simEd (version 2.0.1)

galileo: Monte Carlo Simulation of Galileo's Dice

Description

A Monte Carlo simulation of the Galileo's Dice problem. Returns a vector containing point estimates of the probabilities of the sum of three fair dice for sums 3, 4, \(\ldots\), 18.

Usage

galileo(nrep = 1000, seed = NA, showProgress = TRUE)

Value

An 18-element vector of point estimates of the probabilities. (Because a sum of 1 or 2 is not possible, the corresponding entries in the returned vector have value NA.)

Arguments

nrep

number of replications (rolls of the three dice)

seed

initial seed to the random number generator (NA uses current state of random number generator; NULL seeds using system clock)

showProgress

If TRUE, displays a progress bar on screen during execution

Author

Barry Lawson (),
Larry Leemis (),
Vadim Kudlay ()

Details

Implements a Monte Carlo simulation of the Galileo's Dice problem. The simulation involves nrep replications of rolling three dice and summing the up-faces, and computing point estimates of the probabilities of each possible sum 3, 4, \(\ldots\), 18.

Note: When the value of nrep is large, the function will execute noticeably faster when showProgress is set to FALSE.

Examples

 # set the initial seed externally using set.seed;
 # then use that current state of the generator with default nrep = 1000
 set.seed(8675309)
 galileo()  # uses state of generator set above

 # explicitly set the seed in the call to the function,
 # using default nrep = 1000
 galileo(seed = 8675309)

 # use the current state of the random number generator with nrep = 10000
 prob <- galileo(10000)

 # explicitly set nrep = 10000 and seed = 8675309
 prob <- galileo(10000, 8675309)