# [R] Model To Simulate Dice Roll

Rui Barradas ru|pb@rr@d@@ @end|ng |rom @@po@pt
Thu Apr 21 08:55:20 CEST 2022

```Hello,

For what I understand of the question, the followng might answer it.

The functions below roll dice and simulate R replicates of dice rolls.
Then 12 (one per month) 6 sided dice rolls are simulated 100 times.

The colMeans/apply computes the empiric probabilities of having all 6
sides occur in each row, Jan to Dec and a overall probabilty is the mean
of those probabilities.

The matrix is coerced to data.frame only at the end.

dice <- function(rolls = 1, ndice = 1, sides = 6) {
roll <- function(ndice = 1, sides = 6) {
sample(seq_len(sides), ndice, replace = TRUE)
}
y <- replicate(rolls, roll(ndice = ndice, sides = sides))
if(is.null(dim(y))) y else colSums(y)
}
dice_simul <- function(rolls = 1, ndice = 1, sides = 6, R) {
if(missing(R)) {
stop("number of simulations 'R' is missing with no default.")
}
replicate(R, dice(rolls = rolls, ndice = ndice, sides = sides))
}

dice_rolls <- 100
#dice_rolls <- 1e6
num_dice <- 1
dice_sides <- 6
months <- 12

set.seed(2022)
prob_frame <- t(dice_simul(months, num_dice, dice_sides, R = dice_rolls))
colnames(prob_frame) <- month.name

p <- colMeans(apply(prob_frame, 1, \(x) 1:6 %in% x))
mean(p)
# [1] 0.9116667

prob_frame <- as.data.frame(prob_frame)

Hope this helps,

Às 05:02 de 21/04/2022, Paul Bernal escreveu:
> Dear friend Bert,
>
> Thank you so much for your kind reply. The first thing I need to do is to
> simulate dice rolls, say 120 times.
>
> I want to populate an m by 12 dataframe with the results of each dice roll.
> For example, the result from dice roll #1 would need to go on row 1,
> column1, the result from dice roll #2 would have to go in row 1 column 2,
> and so on.
>
> The reason why I want to store those results in a dataframe is to be able
> to perform some other calculations afterwards.
>
> This is for a project I am doing.
>
> So this is the situation:
> You and five friends – a total of six people – plan to meet once per month
> to have dinner together, with one of you choosing the restaurant each
> month. Rather than scheduling the entire year in advance, you decide to
> make it interesting: each month a single six-sided die will be rolled to
> determine which of you gets to choose the restaurant that month. How likely
> is it that everyone will have a chance to eat at their own favorite
> restaurant? That is, what is the probability p that over the next 12
> months, each of you will have had at least one opportunity to choose where
> to eat?
>
> This is what I am asked to do:
> Write a program to estimate the desired probability p via simulation. The
> program should input a sequence of positive integer number of trials to
> simulate using the language's pseudorandom number generator and calculate
> the corresponding fractions of simulated trials that are “successful"
> (i.e., all 6 parties get at least one opportunity to choose where to eat.
> Alice, Bob, Charley, Fred, Ellen, Don, Don, Don, Don, Alice, Charley, Bob
> is a successful trial. Alice, Bob, Charley, Ellen, Don, Don, Don, Don,
> Ellen, Alice, Charley, Bob is not a successful trial since Fred does not
> get to choose.)
> Turn in a set of 10 trials showing each roll of the dice to show
> correctness. Label the out-comes. Keep in mind that a single trial requires
> rolling the die twelve times. Calculate and print the average probability p
>
> For this reason, I am trying to simulate the n trials, and then populate a
> table with the results from the trials. I have to simulate a dice roll dice
> for each month and for each row. Rows would be equivalent to years, and
> then columns would be equivalent to the month of a particular year.
>
> Once I store the results in a dataframe, everything is much easier.
>
> I installed package dice and performed simulations by doing:
> #declaring variables:
> #1)dice_rolls which is the number of times the dice will be rolled
> #2)num_dice which is the number of dice that will be rolled each time
> #3)dice_sides which is the number of sides of the dice
> #function dice will take each one of these variables as its parameter to
> perform the simulation
> dice_rolls = 120
> num_dice   = 1
> dice_sides = 6
>
> #performing simulation
> dice_simul = dice(rolls = dice_rolls, ndice = num_dice, sides = dice_sides,
> plot.it = TRUE)
>
> I tried the following, but did not work as expected:
>
> for (i in 1:nrow(dice_simul)){
>    for(j in 1:ncol(prob_frame)){
>      for(k in 1:nrow(prob_frame)){
>        prob_frame[k,j] = dice_simul[i,1]
>      }
>    }
> }
>
> I apologize for the long explanation.
>
> Best regards,
>
> Paul
>
>
> El mié, 20 abr 2022 a las 22:47, Bert Gunter (<bgunter.4567 using gmail.com>)
> escribió:
>
>> If I understand you correctly, it's simple.
>> Matrices in R are vectors with a dimension attribute. By default, they
>> are populated column by column. Use 'byrow = TRUE to populate by row
>>
>>> matrix (1:36, ncol = 12, byrow = TRUE)
>>       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
>> [1,]    1    2    3    4    5    6    7    8    9    10    11    12
>> [2,]   13   14   15   16   17   18   19   20   21    22    23    24
>> [3,]   25   26   27   28   29   30   31   32   33    34    35    36
>>
>> I leave it to you to use the 'dimnames' argument of ?matrix  to give
>> names to the column and then subsequently convert to a data frame if
>> you like.
>>
>> Bert Gunter
>>
>> "The trouble with having an open mind is that people keep coming along
>> and sticking things into it."
>> -- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )
>>
>> On Wed, Apr 20, 2022 at 8:38 PM Paul Bernal <paulbernal07 using gmail.com>
>> wrote:
>>>
>>> Dear friends,
>>>
>>> Hope you are doing well. I need to simulate a 1 dice roll for each one of
>>> the twelve months of the year and perform 100 trials, so I thought of
>>> constructing a dataframe with twelve columns and 100 rows the following
>> way:
>>>
>>> num_rows = 100
>>>
>>> prob_frame <- data.frame(matrix(NA, nrow = num_rows, ncol = 12))
>>>
>> colnames(prob_frame)<-c("January","February","March","April","May","June","July","August","September","October","November","December")
>>>
>>> Now, using the dice package, I can simulate n number of dice rolls as
>>> follows:
>>> #performing simulation
>>> dice_simul = dice(rolls = dice_rolls, ndice = num_dice, sides =
>> dice_sides,
>>> plot.it = TRUE)
>>>
>>> What I would like to do is to populate each column and row with the
>> results
>>> of dice_simul.
>>>
>>> Let me show you the structure of dice_simul:
>>>> str(dice_simul)
>>> Classes ‘dice’ and 'data.frame': 100 obs. of  1 variable:
>>>   \$ Red: int  2 2 1 2 5 4 4 6 1 4 ...
>>>> dput(dice_simul)
>>> structure(list(Red = c(2L, 2L, 1L, 2L, 5L, 4L, 4L, 6L, 1L, 4L,
>>> 4L, 2L, 6L, 2L, 2L, 1L, 3L, 6L, 1L, 5L, 5L, 5L, 3L, 4L, 2L, 6L,
>>> 4L, 6L, 6L, 2L, 1L, 2L, 2L, 6L, 4L, 2L, 3L, 5L, 6L, 6L, 4L, 5L,
>>> 4L, 6L, 6L, 3L, 4L, 1L, 5L, 3L, 3L, 5L, 3L, 4L, 1L, 3L, 3L, 2L,
>>> 4L, 1L, 2L, 1L, 6L, 3L, 5L, 5L, 3L, 4L, 4L, 5L, 4L, 1L, 5L, 3L,
>>> 4L, 4L, 3L, 6L, 5L, 2L, 4L, 1L, 1L, 6L, 4L, 3L, 6L, 5L, 6L, 2L,
>>> 6L, 1L, 6L, 6L, 4L, 3L, 4L, 2L, 1L, 5L)), class = c("dice", "data.frame"
>>> ), row.names = c(NA, -100L))
>>>
>>> For example, the first number of dice_simul should go to row 1 for
>> January,
>>> the second number of dice_simul should go to row 1 for February, ... the
>>> twelveth number of dice_simul should go to row 1 for December, the 13th
>>> number should go to row 2 for january, and so on.
>>>
>>> This is what I tried to do but doesn´t work they way I want to:
>>>
>>> #1)dice_rolls which is the number of times the dice will be rolled
>>> #2)num_dice which is the number of dice that will be rolled each time
>>> #3)dice_sides which is the number of sides of the dice
>>> #function dice will take each one of these variables as its parameter to
>>> perform the simulation
>>> dice_rolls = 100
>>> num_dice   = 1
>>> dice_sides = 6
>>>
>>> #performing simulation
>>> dice_simul = dice(rolls = dice_rolls, ndice = num_dice, sides =
>> dice_sides,
>>> plot.it = TRUE)
>>>
>>> num_rows = 100
>>>
>>> prob_frame <- data.frame(matrix(NA, nrow = num_rows, ncol = 12))
>>> colnames(prob_frame) <-
>>>
>> c("January","February","March","April","May","June","July","August","September","October","November","December")
>>>
>>>
>>> for (j in 1:12){
>>>    for (i in 1:num_rows){
>>>      prob_frame[i,j]=dice_simul[i,1]
>>>    }
>>> }
>>> I basically want to populate the twelve months for the first row, then
>> the
>>> twelve months for the second row, and so on, until I get to populate the
>>> twelve months for the last row sequentially.
>>>
>>> How could I accomplish this?
>>>
>>> Any help and/or guidance will be greatly appreciated.
>>>
>>> Best regards,
>>> Paul
>>>
>>>          [[alternative HTML version deleted]]
>>>
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>
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>
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