Rolling elven accuracy using RAW vs. just rolling all three at once

elven_accuracy

library(magrittr)

## Given a vector, calculate both the mean and standard deviation
mean_sd = function(vec) {
    list(mean = mean(vec), 
         sd = sd(vec))
}

d20 = function() sample.int(20, 1)

## RAW
## Roll 2; keep the larger; roll 1 more; take the max
roll_raw = function(x) {
    c(d20(), d20()) %>% 
        max() %>% 
        c(., d20()) |> 
        max()
}
    
## Roll 3
## Roll 3 at once and take the max
roll_three = function(x) max(c(d20(), d20(), d20()))

## How many times to run the simulation? 
N = 10000

set.seed(2023-10-15)
## Run the simulation and report the mean value
## RAW
## $mean
## [1] 15.4533
## $sd
## [1] 3.901864
sapply(1:N, roll_raw) |> 
    mean_sd()

## Just roll 3 at once
## $mean
## [1] 15.5064
## $sd
## [1] 3.853368
sapply(1:N, roll_three) |> 
    mean_sd()