diff --git a/16_reinforcement_learning.ipynb b/16_reinforcement_learning.ipynb
index 96e94a2..9459440 100644
--- a/16_reinforcement_learning.ipynb
+++ b/16_reinforcement_learning.ipynb
@@ -31,9 +31,7 @@
   {
    "cell_type": "code",
    "execution_count": 1,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "# To support both python 2 and python 3\n",
@@ -95,9 +93,7 @@
   {
    "cell_type": "code",
    "execution_count": 2,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "import gym"
@@ -129,9 +125,7 @@
   {
    "cell_type": "code",
    "execution_count": 4,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "obs = env.reset()"
@@ -163,9 +157,7 @@
   {
    "cell_type": "code",
    "execution_count": 6,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "img = env.render(mode=\"rgb_array\")"
@@ -226,9 +218,7 @@
   {
    "cell_type": "code",
    "execution_count": 9,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "def plot_environment(env, figsize=(5,4)):\n",
@@ -273,9 +263,7 @@
   {
    "cell_type": "code",
    "execution_count": 11,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "env.reset()\n",
@@ -311,9 +299,7 @@
   {
    "cell_type": "code",
    "execution_count": 13,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "obs, reward, done, info = env.step(0)"
@@ -393,9 +379,7 @@
   {
    "cell_type": "code",
    "execution_count": 18,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "frames = []\n",
@@ -424,9 +408,7 @@
   {
    "cell_type": "code",
    "execution_count": 19,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "def update_scene(num, frames, patch):\n",
@@ -461,9 +443,7 @@
   {
    "cell_type": "code",
    "execution_count": 21,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "env.close()"
@@ -502,9 +482,7 @@
   {
    "cell_type": "code",
    "execution_count": 23,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "obs = env.reset()"
@@ -547,9 +525,7 @@
   {
    "cell_type": "code",
    "execution_count": 25,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "from PIL import Image, ImageDraw\n",
@@ -633,9 +609,7 @@
   {
    "cell_type": "code",
    "execution_count": 28,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "obs = env.reset()\n",
@@ -677,9 +651,7 @@
   {
    "cell_type": "code",
    "execution_count": 31,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "obs = env.reset()\n",
@@ -722,9 +694,7 @@
   {
    "cell_type": "code",
    "execution_count": 33,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "frames = []\n",
@@ -795,9 +765,7 @@
   {
    "cell_type": "code",
    "execution_count": 35,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "import tensorflow as tf\n",
@@ -846,9 +814,7 @@
   {
    "cell_type": "code",
    "execution_count": 36,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "n_max_steps = 1000\n",
@@ -895,9 +861,7 @@
   {
    "cell_type": "code",
    "execution_count": 38,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "import tensorflow as tf\n",
@@ -965,9 +929,7 @@
   {
    "cell_type": "code",
    "execution_count": 40,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "def render_policy_net(model_path, action, X, n_max_steps = 1000):\n",
@@ -1024,9 +986,7 @@
   {
    "cell_type": "code",
    "execution_count": 42,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "import tensorflow as tf\n",
@@ -1069,9 +1029,7 @@
   {
    "cell_type": "code",
    "execution_count": 43,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "def discount_rewards(rewards, discount_rate):\n",
@@ -1157,9 +1115,7 @@
   {
    "cell_type": "code",
    "execution_count": 47,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "env.close()"
@@ -1309,9 +1265,7 @@
   {
    "cell_type": "code",
    "execution_count": 51,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "n_states = 3\n",
@@ -1336,9 +1290,7 @@
   {
    "cell_type": "code",
    "execution_count": 52,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "def optimal_policy(state):\n",
@@ -1439,23 +1391,28 @@
   {
    "cell_type": "code",
    "execution_count": 57,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
-    "mspacman_color = np.array([210, 164, 74]).mean()\n",
+    "mspacman_color = 210 + 164 + 74\n",
     "\n",
     "def preprocess_observation(obs):\n",
     "    img = obs[1:176:2, ::2] # crop and downsize\n",
-    "    img = img.mean(axis=2) # to greyscale\n",
+    "    img = img.sum(axis=2) # to greyscale\n",
     "    img[img==mspacman_color] = 0 # Improve contrast\n",
-    "    img = (img - 128) / 128 - 1 # normalize from -1. to 1.\n",
+    "    img = (img // 3 - 128).astype(np.int8) # normalize from -128 to 127\n",
     "    return img.reshape(88, 80, 1)\n",
     "\n",
     "img = preprocess_observation(obs)"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Note: the `preprocess_observation()` function is slightly different from the one in the book: instead of representing pixels as 64-bit floats from -1.0 to 1.0, it represents them as 8-bit integers from -128 to 127. The benefit is that the replay memory will take up about 6.5 GB of RAM instead of 52 GB. The reduced precision has no impact on training."
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 58,
@@ -1498,9 +1455,7 @@
   {
    "cell_type": "code",
    "execution_count": 59,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "reset_graph()\n",
@@ -1545,9 +1500,7 @@
   {
    "cell_type": "code",
    "execution_count": 60,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "X_state = tf.placeholder(tf.float32, shape=[None, input_height, input_width,\n",
@@ -1572,9 +1525,7 @@
   {
    "cell_type": "code",
    "execution_count": 62,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "learning_rate = 0.001\n",
@@ -1608,9 +1559,7 @@
   {
    "cell_type": "code",
    "execution_count": 63,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "from collections import deque\n",
@@ -1632,9 +1581,7 @@
   {
    "cell_type": "code",
    "execution_count": 64,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "eps_min = 0.1\n",
@@ -1678,9 +1625,7 @@
   {
    "cell_type": "code",
    "execution_count": 66,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "loss_val = np.infty\n",
@@ -1970,7 +1915,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.5.2"
+   "version": "3.6.3"
   },
   "nav_menu": {},
   "toc": {