diff --git a/DP/Policy Evaluation Solution.ipynb b/DP/Policy Evaluation Solution.ipynb
index a8b949367..a4399cd77 100644
--- a/DP/Policy Evaluation Solution.ipynb	
+++ b/DP/Policy Evaluation Solution.ipynb	
@@ -2,10 +2,8 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 53,
-   "metadata": {
-    "collapsed": false
-   },
+   "execution_count": 1,
+   "metadata": {},
    "outputs": [],
    "source": [
     "import numpy as np\n",
@@ -18,7 +16,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 54,
+   "execution_count": 2,
    "metadata": {
     "collapsed": true
    },
@@ -30,7 +28,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 55,
+   "execution_count": 3,
    "metadata": {
     "collapsed": true
    },
@@ -43,9 +41,9 @@
     "    Args:\n",
     "        policy: [S, A] shaped matrix representing the policy.\n",
     "        env: OpenAI env. env.P represents the transition probabilities of the environment.\n",
-    "            env.P[s][a] is a (prob, next_state, reward, done) tuple.\n",
+    "            env.P[s][a] is a list of transition tuples (prob, next_state, reward, done).\n",
     "        theta: We stop evaluation once our value function change is less than theta for all states.\n",
-    "        discount_factor: lambda discount factor.\n",
+    "        discount_factor: gamma discount factor.\n",
     "    \n",
     "    Returns:\n",
     "        Vector of length env.nS representing the value function.\n",
@@ -54,18 +52,23 @@
     "    V = np.zeros(env.nS)\n",
     "    while True:\n",
     "        delta = 0\n",
+    "        new_V = np.copy(V) # new_V is V_{k+1} \n",
     "        # For each state, perform a \"full backup\"\n",
     "        for s in range(env.nS):\n",
     "            v = 0\n",
     "            # Look at the possible next actions\n",
     "            for a, action_prob in enumerate(policy[s]):\n",
     "                # For each action, look at the possible next states...\n",
+    "                immediate_reward = env.P[s][a][0][2]\n",
+    "                v_prim = 0\n",
     "                for  prob, next_state, reward, done in env.P[s][a]:\n",
     "                    # Calculate the expected value\n",
-    "                    v += action_prob * prob * (reward + discount_factor * V[next_state])\n",
+    "                    v_prim += discount_factor * prob * V[next_state]\n",
+    "                v += action_prob * (immediate_reward + v_prim)\n",
+    "            new_V[s] = v\n",
     "            # How much our value function changed (across any states)\n",
     "            delta = max(delta, np.abs(v - V[s]))\n",
-    "            V[s] = v\n",
+    "        V = new_V \n",
     "        # Stop evaluating once our value function change is below a threshold\n",
     "        if delta < theta:\n",
     "            break\n",
@@ -74,10 +77,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 56,
-   "metadata": {
-    "collapsed": false
-   },
+   "execution_count": 4,
+   "metadata": {},
    "outputs": [],
    "source": [
     "random_policy = np.ones([env.nS, env.nA]) / env.nA\n",
@@ -86,25 +87,23 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 57,
-   "metadata": {
-    "collapsed": false
-   },
+   "execution_count": 5,
+   "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
       "Value Function:\n",
-      "[  0.         -13.99993529 -19.99990698 -21.99989761 -13.99993529\n",
-      " -17.9999206  -19.99991379 -19.99991477 -19.99990698 -19.99991379\n",
-      " -17.99992725 -13.99994569 -21.99989761 -19.99991477 -13.99994569   0.        ]\n",
+      "[  0.         -13.99989315 -19.99984167 -21.99982282 -13.99989315\n",
+      " -17.99986052 -19.99984273 -19.99984167 -19.99984167 -19.99984273\n",
+      " -17.99986052 -13.99989315 -21.99982282 -19.99984167 -13.99989315   0.        ]\n",
       "\n",
       "Reshaped Grid Value Function:\n",
-      "[[  0.         -13.99993529 -19.99990698 -21.99989761]\n",
-      " [-13.99993529 -17.9999206  -19.99991379 -19.99991477]\n",
-      " [-19.99990698 -19.99991379 -17.99992725 -13.99994569]\n",
-      " [-21.99989761 -19.99991477 -13.99994569   0.        ]]\n",
+      "[[  0.         -13.99989315 -19.99984167 -21.99982282]\n",
+      " [-13.99989315 -17.99986052 -19.99984273 -19.99984167]\n",
+      " [-19.99984167 -19.99984273 -17.99986052 -13.99989315]\n",
+      " [-21.99982282 -19.99984167 -13.99989315   0.        ]]\n",
       "\n"
      ]
     }
@@ -121,10 +120,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 51,
-   "metadata": {
-    "collapsed": false
-   },
+   "execution_count": 6,
+   "metadata": {},
    "outputs": [],
    "source": [
     "# Test: Make sure the evaluated policy is what we expected\n",
@@ -158,9 +155,9 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.5.1"
+   "version": "3.6.0"
   }
  },
  "nbformat": 4,
- "nbformat_minor": 0
+ "nbformat_minor": 1
 }