orrymr

n_ <- 2000
m_ <- 10000

g <- ggplot(roll(m = m_, n = n_),
            mapping = aes(x = V1)) +
  geom_vline(xintercept = 3.5, colour = "tomato3") +
  labs(
    subtitle = str_interp('Density of means of dice 
                          rolls for ${n_} dice over ${m_} rolls.'),
    x = 'Mean Score',

orrymr

n_ <- 20
m_ <- 10000

g <- ggplot(roll(m = m_, n = n_),
            mapping = aes(x = V1)) +
  geom_vline(xintercept = 3.5, colour = "tomato3") +
  labs(
    subtitle = str_interp('Density of means of dice
                          rolls for ${n_} dice over ${m_} rolls.'),
    x = 'Mean Score',

orrymr

n_ <- 4
m_ <- 10000

g <- ggplot(roll(m = m_, n = n_),
            mapping = aes(x = V1)) +
  geom_vline(xintercept = 3.5, colour = "tomato3") +
  labs(
    subtitle = str_interp('Density of means of dice
                          rolls for ${n_} dice over ${m_} rolls.'),
    x = 'Mean Score',

orrymr

n_ <- 2
m_ <- 10000

g <- ggplot(roll(m = m_, n = n_),
            mapping = aes(x = V1)) +
  geom_vline(xintercept = 3.5, colour = "tomato3") +
  labs(
    subtitle = str_interp('Density of means of dice
                          rolls for ${n_} dice over ${m_} rolls.'),
    x = 'Mean Score',

orrymr

g <- g +
  geom_density()
  
g

orrymr

n_ <- 1
m_ <- 10000

g <- ggplot(roll(m = m_, n = n_),
            mapping = aes(x = V1)) +
  geom_vline(xintercept = 3.5, colour = "tomato3") +
  labs(
    subtitle = str_interp('Density of means of dice
                          rolls for ${n_} dice over ${m_} rolls.'),
    x = 'Mean Score',

orrymr

#roll, as in roll di(c)e
# m = number of times
# n = number of dice

roll <- function(m, n){
  set.seed(1234)
  means <- plyr::ldply(1:m, function(x){
    return(mean(sample(1:6, n, replace = TRUE)))
  }) 
}

orrymr

number_of_rolls <- 1000000 # Or, we could manually roll a die 1 million times. Nah, let's let the computer do it.
mean(sample(1:6, number_of_rolls, replace = TRUE))
# [1] 3.499435

orrymr

row1 <- c(2, 3, 4, 5, 6, 7) / 2
row2 <- c(3, 4, 5, 6, 7, 8) / 2
row3 <- c(4, 5, 6, 7, 8, 9) / 2
row4 <- c(5, 6, 7, 8, 9, 10) / 2
row5 <- c(6, 7, 8, 9, 10, 11) / 2
row6 <- c(7, 8, 9, 10, 11, 12) / 2

dice <- matrix(c(row1, row2, row3, row4, row5, row6), nrow = 6, byrow = TRUE)
dice

orrymr

mean_value <- sum(seq(1:6) * (1 / 6))
print(mean_value)
# [1] 3.5