Loaded dice simulation in clojure

loaded_dice_basline.cljc

(ns clj-loaded-dice.core)


(defn make-loaded-dice
  "Create the data structure for the loaded dice."
  [& probabilities]
  (let [total-probability (apply + probabilities)]
    (->>
      ;; normalize the probabilities to sum up to 1
      (map #(/ % total-probability) probabilities)
      ;; Get the top of the probability for the given side
      (reduce (fn [memo p]
                (conj memo (+ p (if (seq memo) (last memo) 0))))
              [])
      ;; Add the sides of the dice
      (map-indexed (fn [i e] [(+ 1 i) e])))))


(defn roll-loaded-dice
  "Rolls a single loaded dice."
  [dice]
  (let [roll (rand)]
    ;; Since the output of (rand) is 1.0 exclusive, we
    ;; can safely use the > operator
    (some (fn [[side sum]] (when (> sum roll) side)) dice)))


(defn roll-multiple-dices
  "Rolls dice-count loaded dices throw count times and sums up the
  results of each roll."
  [throw-count dice-count dice]
  (map
    (fn [_]
      (apply + (map
                 (fn [_] (roll-loaded-dice dice))
                 (range dice-count))))
    (range throw-count)))

repl_output.cljc

(roll-multiple-dices 100 4 (make-loaded-dice 0.1 0.4 0.7))
=> (7 8 11 10 10 12 9 10 9 10 8 9 10 10 10 11 9 12 12 11 10 12 10 11 9 11 10 9 10 9 12 10 10 10 11 9 9 12 7 8 10 11 12 11 11 11 11 12 8 12 10 10 9 11 10 11 12 10 10 10 9 9 10 10 11 11 9 8 8 9 9 9 10 7 8 8 10 11 11 11 12 10 12 9 10 10 10 10 12 8 10 9 11 11 11 10 11 8 7 9)

(roll-multiple-dices 100 4 (make-loaded-dice 0.1 0.1 0.1))
=> (7 10 7 9 10 7 5 9 6 9 7 7 8 9 10 9 10 12 8 9 7 7 10 10 9 8 8 9 8 11 8 7 10 6 4 10 8 11 7 6 5 9 8 9 7 8 9 6 7 10 10 7 9 8 9 6 6 8 9 9 10 11 12 9 12 10 10 6 8 8 7 6 7 8 7 9 7 5 9 9 7 7 10 10 7 8 8 7 10 9 10 6 9 8 8 6 12 6 7 8)