From c0cd582019d4e33a585df2ba19992a6cf474b35c Mon Sep 17 00:00:00 2001
From: andyeisenberg <andyjeisenberg@gmail.com>
Date: Thu, 12 Mar 2026 14:58:10 -0400
Subject: [PATCH] Boxes paradox

---
 source/fun/boxes.ptx | 74 ++++++++++++++++++++++++++++++++++++++++++++
 source/main.ptx      |  7 +++++
 2 files changed, 81 insertions(+)
 create mode 100644 source/fun/boxes.ptx

diff --git a/source/fun/boxes.ptx b/source/fun/boxes.ptx
new file mode 100644
index 0000000..bbcf0ff
--- /dev/null
+++ b/source/fun/boxes.ptx
@@ -0,0 +1,74 @@
+<?xml version="1.0" encoding="UTF-8"?>
+
+<!-- When creating a new activity, make a copy of this file with appropriate name -->
+<worksheet xml:id="boxes">
+  <title>Boxes</title>
+
+  <!-- Optional introduction -->
+  <introduction>
+    <p>
+      The following is not for credit and will not be covered on any quiz or exam.
+      This is just for fun.
+    </p>
+  </introduction>
+
+
+  <page>
+    <!-- Exercises start here. -->
+    <exercise>
+      <introduction>
+        <p>
+          A superintelligent robot named Bob waits in a room with two boxes.
+          Box 1 contains $1000.
+          Box 2 is a mystery box containing a secret amount of money.
+          Bob will offer you the choice:
+          <ol>
+            <li>
+              <p>
+                You can take the mystery box alone, or
+              </p>
+            </li>
+
+            <li>
+              <p>
+                You can take both boxes.
+              </p>
+            </li>
+          </ol>
+          Bob is very accurate at predicting ahead of time what people will do.
+          If Bob thinks that you'll choose to take only the mystery box, he'll put $1 million dollars in the mystery box.
+          If Bob thinks that you'll choose to take both boxes, he'll put nothing in the mystery box.
+          Bob made his prediction and placed $1 million or $0 in the mystery box before you entered the rooms and learned the rules of the game.
+        </p>
+
+        <p>
+          Would you take just the mystery box? Or would you take both boxes?
+        </p>
+      </introduction>
+
+
+      <task workspace="1in">
+        <statement>
+          <p>
+            Let <m>\alpha</m> be the probability that Bob accurately predicts your choice.
+            Write an expected value formula for the strategy of choosing just the mystery box in terms of <m>\alpha</m>.
+            Write an expected value formula for the strategy of choosing both boxes in terms of <m>\alpha</m>.
+            Which strategy has a higher expected value?
+          </p>
+        </statement>
+      </task>
+
+
+      <task workspace="1in">
+        <statement>
+          <p>
+            Let <m>\beta</m> be the probability that Bob predicts that you'll take both boxes.
+            Write an expected value formula for the strategy of choosing just the mystery box in terms of <m>\beta</m>.
+            Write an expected value formula for the strategy of choosing both boxes in terms of <m>\beta</m>.
+            Which strategy has a higher expected value?
+          </p>
+        </statement>
+      </task>
+    </exercise>
+  </page>
+</worksheet>
\ No newline at end of file
diff --git a/source/main.ptx b/source/main.ptx
index 85332b5..d2c8e33 100644
--- a/source/main.ptx
+++ b/source/main.ptx
@@ -62,7 +62,14 @@
       <title>Exam Review</title>
 
       <xi:include href="./review/Exam-1-Review.ptx"/>
+
+    </chapter>
      
+    <chapter xml:id="fun">
+      <title>Just for Fun</title>
+
+      <xi:include href="./fun/boxes.ptx"/>
+
     </chapter>