[R] Model To Simulate Dice Roll

David Carlson dc@r|@on @end|ng |rom t@mu@edu
Sat Apr 23 06:24:31 CEST 2022 

Sorry, The last three lines should read:

all <- apply(results, 1, function(x) length(intersect(x,
seq(sides)))==sides)
sum(all)/reps
results <- as.data.frame(results)

To generalize them for values of sides other than 6.

On Fri, Apr 22, 2022 at 11:05 PM Paul Bernal <paulbernal07 using gmail.com> wrote:

> Thank you so much David! El El vie, 22 de abr. de 2022 a la(s) 11:04 p.
> m., David Carlson <dcarlson using tamu.edu> escribió: Since the rolls are
> independent, it is not necessary to separate the rolls into two stages:
> sides <- 6 ‍ ‍ ‍ ‍ ‍ ‍ ‍ ‍
> ZjQcmQRYFpfptBannerStart
> This Message Is From an External Sender
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>
> ZjQcmQRYFpfptBannerEnd
> Thank you so much David!
>
> El El vie, 22 de abr. de 2022 a la(s) 11:04 p. m., David Carlson <
> dcarlson using tamu.edu> escribió:
>
>> Since the rolls are independent, it is not necessary to separate the
>> rolls into two stages:
>>
>> sides <- 6
>> months <- 12
>> reps <- 100
>>
>> set.seed(2022)
>> results <- matrix(sample.int
>> <https://urldefense.com/v3/__http://sample.int__;!!KwNVnqRv!GvZvIF7bCsJmP-MoZAjpwRSwA0SLF9dwlLokWfsqj07fpKB_yoDtZ64yl90ktreESKpQkxnxfP7vuF2jfsHvZA$>(sides,
>> months*reps, replace=TRUE), reps, months, byrow=TRUE)
>> colnames(results) <- month.name
>> <https://urldefense.com/v3/__http://month.name__;!!KwNVnqRv!GvZvIF7bCsJmP-MoZAjpwRSwA0SLF9dwlLokWfsqj07fpKB_yoDtZ64yl90ktreESKpQkxnxfP7vuF14dyuUpA$>
>> all6 <- apply(results, 1, function(x) length(intersect(x, 1:6))==6)
>> sum(all6)/reps
>> # 0.53 which matches Rui's result
>> results <- as.data.frame(results)
>>
>> David L. Carlson
>>
>>
>>
>> On Thu, Apr 21, 2022 at 4:04 AM Rui Barradas <ruipbarradas using sapo.pt>
>> wrote:
>>
>>> 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
>>> ZjQcmQRYFpfptBannerStart
>>> This Message Is From an External Sender
>>> This message came from outside your organization.
>>>
>>> ZjQcmQRYFpfptBannerEnd
>>>
>>> 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 <https://urldefense.com/v3/__http://month.name__;!!KwNVnqRv!GvZvIF7bCsJmP-MoZAjpwRSwA0SLF9dwlLokWfsqj07fpKB_yoDtZ64yl90ktreESKpQkxnxfP7vuF14dyuUpA$>
>>> > 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 <https://urldefense.com/v3/__http://plot.it__;!!KwNVnqRv!GvZvIF7bCsJmP-MoZAjpwRSwA0SLF9dwlLokWfsqj07fpKB_yoDtZ64yl90ktreESKpQkxnxfP7vuF1nNnEZyA$> = 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 <https://urldefense.com/v3/__http://plot.it__;!!KwNVnqRv!GvZvIF7bCsJmP-MoZAjpwRSwA0SLF9dwlLokWfsqj07fpKB_yoDtZ64yl90ktreESKpQkxnxfP7vuF1nNnEZyA$> = 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 <https://urldefense.com/v3/__http://plot.it__;!!KwNVnqRv!GvZvIF7bCsJmP-MoZAjpwRSwA0SLF9dwlLokWfsqj07fpKB_yoDtZ64yl90ktreESKpQkxnxfP7vuF1nNnEZyA$> = 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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>>> >>>
>>> >>
>>> >>     [[alternative HTML version deleted]]
>>> >>
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