Conversion script: link fix

2010-04-06T01:15:55Z

link fix

Conversion script: link fix

2010-04-06T00:35:39Z

link fix

Conversion script: link fix

2010-04-05T08:06:38Z

link fix

Conversion script: link fix

2010-04-03T09:02:55Z

link fix

Capric: Excellency modelling

2008-01-18T23:56:10Z

Excellency modelling

New page

As the ExcellencyMath page shows, calculating distributions for dice is rather tedious, especially at high pools.

To make this process easier, here is some R code which can be used to calculate success distributions for arbitrary numbers of dice and excellencies. These functions use three state multinomial calculations to generate their distributions, so they can get a little slow at high pools.

For information on R, including how to install and run, visit [http://www.r-project.org/ the R homepage].

All functions return percent chances of generating at least the given number of successes, and assume solar costing. General syntax for functions:
:nd(dice, [limit]) - normal heroic roll. dice is number of dice, limit is how high to go.
:nond(dice, [limit]) - normal unheroic roll. dice is number of dice, limit is how high to go.
:fe(dice, motes, [limit]) - first excellency. dice is base pool, motes is how many motes to sink, limit is how high to go.
:se(dice, motes, [limit]) - second excellency. dice is base pool, motes is how many motes to sink, limit is how high to go.
:te(dice, [limit]) - third excellency. dice is base pool, limit is how high to go.
:compe(dice, motes, [limit]) - compares the previous 5 roll types. dice is base pool, motes is how many motes to sink, limit is how high to go.

----

<pre>
## Function to generate states of dice
# Exalted has four dice states, only three of which are relevant
#at any one time:
# 0- A '1'. In the absence of successes, this generates a botch
# 1- A failure, typically 2-6
# 2- A success, typically 7-9
# 3- A '10'. For heroic mortals and above, this gives 2 successes.
#
# As 1s don't interact with 10s, a three state table is sufficient
#to cover all the possible states from any particular roll.

rollstates <- function(dice) {
tmp<-t(as.matrix(expand.grid(0:dice, 0:dice)))
tmp<-tmp[, colSums(tmp)<=dice]
tmp<-rbind(tmp, dice - colSums(tmp))
dimnames(tmp)<-list(c("f","s","110"),NULL)
tmp }

# Caluculates numbers of successes each state will generate and then returns the
# probability that those states will be generated by some dice. Can be used for botches
# also, but defaults to successes.
success<- function(successes, dice, cumulative = TRUE, multipliers = c(0,1,2), distribution = c(6,3,1)) {
states<-rollstates(dice)
suc<-states*multipliers
stateset<-if (cumulative) states[, colSums(suc)>=successes] else states[,colSums(suc)==successes]
round(sum(apply(as.matrix(stateset), 2, function(x) dmultinom(x, prob=distribution)))*100,3) }

#Normal rolls
nd<- function(dic, limit=2*dic) {
#Botch
X<-success(1,dic,TRUE,c(1,0,-9001), c(1,5,4))
#Failure
X<-rbind(X, success(0,dic, FALSE))
#Success table
X<-rbind(X, as.matrix(apply(as.matrix(1:limit), 1, function(x) success(x, dic))))
#Rename
dimnames(X)<-list(c("Botch","Fail", 1:limit), "Normal")
X }

#Non-heroic rolls
nond<- function(dic, limit=2*dic) {
#Botch
X<-success(1,dic,TRUE,c(1,0,-9001), c(1,5,4))
#Failure
X<-rbind(X, success(0,dic, FALSE))
#Success table
X<-rbind(X, as.matrix(apply(as.matrix(1:limit), 1, function(x) success(x, dic, TRUE, c(0,1,1), c(6,3,1)))))
#Rename
dimnames(X)<-list(c("Botch","Fail", 1:limit), "Unheroic")
X }

#First excellency
fe<-function(pool, motes, limit=2*(pool+motes)) {
X<-nd(pool+motes, limit)
colnames(X)<-"First"
X}

#Second excellency
se<-function(pool, motes, limit=2*pool+floor(motes/2)) {
#Number of successes
suc<-floor(motes/2)
if (suc>0) {
#Botch chance is 0, autosuccesses
X<-rbind(0,0, as.matrix(rep.int(100, suc)))
#Normal after that, but no botches
norm<-nd(pool, limit-suc)
X<-rbind(X, as.matrix(norm[rownames(norm)!="Botch"&rownames(norm)!="Fail",])) }
#Otherwise very normal
else X<-nd(pool,limit)
dimnames(X)<-list(c("Botch","Fail", 1:limit), "Second")
X}

#Rollagain
rollagain<- function (percent, bad) {
p<-percent/100
if (bad) round(100*(p)^2,3)
else round(100*(p+(1-p)*p), 3) }

#Third excellency
te<-function(pool, limit=2*pool) {
base<-nd(pool, limit)
#Bad ones first
third<-as.matrix(rollagain(base[rownames(base)=="Botch",], TRUE))
third<-rbind(third,as.matrix(rollagain(base[rownames(base)=="Fail",], TRUE)))
#Then the good ones
third<-rbind(third,as.matrix(apply(as.matrix(base[rownames(base)!="Fail"&rownames(base)!="Botch"],), 1, rollagain, bad=FALSE)))
dimnames(third)<-list(c("Botch", "Fail", 1:limit),"Third")
third}

#compare
compe<-function(pool, motes, limit=(pool+motes)*2) {
cbind(nond(pool, limit),nd(pool, limit), fe(pool, motes, limit), se(pool, motes, limit), te(pool, limit)) }

</pre>

← Older revision		Revision as of 09:02, 3 April 2010
Line 1:		Line 1:
−	As the ExcellencyMath page shows, calculating distributions for dice is rather tedious, especially at high pools.	+	As the [[ExcellencyMath]] page shows, calculating distributions for dice is rather tedious, especially at high pools.

	To make this process easier, here is some R code which can be used to calculate success distributions for arbitrary numbers of dice and excellencies. These functions use three state multinomial calculations to generate their distributions, so they can get a little slow at high pools.		To make this process easier, here is some R code which can be used to calculate success distributions for arbitrary numbers of dice and excellencies. These functions use three state multinomial calculations to generate their distributions, so they can get a little slow at high pools.

← Older revision	Revision as of 01:15, 6 April 2010
(No difference)

← Older revision	Revision as of 00:35, 6 April 2010
(No difference)

← Older revision	Revision as of 08:06, 5 April 2010
(No difference)

ExcellencyModelling - Revision history

Conversion script: link fix

Conversion script: link fix

Conversion script: link fix

Conversion script: link fix

Capric: Excellency modelling