Coin Game

gistfile1.txt

;; gorilla-repl.fileformat = 1

;; **
;;; # Coin Board Game or Die
;;; From the puzzle found here: http://fivethirtyeight.com/features/can-you-survive-this-deadly-board-game/
;;; 
;; **

;; @@
; namespace and includes...
(ns coin-game
  (:require [gorilla-plot.core :as plot]))

;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-nil'>nil</span>","value":"nil"}
;; <=

;; **
;;; ## Get a sequence of die rolls that add up to the board length
;;; Demonstrate recursion
;; **

;; @@
; gives a sorted set of spaces touched by a pawn driven by a 6 sided die.
(defn rnd-seq-sum [total] 
  (loop [sm 0
         result []]
    (let [r (inc(rand-int 6))
          new-sum (+ r sm)
          res (conj result new-sum)
          ]
      (if (>= new-sum total)
        (apply sorted-set res)
        (recur new-sum res)))))

(rnd-seq-sum 100)
;; @@
;; =>
;;; {"type":"list-like","open":"<span class='clj-set'>#{</span>","close":"<span class='clj-set'>}</span>","separator":" ","items":[{"type":"html","content":"<span class='clj-long'>3</span>","value":"3"},{"type":"html","content":"<span class='clj-long'>9</span>","value":"9"},{"type":"html","content":"<span class='clj-long'>12</span>","value":"12"},{"type":"html","content":"<span class='clj-long'>15</span>","value":"15"},{"type":"html","content":"<span class='clj-long'>20</span>","value":"20"},{"type":"html","content":"<span class='clj-long'>25</span>","value":"25"},{"type":"html","content":"<span class='clj-long'>27</span>","value":"27"},{"type":"html","content":"<span class='clj-long'>32</span>","value":"32"},{"type":"html","content":"<span class='clj-long'>34</span>","value":"34"},{"type":"html","content":"<span class='clj-long'>37</span>","value":"37"},{"type":"html","content":"<span class='clj-long'>38</span>","value":"38"},{"type":"html","content":"<span class='clj-long'>40</span>","value":"40"},{"type":"html","content":"<span class='clj-long'>43</span>","value":"43"},{"type":"html","content":"<span class='clj-long'>47</span>","value":"47"},{"type":"html","content":"<span class='clj-long'>50</span>","value":"50"},{"type":"html","content":"<span class='clj-long'>54</span>","value":"54"},{"type":"html","content":"<span class='clj-long'>55</span>","value":"55"},{"type":"html","content":"<span class='clj-long'>59</span>","value":"59"},{"type":"html","content":"<span class='clj-long'>61</span>","value":"61"},{"type":"html","content":"<span class='clj-long'>66</span>","value":"66"},{"type":"html","content":"<span class='clj-long'>70</span>","value":"70"},{"type":"html","content":"<span class='clj-long'>74</span>","value":"74"},{"type":"html","content":"<span class='clj-long'>80</span>","value":"80"},{"type":"html","content":"<span class='clj-long'>82</span>","value":"82"},{"type":"html","content":"<span class='clj-long'>88</span>","value":"88"},{"type":"html","content":"<span class='clj-long'>93</span>","value":"93"},{"type":"html","content":"<span class='clj-long'>96</span>","value":"96"},{"type":"html","content":"<span class='clj-long'>101</span>","value":"101"}],"value":"#{3 9 12 15 20 25 27 32 34 37 38 40 43 47 50 54 55 59 61 66 70 74 80 82 88 93 96 101}"}
;; <=

;; **
;;; ##Play game
;; **

;; @@
; Determin win based on if there is an intersection of the win set and the spaces touched by the "pawn" in a game
(defn play-game [win-set board-length]
  (let [rnd-seq (rnd-seq-sum board-length)]
    (not (empty? (clojure.set/intersection win-set rnd-seq)))))

(play-game #{4 5 6} 10)
  
;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-unkown'>true</span>","value":"true"}
;; <=

;; **
;;; ##Count wins
;;; 
;; **

;; @@
(defn percent-win [count win-set board-length]
  (let [wins 
        	(reduce (fn [acc _] 
                       (if (play-game win-set board-length) 
                         (inc acc) 
                         acc)) 
             	0 (range count))
        ratio (/ wins count)]
      (* 100.0 ratio)
  ))

(percent-win 10000 #{4 5 6} 10)
(percent-win 10000 #{5 6 7} 10)
(percent-win 10000 #{7 8 9} 10)
(percent-win 10000 #{8 9 10} 10)
;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-double'>70.30999999999999</span>","value":"70.30999999999999"}
;; <=

;; **
;;; ##Plot
;;; Show results for contiguous selections.  X axis is the first item in the sequence.  That is for x=10 the winning set is [10 11 12]
;; **

;; @@
(def data (map #(percent-win 1000 (into #{} (range % (+ 3 %))) 100) (range 1 100)))
data

(plot/list-plot data :symbol-size 20)

;; @@
;; =>
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;; <=

;; **
;;; # The best choice is at locations [4 5 6]
;; **

;; @@

;; @@