Simulating unfair dice

What if our dice were unfair in some way? Maybe they are weighted oddly.

Turns out this is easy to try - you can just pass the weights into sample():

simulate_two_dice <- function(
    number_of_rolls,
    die_model = rep( 1/6, 6 )
) {
    die1 = sample( 1:6, size = number_of_rolls, replace = T, prob = die_model )
    die2 = sample( 1:6, size = number_of_rolls, replace = T, prob = die_model )
    return(
        tibble::tibble(
            roll = 1:number_of_rolls,
            sum_of_dice = die1 + die2
        )
    )
}

So by default this gives you rolls of two fair die - but if you change the probabilities, they'll be unfair.

Question

What does the histogram look like if you try unfair dice?

For example here's a simulation of a dice that never rolls 5:

(
    ggplot(
        data = simulate_two_dice(
            10000,
            die_model = c( 0.2, 0.2, 0.2, 0.2, 0, 0.2 )
        )
    )
    + geom_histogram(
        aes( x = result ),
        breaks = (2:13)-0.5
    )
)

How does it look?

Play around with the probabilities. (Remember the probabilities ought to sum to 1!)

Note

Apart from plotting, you could also just count the values in the simulation. The 'base R' way to do this is table():

simulation = simulate_two_dice( 100, c( 0.2, 0.2, 0.2, 0.2, 0, 0.2 ))
table( simulation$sum_of_dice )

The tidyverse way is group_by() and summarise(), count():

simulation %>% group_by( sum_of_dice ) %>% count()