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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0answers
95 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 ...
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1answer
199 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 ...
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4answers
4k 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 ...
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1answer
626 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
324 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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2answers
3k views

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 ...
3
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1answer
100 views

What is the average expected rounds to 1 Wound, and how is it accurately calculated?

Take a character with Fighting skill d10 who does 2d6 damage, and a standardized bandit as the target. The bandit has d6 in all Traits and in Fighting, so has a Parry of 5, and wears leather armor ...
5
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3answers
380 views

How can I calculate the difference between two rolls in AnyDice?

How do I calculate the following in AnyDice? 2d6, subtract lowest result from highest.
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1answer
95 views

How can I model the probabilities for highest and lowest of opposing dice pools?

This is a variation of a dice mechanic I'm working on. You create a d6 pool of Edge dice and Snag dice and roll all of them. Compare the highest Edge die and the highest Snag die. If the Edge die ...
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3answers
951 views

How can I calculate the sum of 2 random dice out of a 3d6 pool in AnyDice?

With AnyDice it's pretty easy to calculate probalities for highest and lowest 2 of a 3d6 pool, namely with: output [highest 2 of 3d6] output [lowest 2 of 3d6] ...
4
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1answer
116 views

How can I model the probabilities for this mechanic involving cancelling out dice pools in AnyDice?

So I'm struggling with the probabilities for a dice mechanic. You create a d6 pool of Edge dice and Snag dice and roll all of them. Each Snag die cancels an Edge die of a lower value. After ...
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4answers
2k views

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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1answer
67 views

How can I calculate the probability of complete success with this mixed dice pool using AnyDice?

I've playing around with dice probabilities and have a spreadsheet that handles the calculation for basic probabilities rolling a set of dice and counting the number of successes. I am completely new ...
16
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3answers
936 views

What is the average number of draws it takes before you can not draw any more cards from the Deck of Many Things?

When thinking about this question regarding an upper limit on the number of draws, I wondered what would be the expected number of draws you can actually pull off if you called for a large number of ...
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1answer
331 views

What is my average burst/nova melee damage and how do I calculate it?

I'm trying to figure out what my average burst/nova damage with this character would be (using a melee attack) but I'm at a loss for how to calculate all of it. Assume the target has an AC of 15 but ...
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2answers
184 views

AnyDice: How to calculate the winner in opposed rolls over multiple rounds?

I am having some difficulty doing opposed rolls over multiple rounds. I am looking for a character vs. character statistics. I call them "Rookie" and "Enemy" respectively. I want to know what the ...
7
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1answer
117 views

How can I calculate the probability of meeting a certain Difficulty Value on 3d6 with critical success/failure modifiers?

In one Fuzion-system variant 3d6 is used to resolve skill checks. A Task is given a Difficulty Value (DV) from 10 (easy) to impossible (30 and beyond). Characters can have primary attribute levels ...
2
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1answer
84 views

How do I find the odds in a dice pool contest?

I'm designing a system where overall success is determined using a dice pool where you count the number of max-value faces among dice rolled and compare this number to some difficulty number. In this ...
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1answer
102 views

A generalized formula for the probability of a roll? [duplicate]

I'm looking for a formula to calculate the chance that (n) rolls of a d(y) produces any of (x) specific numbers (k) times, where x,y,n,k > 0, k <= n, and x <= y. AnyDice is a neat thing to know ...
2
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0answers
91 views

Equipping the dagger vs the shield [closed]

I want to figure out what is the better option, straight up damage or a chance to deflect in a game. I have two options, the first is to equip another dagger for 10% more damage. However, this ...
5
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2answers
176 views

How can I calculate the expected number of stunt points per attack?

If I hit on a 3, the Dragon Dice can show anything, the chance of getting a double is 44.44%, so on average it is 1.55 (3.5 * 0.44) Stunt Point per attack. If I hit only on a 18, the Dragon Dice can ...
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5answers
7k views

Would it be fair to use 1d30 (instead of rolling 2d20 and taking the higher die) for advantage rolls?

Would it be fair to use 1d30 - in place of 2d20 and taking the higher die - for advantage rolls? Recently I have acquired several d30 dice in a bag of factory seconds. I want to offer my players the ...
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5answers
4k views

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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4answers
832 views

How do I calculate how many of an item I'll have in this inventory system?

I beta tested a game last week with a pretty fun system. This system is called "Dés d'usure" (in French, because it will be a French game). I translate it into "Wear dice", but I'm unsure. When you ...
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2answers
293 views

What is the average point buy of a stat array from a 6x6 matrix of “roll 4d6, drop the lowest die”?

For character creation my group sometimes uses a weird method to generate stats. We roll 6 stat arrays using 4d6d1 (rolling 4d6 and dropping the lowest), and arrange them on top of one another to make ...
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2answers
181 views

How to calculate conditional probabilities in AnyDice?

While writing the addendum to this answer, which considers the relative value of skill vs. characteristic in the "3d20 system" of Neuroshima, I found myself wanting an answer to a deceptively simple ...
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5answers
6k views

If I score a critical hit on an 18 or higher, what are my chances of getting a critical hit if I roll 3d20?

I have Elven Accuracy so with advantage on an attack roll using Dexterity, Intelligence, Wisdom, or Charisma, you can reroll one of the dice once. So what are my crit chance with a crit range of 18/...
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6answers
5k views

Does the shape of a die affect the probability of a number being rolled?

Let's say I have a standard D4 and a custom D8 that has printed 1-4 and then 1-4 again (for a total of 8 sides). Would both of these dice distribute the probably of rolling any given number equally? ...
17
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7answers
3k views

How can the DM most simply and fairly choose 1 out of an odd number of characters to be targeted by an attack or effect?

When DMing and randomly determining a character to take damage or an effect, it's easy to roll a die if you have an even number of characters. But what about if you have an odd number of characters? ...
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1answer
199 views

How can I generate a heat map from AnyDice results?

I want to show some effects of changing dice rolls on a heat map, where on one axis I have task difficulty (level of a spell, quality of lock to pick etc), and on another character level / proficiency ...
5
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4answers
363 views

Is it still a binomial distribution when rolling dice with different probabilities that must be met to count a success?

How do you calculate the probability of success when success is two different criteria/probabilities? I'm theorizing a resolution system for a homebrewed mechanic that involves rolling a pool of ...
4
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2answers
358 views

With a known probability, how can I determine a roll to fit that probability to a population of n?

I'm working on making some homebrew settlement downtime activity, and I'd like to create a table that can provide some various outcomes for a group. So I"m looking for the math that allows to figure ...
16
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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?
52
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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 ...
17
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1answer
661 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 ...
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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 ...
17
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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
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0answers
129 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 ...
9
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2answers
573 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 ...
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2answers
1k 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 ...
3
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1answer
765 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 ...
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2answers
93 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 ...
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2answers
1k 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 ...
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2answers
5k 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 ...
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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-...
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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
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1answer
262 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
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1answer
192 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
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2answers
190 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
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1answer
349 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 ...