[R] Model To Simulate Dice Roll
Rui Barradas
ru|pb@rr@d@@ @end|ng |rom @@po@pt
Thu Apr 21 11:04:29 CEST 2022
Hello,
There's an error in my code, inline.
Às 07:55 de 21/04/2022, Rui Barradas escreveu:
> 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
> head(prob_frame)
>
# --- wrong
> p <- colMeans(apply(prob_frame, 1, \(x) 1:6 %in% x))
> mean(p)
> # [1] 0.9116667
This should be
yes_no <- apply(prob_frame, 1, \(x) all(1:6 %in% x))
p <- mean(yes_no)
p
# [1] 0.53
Rui Barradas
>
> prob_frame <- as.data.frame(prob_frame)
>
>
> Hope this helps,
>
> Rui Barradas
>
>
> 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 the set. Please refer to your friends by name.
>>
>> 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
>>> instead. For example:
>>>
>>>> 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]]
>>>>
>>>> ______________________________________________
>>>> R-help using r-project.org mailing list -- To UNSUBSCRIBE and more, see
>>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>>> PLEASE do read the posting guide
>>> http://www.R-project.org/posting-guide.html
>>>> and provide commented, minimal, self-contained, reproducible code.
>>>
>>
>> [[alternative HTML version deleted]]
>>
>> ______________________________________________
>> R-help using r-project.org mailing list -- To UNSUBSCRIBE and more, see
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>
> ______________________________________________
> R-help using r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
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