A player rolls four 20-sided dice, takes the lowest value, ignores the rest. What is the probability of this value at least 7?

I’m designing a tabletop game, and I need to figure out how to calculate a few probabilities:

  1. Roll 3 20-sided dice, take the highest value. What is the probability of it being 7 or higher? 15 or higher?
    1. Roll 4 20-sided dice, take the highest value. What is the probability of it being 7 or higher? 15 or higher?
    1. Roll 3 20-sided dice, take the lowest value. What is the probability of it being 7 or higher? 15 or higher?
    1. Roll 4 20-sided dice, take the lowest value. What is the probability of it being 7 or higher? 15 or higher?

How can I do this? Could you explain to me how this works, or even better – give me a simple formula?

I can’t do the shortcut to roll a dice on beyond20

When I try to roll the dice from D&D beyond I can only roll it if I (as an example) click on my longsword and then go to the top right and click "beyond20", at first before I changed the settings if I hovered over "longsword" it would popup an icon in red, but now its grey and I can’t click it. Which setting do I have to enable/disable to fix this. I have tried looking over through the settings somewhere around five times.

How to calculate the probabilities for eliminative dice pools (dice cancelling mechanic) in Neon City Overdrive?

The game Neon City Overdrive uses the following resolution mechanic for checks:

  1. create a pool of Action Dice and (possibly) another pool of differently-colored Danger Dice (all d6, generally up to 5 or 6 dice in each pool)
  2. roll all the dice
  3. each Danger Die cancels out an Action Die with the same value – both are discarded
  4. the highest remaining Action Die (if there is any) is the result (the precise meaning of which is irrelevant for the purposes of this question)
    • any extra Action Dice showing 6 (i.e. in addition to the single highest die read as the result) provide a critical success (called a boon)

I’m struggling to find the proper way to model the probabilities of this mechanic in anydice.

I realize that a good starting point would be this answer to a very similar question regarding the mechanic in Technoir (which clearly was a source of inspiration for Neon City Overdrive). Unfortunately, despite my best efforts I can’t say I fully comprehend how the code provided there works, and there’s an important difference between the two games: in Technoir a single "negative die" eliminates all matching "positive dice", whereas in NCO this happens on a one-to-one basis.

I would be very grateful for any help.

Does injury affect the helping dice I grant to others?

My character has a skill at B5. Let’s say it’s Navigation. Because I have five dice in the skill, if I use my Navigation to help another character, they’ll gain +2D instead of the more typical +1D.

During a scuffle with pirates, my character sustains a nasty broken leg. This is a midi wound, worth -2D to all of my checks. If I try to help another character using my Navigation, do they still get the full +2D now, or only +1D because I’m injured?

Subtracting opposed dice in Anydice

In some games, opposed dice rolls are subtracted. An example (although this is a boardgame, not an rpg) is Twilight Struggle. Not only is it important to determine who won, but by how much. A similar situation would be when the DM creates a mechanic where opposed skill checks on say d20s are compared (who won by the most). I’m wondering how to do this in anyDice.

What is an easy way of doing this in anyDice?

When a druid uses Wild Shape to transform into a beast, how many Hit Dice does it have?

Suppose that, for whatever reason, my mid- to high-level druid is in a party that has decided to take a short rest. Instead of spending a use of their Wild Shape to assume a new form with full hit points, my druid decides to spend the short rest in beast form, and spend some of its hit dice on healing.

How many hit dice does the Wilde have upon being transformed into? All? None? Some?

RPG with core mechanic based on grouping dice under a specific sum

A few years back, I read an RPG which used the core dice mechanic of rolling a number of d10s, then arranging the dice into sets, such that the dice in each set added up to no more than a specified limit. Both the number of sets and the number of dice in each set were involved in determining the final result, but I’m pretty sure the actual numbers on the dice and their sum were not relevant aside from limiting which dice could be grouped together.

Many/most of the examples of using the dice mechanic were framed in a context of combat, emphasizing that several groups of only two dice each would represent a flurry of multiple quick, weak strikes, while a single group of, say, six dice is a single, powerful blow.

I know that “roll a bunch of d10s and group them” might sound like ORE, but this system was definitely not ORE. In ORE, the grouping is dictated by which dice roll the same number as each other, while in the system I’m trying to remember, the player chooses how they wish to group the dice and, in the case of opposed rolls, the rolling and grouping are done in secret, creating a strategic element of trying to guess how the other person will choose to group their dice (lots of small groups, one big group, or a mix of small and large) so that you can group yours in the most effective way to counter them.

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

I’ve been playing with a group that frequently allows players to double the value of dice rolled for crits (and other things) rather than rolling double the dice. Example, someone crits with 2d6 and rolls for 8 damage, which they then double for 16 total crit damage, rather than rolling 4d6.

This mostly just bugs me on principle, but I was curious what doubling the value rather than doubling the dice does mathematically. Does it actually make a difference? Is there a greater chance to hit extreme ends of the range of values (low and high)? Does the amount and type of dice create greater inconsistencies between the two scenarios?