Merge pull request #23 from timothypratley/main

add five-pirates-treasure

Author: timothypratley

src/math/stats/quantquestions/what_are_the_odds/five_pirates_treasure.clj

@@ -0,0 +1,51 @@
+^{:kindly/hide-code true
+  :clay             {:title  "Five Pirates Treasure Splitting"
+                     :quarto {:type     :post
+                              :author   [:timothypratley]
+                              :date     "2025-06-18"
+                              :category :math
+                              :tags     [:probability :stats]
+                              :keywords [:quantquestions]}}}
+(ns math.stats.quantquestions.what-are-the-odds.five-pirates-treasure)
+
+(def pirates
+  ["Green Boots" "Red Rackham" "Blue Thunder" "Black Beard" "Tim"])
+
+;; With only one pirate, they get all the booty
+;; * Green Boots: 100
+
+;; With 2 pirates, whoever proposes the split gets all the booty
+;; * Red Rackham 100
+;; * Green Boots 0
+
+;; With 3 pirates, the pirate who would miss out in the next round is incentivised by 1 coin
+;; * Blue Thunder 99
+;; * Red Rackham  0
+;; * Green Boots  1
+
+;; With 4 pirates, 1 vote needed, the pirate who would miss out is incentivised by 1 coin
+;; * Black Beard  99
+;; * Blue Thunder 0
+;; * Red Rackham  1
+;; * Green Boots  0
+
+;; With 5 pirates, 2 votes needed, the 2 pirates who would miss out in the next round get a coin each
+;; * Tim          98
+;; * Black Beard  0
+;; * Blue Thunder 1
+;; * Red Rackham  0
+;; * Green Boots  1
+
+;; Probably you can spot a pattern emerging here...
+
+(defn split [coins pirates]
+  (let [n (count pirates)]
+    (-> (mapv vector
+              (reverse pirates)
+              (cycle (if (odd? n) [1 0] [0 1])))
+        (assoc-in [0 1] (- coins (/ (if (odd? n) (dec n) n) 2))))))
+
+(split 100 pirates)
+
+^:kind/table
+(split 100 pirates)