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201 votes
Accepted

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 ...
Icyfire's user avatar
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90 votes
Accepted

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 ...
nitsua60's user avatar
  • 102k
84 votes
Accepted

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 ...
Ilmari Karonen's user avatar
82 votes
Accepted

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 ...
nitsua60's user avatar
  • 102k
82 votes
Accepted

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 ...
Premier Bromanov's user avatar
79 votes

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 ...
Oblivious Sage's user avatar
  • 55.3k
76 votes

Does the chance of rolling a 1 in a pool of d10s increase as the number of dice increases?

Yes it does. Your instinct is right. The more dice, the more likely you are to roll some 1s. If I'm reading you right you're just interested in whether any 1s appear in your rolled pool. It may not ...
nitsua60's user avatar
  • 102k
69 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?

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 ...
Szega's user avatar
  • 61.8k
68 votes
Accepted

What are the statistical implications of doubling damage on crit instead of doubling the dice rolled?

Given the example of (2d6)×2 (henceforth referred to as 'Doubled Damage') vs (4d6) (referred to as 'Doubled Dice'): When you double the damage rolled instead of doubling the dice rolled, you ...
LegendaryDude's user avatar
67 votes
Accepted

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.* ...
nitsua60's user avatar
  • 102k
66 votes
Accepted

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 ...
Icyfire's user avatar
  • 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 ...
CR Drost's user avatar
  • 1,671
63 votes

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) ...
divibisan's user avatar
  • 3,566
62 votes
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 ...
Ryan C. Thompson's user avatar
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 "...
Icyfire's user avatar
  • 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 ...
mattdm's user avatar
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53 votes
Accepted

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 ...
kviiri's user avatar
  • 54.1k
52 votes
Accepted

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 ...
Adam's user avatar
  • 26.6k
52 votes
Accepted

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 ...
Xirema's user avatar
  • 52.7k
50 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 ...
SeraphsWrath's user avatar
  • 7,438
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 ...
Mark Omo's user avatar
  • 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{...
TimothyAWiseman's user avatar
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 ...
Yakk's user avatar
  • 15.7k
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, ...
Ruse's user avatar
  • 18.2k
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 ...
Gandalfmeansme's user avatar
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 ...
Plutoro's user avatar
  • 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 ...
Someone_Evil's user avatar
  • 48.6k
44 votes
Accepted

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 ...
Someone_Evil's user avatar
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