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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.

2
votes
1answer
55 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 ...
-1
votes
1answer
91 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
votes
0answers
82 views

Equipping the dagger vs the shield [on hold]

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
votes
2answers
140 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 ...
10
votes
5answers
6k 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 ...
25
votes
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 ...
20
votes
4answers
810 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 ...
6
votes
2answers
211 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 ...
5
votes
1answer
57 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 ...
19
votes
5answers
5k 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/...
18
votes
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? ...
12
votes
5answers
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? ...
13
votes
1answer
224 views

Does 3d6 per attribute represent the entire (human) population or just adventurers?

In more "old school" D&D editions charterer creation required the generation of character attributes by rolling 3d6 for each one of the six (most commonly) attributes (Strength, Dexterity, ...
6
votes
1answer
111 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 ...
4
votes
4answers
260 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
votes
2answers
338 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
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?
52
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
537 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 ...
17
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
111 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
319 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
785 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
458 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
83 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
642 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
2k 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
184 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
171 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
182 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
288 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
860 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
3k 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
212 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, ...
25
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
16k 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
7k 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
580 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
80 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
792 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
455 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
3k 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
374 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
553 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 ...