combodice: Combine dice
In AkselA/R-ymse: Ymse (Various)

Description Usage Arguments Details Value See Also Examples

Generate probability density functions for combinations of dice.

1 2	combodice(x, FUN, ..., method = c("outer", "expand.grid", "convolve"), name)

`x`	a list of dice objects, or objects that can be interpreted as such
`FUN`	function passed on to `outer` or `apply`, depending on method
`...`	further arguments passed to `FUN`
`method`	method for computation. One of outer, expand.grid or convolve
`name`	name used for the resulting PDF. Will use x object if none is given

Each of the methods have their advantages and disadvantages. Outer and expand.grid work with roughly the same speed and memory, and can take the same kind of input, but FUN is interpreted differently, reflecting their use of outer and apply respectively. Convolve is much quicker than the other two, but is restricted to only summing distributions. While the first two can handle non-integer values, but only integer probabilities, the third can handle non-integer probabilities, but only integer values.

A table giving the relative probability of each value

dusd

# Fudge dice
dF.2 <- as.table(c("-1"=2, "0"=2, "1"=2))
dF.1 <- as.table(c("-1"=1, "0"=4, "1"=1))
fudgedice2221 <- list(dF.2, dF.2, dF.2, dF.1)

combodice(fudgedice2221)

# Heterogeneous-class list and non-integer values
die1 <- as.table(c("2.6"=2, "3"=1, "5"=1))
die2 <- c(0, 1.4)
die3 <- as.dice(as.table(c("1"=2, "2"=2, "3"=2)))
diel <- list(die1, die2, die3)

combodice(diel)

# Regular d6 pair
re <- combodice(list(1:6, 1:6))

# Sichermann pair
si <- combodice(list(c(1, 2, 2, 3, 3, 4), c(1, 3, 4, 5, 6, 8)))
re; si # Identical

# One regular and one "average" d6
combodice(list(1:6, c(2, 3, 3, 4, 4, 5)))

# One 1/2 coin, one D4 and one d6, multiplied together
combodice(list(1:2, 1:4, 1:6), "*")

# Probability of getting n 1s throwing 1d4, 1d6 and 2d8
f <- function(x) sum(x == 1)
combodice(list(1:4, 1:6, 1:8, 1:8), FUN=f, method="exp")

# 3d6, discarding the lowest
discard_lowest <- function(x) sum(x[-which.min(x)])
combodice(list(1:6, 1:6, 1:6), discard_lowest, method="exp")

# 1d4, 2d6 and 1d20, discarding lowest and highest
olympic <- function(x) sum(x[-c(which.min(x), which.max(x))])
combodice(list(1:4, 1:6, 1:6, 1:20), olympic, method="exp")

# Dice pool. 3 d10 with target value 7
f <- function(x) sum(x >= 7)
combodice(lapply(rep(1, 3), seq, 10), f, method="ex")/10^3

# Equivalent using binomial PDF
dbinom(0:3, 3, 0.4)

# I have a d20 with a slight bump at the 4 and 10 facets,
# which makes 16 and 11 less likely, but the nearby 3, 18, 19 and 20
# correspondingly more likely. How does this affect the PDF?
d20l <- dice(20)
d20l[c(16, 11)] <- 0.6
d20l[c(3, 20, 18, 19)] <- 1.2
mean(d20l)

c0 <- combodice(list(dice(6), dice(10), dice(20)), method="conv", name="fair")
cl <- combodice(list(dice(6), dice(10), d20l), method="conv", name="uneven")

set_mar()
plot(c0, type="o", pch=16, col="grey")
points(cl, col=2, type="o", lwd=1, pch=16, cex=0.6)
legend("topright", c("fair", "bumpy"), bty="n", col=c("grey", "red"), lwd=2:1)