201
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Does microwaving a die significantly alter its balance?
It doesn't do anything.
As a chemist, I had to give this a try.
First, I started with a die that had a clear bias toward ~18, according to the saltwater test. The first picture is the initial drop ...
- 63.7k
90
votes
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What dice mechanic gives a bell curve distribution that narrows and increases mean as skill increases?
(SKILL+CONSTANT) dX, keep highest CONSTANT
I don't know exactly the behavior you're going for, so there'll be a few arbitrary numbers in my example:
skills can be ranked from 0 to 5
dice rolled are ...
- 102k
84
votes
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How to approximate rolls for potions of healing using only d6's?
Let's not overcomplicate it: a simple Nd6 + X formula will work just fine.
Specifically, the effects of Greater (4d4 + 4) and Superior (8d4 + 8) healing potions are quite closely replicated by ...
- 24.5k
82
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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?
TL;DR
A GM shouldn't roll all-or-none saves. If reduced rolling is necessary, instead they should figure the expected number of saves, then add a d4 and subtract a d4. Below are pictured the results ...
- 102k
82
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What is the difference between rolling more dice versus fewer dice?
From what I can gather what you're asking, you want to know the probabilistic difference between rolling 10d10 and 5d20. You've rightly pointed out that each roll has the same maximum and that each ...
- 18.7k
79
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If I score a critical hit on an 18 or higher, what are my chances of getting a critical hit if I roll 3d20?
For "at least one" probability problems, it's usually easier to start by calculating the chance that none of the dice crit, as that saves you the hassle of combining the probabilities of ...
- 55.3k
69
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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?
Overall, this will make area/multi-target spells less reliable, but more potent.
Numbers
The chance of a single individual to save is not affected by this change. The number of individuals affected ...
- 61.8k
67
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Is it possible to emulate common polyhedral dice rolls using just a d6, and if so, how?
It's pretty trivial if you allow occasional discarding of rolls/rerolls.
d2 (gonna need this later): if result is odd, read as a 1. If result is even, read as a 0.
d4: discard any results of 5 or 6.*
...
- 102k
66
votes
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Dice Rolling Method Fairness
This is a classic clustering fallacy
Wikipedia defines the clustering fallacy as:
...the tendency to erroneously consider the inevitable "streaks" or "clusters" arising in small samples from ...
- 63.7k
66
votes
Simulating these special dice on more regular dice
Look at the pips a certain way
Tell your kids that the pips on the dice represent where you hit. A pip in the center means that you hit on-target, a pip on the sides means that you missed.
As special ...
- 1,671
63
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If I score a critical hit on an 18 or higher, what are my chances of getting a critical hit if I roll 3d20?
The other answers do a good job of answering the question, but I'll point out how you can answer questions like this in the future:
https://anydice.com/ is a very powerful (if slightly complicated) ...
- 3,576
62
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Accepted
Is it okay to roll multiple attacks that all have advantage in one cluster?
Rolling 12d20 and taking the 6 highest is not equivalent
Taking the 6 highest rolls out of 12d20 is not equivalent to 6 attacks with advantage. It is significantly better. I could lay out the ...
- 63.1k
55
votes
Accepted
Is GameScience's non-cylindrical seven-sided die a balanced/fair die?
The real experiment is difficult
The linked dice in the question are out of stock, so only people who already have a lot of these dice and are willing to do the statistical tests can give the "...
- 63.7k
53
votes
Accepted
In what paradigm is +1 to hit the same as improving your chance to hit by 5%?
It's not just in extreme cases that this doesn't add up, though. Let's say that you hit a target on a 16+. If you get a +1, you now hit them on a 17+, which is a 6.25% increase in your chance of ...
- 30k
53
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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?
Dice work just fine for the most common numbers of players
I work with probabilities a lot. Dice allow you to represent many common probabilities, but when you want to roll to pick from options, I've ...
- 54.1k
53
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What are the odds of rolling high all the time?
This may not be as unlikely as you think
Preamble: Probability is Hard
So distributions like this are tricky, because a lot of people assume, wrongly, that they only need to calculate the odds of ...
- 52.9k
52
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What are my chances of rolling a natural 19/20 critical if I roll 3d20?
About 27%, or a little over 1/4
This is a pretty easy calculation to run in anydice:
As you can see, the percentage chance of rolling at least a 19 one of the d20 rolls is 27.10% So you can expect, on ...
- 26.7k
51
votes
Accepted
Mathematically, is a +2 bonus to AC better than attackers having disadvantage?
In this case, the Cloak is better
To explain this, let's first look at some stats.
When no bonuses are involved, the Chances of rolling a 20 normally is 5% (1/20), while the chance for rolling 18 or ...
- 7,448
48
votes
Is GameScience's non-cylindrical seven-sided die a balanced/fair die?
No
(With 99.5% Confidence)
I purchased 5 of these dice to test their fairness. I rolled the dice 2250 times (450 sets), by hand in the dice bowl pictured above, and recorded the results.
Face
Count
...
- 1,570
47
votes
Simulating these special dice on more regular dice
Map the answers to the face of a 6-sided die
There are exactly 6 faces listed for your dice. They can thus be replaced by any fair six sided die by creating a translation table such as:
$$
\begin{...
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46
votes
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?
This would be a great change if you were in a fight where you were almost certainly going to lose.
Imagine a spell that defeats 1/2 of the creatures it targets. You use it on 2000 creatures. If ...
- 16.1k
46
votes
Accepted
Which feat, Resilient (Con) or War Caster, improves the chances of maintaining concentration more?
The proficiency bonus is the primary factor
I made a graph to compare Resilient and War Caster.
How to read the graph.
The horizontal axis is the save DC, the vertical axis is the chance of success, ...
- 18.3k
46
votes
Accepted
What is the statistical difference, if there is one, between attacking twice (action and bonus action) and attacking once with advantage?
It depends on your situation (typically, getting Sneak Attack is key)
Let's get something out of the way first: in the simple analysis, attacking twice is usually much better than attacking once with ...
- 38.4k
45
votes
Accepted
Expected damage of a moonblade with 𝑛 runes?
I wrote a python script to calculate answers accurate to several decimal places. I created a Moonblade object, and added a specified number of runes just as the rules suggest (with the one alteration ...
- 685
45
votes
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?
AnyDice is straight forward for this
If you want to save yourself going through the maths, AnyDice will solve this for you.
While doing more complex things can get tricky (up to not possible), it's ...
- 48.8k
44
votes
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Roll Xd6, keeping highest value and adding +1 for each duplicate of that value?
There's a couple little tricks we can use here. Firstly, we want to look at the individual values of a roll, so we need to cast the roll to a sequence. We do this by appending ...
- 48.8k
43
votes
Accepted
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?
Use a Tree Diagram
Because I am bad at remembering formulas and bad at probabilities in general I like to use a tree diagram. The other answers provide good straight forward solutions you can apply ...
- 768
43
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How can I map a single d20 to a number of hits? (use case: Animate Objects)
Use the DMG rules for handling mobs
The DMG (page 250) presents some rules for the situation depicted. It consists in computing the target number on the d20 for a successful hit, and then check the ...
- 32.2k
41
votes
Accepted
Are these two methods of handling Elven Accuracy "Double Advantage" mathematically equivalent?
As other answers have stated, this method is equivalent for the higher/highest die but is ambiguous as to the value of the lower die.
That said, here is an intuitive way to think about this and ...
- 45.4k
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