...
-4
votes
1answer
141 views

Probabilities when rolling more dice than needed

I would like to know whether adding an extra die whose result does not count towards a total into a normal dice roll would affect the probabilities. i.e. in Earthdawn, if a player rolls 2D8+1D6 and ...
3
votes
2answers
188 views

How do I calculate DPR under my DM's crit house rule?

In 1st edition AD&D, my DM uses a system where on crit you do max damage and roll an additional die, i.e., if you crit with long sword you do 8 points of damage plus another d8 and whatever bonus ...
4
votes
1answer
581 views

If the saltwater float can (with difficulty) be used to determine a dies balance, would a more dense liquid such as galium be better at doing so? [closed]

In another question I asked if the Saltwater float present in a specific youtube video was capable of determining any differences in mass between the faces of a die in determining the balance of a ...
4
votes
1answer
505 views

Creating a 5th edition die roller in AnyDice: how to handle bonus damage on first hit?

I have been trying to create a complete probability generator for fifth edition D&D attack rolls in AnyDice, including features such as advantage/disadvantage, different crit ranges, bonus crit ...
5
votes
3answers
377 views

Modelling opposed dice pools with a swap

I have a dice pool system that awards for instance damage to the loser of an opposed roll. Players roll their pool of dice, with each player's target number being the highest number rolled by their ...
66
votes
3answers
15k views

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 ...
2
votes
1answer
178 views

How do I count the number of duplicates in anydice?

Let's say I have the following roll: 6 6 5 5 5 4. I want to count the number of duplicates, in this case 3 (6 and ...
3
votes
1answer
82 views

Modelling a custom attack resolution in AnyDice: highest non-draw die of pool

I'm experimenting with the probabilities of various "die pool" attack resolutions for a game I'm designing, knowing that pools will generally be 1-4 dice, with sacrifices to temporarily boost a die ...
29
votes
6answers
7k views

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 ...
4
votes
1answer
2k views

How does Meat Grinder mode affect death saving throw probabilities?

The module Tomb of Annihilation features an optional 'Meat Grinder' mode. By using this optional rule, the difficulty of death saving throws is increased from 10 to 15. The probabilities of living ...
15
votes
3answers
3k views

In what paradigm is +1 to hit the same as improving your chance to hit by 5%?

People all the time are saying that +1 to hit is a 5% better chance of hitting. I assume this is because when you roll to hit you roll a d20 and 1 is 5% of 20, but that doesn't really make a whole ...
8
votes
2answers
481 views

How to create an encounter deck with a bell-curve distribution?

So I'm running a somewhat sandbox typed game and it relies quite a bit on random encounters for various locales. Because the players are allowed to muck around, there tends to be quite a bit of change ...
2
votes
2answers
226 views

2 dice pools roll matching highest [closed]

Playing with building a battle system in which opponents each roll a number of d6 equal to their Combat skill, and I want to determine the likelihood of both parties rolling the same highest value. ...