Package 'dice'

Calculate probabilities of various dice-rolling events

Description

This package provides utilities to calculate the probabilities of various dice-rolling events, such as the probability of rolling a four-sided die six times and getting a 4, a 3, and either a 1 or 2 among the six rolls (in any order); the probability of rolling two six-sided dice three times and getting a 10 on the first roll, followed by a 4 on the second roll, followed by anything but a 7 on the third roll; or the probabilities of each possible sum of rolling five six-sided dice, dropping the lowest two rolls, and summing the remaining dice.

Details

Package:	dice
Type:	Package
Version:	1.2
Date:	2014-10-13
License:	GPL (>= 2)

Although initially conceived as a utility for role-playing game calculations, functions in the dice package can be used to answer questions in any dice-rolling context (e.g., calculating probabilities for the game of craps, solving problems for an introductory probability course, etc.)

The dice package requires the gtools package.

For a complete list of functions, use library(help="dice").

Author(s)

Dylan Arena <[email protected]>

References

The implementation for the getSumProbs function originated with the ideas presented in the following forum thread:

http://www.enworld.org/showthread.php?t=56352&page=1&pp=40

Examples

getEventProb(nrolls = 6,
             ndicePerRoll = 1,
             nsidesPerDie = 4,
             eventList = list(4, 3, c(1,2)),
             orderMatters = FALSE)

getEventProb(nrolls = 3,
             ndicePerRoll = 2,
             nsidesPerDie = 6,
             eventList = list(10, 4, c(2:6, 8:12)),
             orderMatters = TRUE)

getSumProbs(ndicePerRoll = 5,
            nsidesPerDie = 6,
            nkept = 3,
            dropLowest = TRUE)

---

Calculate the probability of a specified set of dice-rolling events

Description

For a specified dice-rolling process, getEventProb calculates the probability of an event (i.e., a non-empty set of outcomes) that is specified by passing a list object in to eventList.

Usage

getEventProb(nrolls, ndicePerRoll, nsidesPerDie, eventList, orderMatters = FALSE)

Arguments

nrolls	A single positive integer representing the number of dice rolls to make
ndicePerRoll	A single positive integer representing the number of dice to use in each dice roll
nsidesPerDie	A single positive integer representing the number of sides on each die (getEventProb's dice-rolling process involves only one type of die per call)
eventList	A list object, each element of which is a vector that constrains a single dice roll in the dice-rolling process (see Details below)
orderMatters	A logical flag indicating whether the order of the elements of eventList should constrain the event space; if TRUE, eventList must specify constraints for every dice roll–i.e., it must contain exactly nrolls elements (some of which may be "empty" constraints listing all possible outcomes of a dice roll, i.e., a vector from ndicePerRoll to (ndicePerRoll * nsidesPerDie))

Details

The crux of this function is eventList, which sets the conditions that acceptable dice-rolls must meet. E.g., to get the probability of rolling at least one 6 when rolling four six-sided dice, eventList would be list(6) and orderMatters would be FALSE; to get the probability of rolling a 6, followed by a 5, followed by either a 1, 2, or 3 when rolling three six-sided dice, eventList would be list(6,5,1:3) and orderMatters would be TRUE.

Value

A single number representing the probability of an event that meets the constraints of the specified dice-rolling process

Author(s)

Dylan Arena

Examples

## Probability of rolling at least one 6 when rolling four six-sided dice

getEventProb(nrolls = 4,
             ndicePerRoll = 1,
             nsidesPerDie = 6,
             eventList = list(6))

## Probability of rolling a 6, followed by a 5, followed by either a 1, 2,
## or 3 when rolling three six-sided dice

getEventProb(nrolls = 3,
             ndicePerRoll = 1,
             nsidesPerDie = 6,
             eventList = list(6, 5, 1:3),
             orderMatters = TRUE)

## Probability of rolling no 10's when rolling two ten-sided dice

getEventProb(nrolls = 2,
             ndicePerRoll = 1,
             nsidesPerDie = 10,
             eventList = list(1:9,1:9))

---

Calculate the probabilities of all possible outcome sums of a dice roll

Description

For a specified number of dice with a specified number of sides per die (and dropping a specified number of dice–those with either the lowest or highest values), getSumProbs calculates the probabilities of all possible outcome sums (i.e., all possible sums of those dice whose results are not dropped); the function also accommodates modifiers (either to each die roll or to the sum), such as rolling five four-sided dice and adding 1 to the outcome of each roll, or rolling one twenty-sided die and adding 12 to the outcome. (Such modified rolls frequently occur in the context of role-playing games, e.g., Dungeons & Dragons, Mutants & Masterminds, or BESM.)

Usage

getSumProbs(ndicePerRoll, 
nsidesPerDie, 
nkept = ndicePerRoll, 
dropLowest = TRUE,
sumModifier = 0,
perDieModifier = 0,
perDieMinOfOne = TRUE)

Arguments

ndicePerRoll	A single positive integer representing the number of dice to roll
nsidesPerDie	A single positive integer representing the number of sides on each die (getSumProbs's dice-rolling process involves only one type of die per call)
nkept	A single positive integer representing the number of dice whose values to include when calculating the sum (the dice to be kept will always be those with the highest values)
dropLowest	A single logical indicating whether to drop the lowest outcome values (FALSE drops the highest values instead)
sumModifier	A single integer representing an amount to add to or subtract from the outcome sum
perDieModifier	A single integer representing an amount to add to or subtract from each die roll
perDieMinOfOne	A logical flag indicating whether each die roll should be considered to have a minimum value of 1 (as is often true in role-playing-game contexts)

Value

probabilities	A matrix with a row for each possible outcome sum and three columns: one that lists each sum, one for the probability of that sum, and one for the number of ways to roll that sum
average	A single number representing the expected value of the specified dice-rolling process

Author(s)

Dylan Arena

References

This function's implementation originated with the ideas presented in the following forum thread:

http://www.enworld.org/showthread.php?t=56352&page=1&pp=40

Examples

## Rolling four six-sided dice and keeping the three highest die rolls

getSumProbs(ndicePerRoll = 4,
            nsidesPerDie = 6,
            nkept = 3)

## Rolling five four-sided dice and adding 1 to each die roll

getSumProbs(ndicePerRoll = 5,
            nsidesPerDie = 4,
            perDieModifier = 1)

## Rolling one twenty-sided die and adding 12 to the result

getSumProbs(ndicePerRoll = 1,
            nsidesPerDie = 20,
            sumModifier = 12)

---