R program for a small problem: probability to find 3 choices within 6 die-rolls (repetitions allowed, and counted)

dice_problem.r

roll <- function(rolls=6, die=1:6) {
  dice <- sample(die, size = rolls, replace = TRUE)
}

verify <- function(a_roll=roll(), target=c(1,2,3)) {
  if(length(a_roll) < length(target)) { # target requires more rolls
    return (FALSE)
  }
#  cat("The roll being processed: ", a_roll, "\n")
  for(choice in target) {
#    cat("Currently looking at target: ", choice, " | Within roll: ", a_roll, "\n")
    pre <- length(a_roll)
    for(i in 1:pre) {
      if(choice == a_roll[i]) { # looking for a match
        a_roll <- a_roll[-i]
#        cat("Found a match at index: ", i, "\n")
        break
      }
    }
    post <- length(a_roll)
#    cat("pre-length: ", pre, " | post-length: ", post, "\n")
    if(pre == post) { # we haven't found a match : ABORT
      return (FALSE)
    }
  }
  return (TRUE) # found a match for all choices : WIN
}

#################################################################################

results <- c() # future results

test <- function(trials=10000, test_target=c(1,3,1)) {
  for(i in 1:trials) {
    result <- verify(target=test_target)
    results <- append(results, result)
  }
  print(table(results))
  wins <- length(which(results==TRUE))
  losses <- length(which(results==FALSE))
  percentage <- 100*wins/length(results)
  cat("Win percentage: ", percentage, "%\n")
}

Results:

> test(trials=100000, test_target=c(1,2,3))
results
FALSE  TRUE 
75744 24256 
Win percentage:  24.256 %

> test(trials=100000, test_target=c(1,1,3))
results
FALSE  TRUE 
85016 14984 
Win percentage:  14.984 %

> test(trials=100000, test_target=c(1,1,1))
results
FALSE  TRUE 
93718  6282 
Win percentage:  6.282 %

Thus, it depends on the amount of duplicates in the desired target numbers.