Part 3 - Tabular Q-Learning.ipynb

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    "# Tabular Q Learning, a Tic Tac Toe player that gets better and better \n",
    "\n",
    "In this part, we will introduce our first player which actually uses a machine learning approach to playing Tic Tac Toe. The machine learning approach we will use is called *Reinforcement Learning*, and the particular variant we will use is called *Tabular Q Learning*. In the following we will introduce all 3 concepts, *Reinforcement Learning*, *Q function*, and *Tabular Q function*, and then put them all together to create a Tabular Q-Learning Tic Tac Toe player."
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    "## What is Reinforcement learning?\n",
    "The basic idea behind reinforcement learning is quite straight forward: Learn by doing and observing the results of your actions. This concept is motivated by how humans seem to learn in many cases: We do something and if it had positive consequences we are more likely to do it again, whereas if it had negative consequences we are generally less likely to do it again.\n",
    "\n",
    "At each step, the player (also interchangeably called agent) takes a good look at the current environment and makes an *educated guess* of what it thinks is the best action in the given situation. It executes the selected action and observes  how that action has changed the environment and also receive feedback on how good or bad its action was in that particular situation: If it chose a good action it will get a positive reward, if it chose a bad action it will get a negative reward. Based on that feedback, it can then adjust its *educated guessing process*. When it encounters the same situation again in the future, it should hopefully be more more likely to chose the same action again if the feedback was positive and more likely to chose a different action if it was negative.\n",
    "\n",
    "The following graphic illustrates this process:\n",
    "![Title](./Images/Reinforcement.PNG)\n",
    "\n",
    "In many situations, the feedback / reward that the agent gets after choosing an action will not necessarily be very strong or conclusive. E.g. when making a move at the beginning of a game of Tic Tac Toe, it will be unclear if the chosen action was good or bad and thus the reward will be neutral. \n",
    "\n",
    "In fact, going forward we will only ever return a positive or negative reward for the final move in a game. If the player won, the last move will get a positive reward, if it lost it will get a negative reward, and in the case of a draw it will get no reward.\n",
    "\n",
    "One fundamental concept of *Reinforcement Learning* is to have a process of attributing that final reward back to previous actions to reflect the fact that those previous move likely contributed to the ultimate success or failure in some way. Based on the assumption, that the longer in the past an action has happened, the less likely it is that it was instrumental in the final outcome, we will discount the final reward at each step back in time.\n",
    "\n",
    "Let's look at an example: Let's assume we have played a game of Tic Tac Toe, choosing moves based on our current best guesses and won. None of our moves got a positive or negative reward apart from the very last one which got a 1 as it won the game. Now, it is more than likely that the victory was due not only because of the quality of the last move, but because at least some of our previous moves were *good* moves as well. The further in the past, the less likely it is that they contributed significantly to the outcome. So, we might give the second last move a discounted reward of 0.8, the one before that a reward of 0.5, the one before that a reward of 0.1 etc.\n",
    "\n",
    "Over many games, the theory goes, that if there are moves that are particularly strong and important at the beginning of the game they will still end up with a very high likelihood of getting chosen as they will receive positive rewards over and over again, adding up over time despite the fact that they only ever received highly discounted rewards. If I remember correctly, with certain constraints on the set-up and number of iterations this can be proven to be true.\n",
    "\n",
    "<div class=\"alert alert-block alert-info\">\n",
    "A more detailed introduction to Reinforcement Learning can be found on [Wikipedia](https://en.wikipedia.org/wiki/Reinforcement_learning) and the ultimate, authoritative introduction is probably the book [Reinforcement Learning - An Introduction](https://mitpress.mit.edu/books/reinforcement-learning) by Richard S. Sutton and Andrew G. Barto. Draft versions of this book seem to be easily findable and down-loadable over the Internet, but as I'm not sure about the legality of those I will not provide links here. In the January 2018 Draft version, the tabular Q-learning approach from this tutorial can be found in part 1, chapter 6.5 (\" Part 1: Tabular Solution Methods -> 6 Temporal Difference Learning -> 6.5 Q-Learning: Off-policy TD Control\").<br><br>\n",
    "\n",
    "I learned most of what I know about implementing reinforcement learning  with TensorFlow from the excellent [tutorials by Arthur Juliani](https://medium.com/emergent-future/simple-reinforcement-learning-with-tensorflow-part-0-q-learning-with-tables-and-neural-networks-d195264329d0).\n",
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    "## What is the Q function?\n",
    "The next concept we need to understand is the Q function. The Q stands for *Quality* and the Q function is the function that assigns a quality score to an State - Action pair. I.e. given a state $S$ and an action $A$ the function $Q(S,A) \\mapsto I\\!R$ will return a real number reflecting the quality of doing this action $A$ in the state $S$.\n",
    "\n",
    "We will assume that this function exists and is deterministic, but its concrete mapping of states and actions to quality values is not necessarily known to us. Q-learning is all about learning this mapping and thus the function Q.\n",
    "\n",
    "If you think back to our previous part about the Min-Max Algorithm, you might remember that the values we computed there for each state  seem very similar to the values that the Q function returns. \n",
    "And indeed they are related. In MinMax we assigned quality values to states, whereas here we assign quality values to actions that can be chosen in a given state. \n",
    "\n",
    "In a deterministic environment like playing Tic Tac Toe against an opponent that always plays the best possible move, the value of a particular action in a particular state is indeed closely reflecting the value of the following state. When playing against a Random Player, however, this is not necessarily the case anymore. Depending on which move the randomly playing opponent choses in reaction to our our action, we will end up in different next states with different Q values. The Q value of the action will thus be the combinations of the values of all possible next states and their respective probabilities of occurring. This makes the Q function dependent on the opponent. If the opponent is an ideal player, always choosing the best possible move, the Q function is indeed again closely reflecting the Min Max scores.\n",
    "\n",
    "\n",
    "## What is the tabular Q function?\n",
    "Tabular in this context simply means that we will store the Q function in a lookup table. I.e. we create a table where we store the Q value for each possible State and Move. It may look something like this (the values in this example are completely made up and not the real Q function for Tic Tac Toe):\n",
    "![Title](./Images/QTable.PNG)\n",
    "\n",
    "## How Do we use the Q function to play Tic Tac Toe?\n",
    "Assuming we know the Q function, we can play Tic Tac Toe, by looking up the Q values for all possible moves in the current situation and chose the one with the highest value. If there is more than one possible move with the same highest value, we chose randomly amongst them. Having the highest value means that this move is the best move in this situation.\n",
    "\n",
    "Going forward we will also use the term *Policy* to refer to strategies such as this."
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    "## How do we compute the actual Q function fro Tic Tac Toe?\n",
    "This is where we put all the above together:\n",
    "\n",
    "First we create a Q table with a row for every possible state and initialize the values to be the same for every state. I.e. all moves are equally likely to be picked.\n",
    "\n",
    "Now we use Reinforcement Learning to learn the real Q function. We do this by repeatedly playing Tic Tac Toe against an opponent and at the end of each game update the Q value of all moves in the game according to the game result. For a win we will award a reward of 1 to the last move, for a loss a reward of 0 and for a draw we will give a reward of 0.5.\n",
    "\n",
    "The final move will get the reward as its new Q value. For all the other moves in that game we will use the following formula to update their Q values:\n",
    "\n",
    "$$ Q(S,A) = Q(S,A) + \\alpha * (\\gamma * max_a Q(S', a) - Q(S,A))$$\n",
    "\n",
    "with $S$ being the current state, $A$ the current action, $S'$ the state after doing $A$, $\\alpha$ being the learning rate, $\\gamma$ being the discount factor, and $max_a Q(S', a)$ the highest Q value of any move in the next state $S'$, i.e. the Q value of the best move in the following state.\n",
    "\n",
    "We can also rewrite this formula as:\n",
    "\n",
    "$$ Q(S,A) = (1-\\alpha) * Q(S,A) + \\alpha * \\gamma * max_a Q(S', a)$$\n",
    "\n",
    "which maybe makes it easier to see what the learning rate does. It is basically determining how much we change our current Q value towards the discounted maximum of its successors. If we would chose $\\alpha$ as 0, we wouldn't change anything, if we chose $\\alpha$ as 1 we completely replace the old value with the new value, if we chose $\\alpha$ as 0.5, we would get the average between the old value and the new value. In the computer player below we will chose $\\alpha$ to be 0.9 and $\\gamma$ to be 0.95.\n",
    "\n",
    "<div class=\"alert alert-block alert-info\">\n",
    "A short detour to explain this formula step by step: Let's start with the inner-most bit:\n",
    "\n",
    "$$ Q(S,A) = max_a Q(S', a)$$\n",
    "\n",
    "This basically says: If we do action $A$ in state $S$ we will get to state $S'$ and the value of doing action $A$ in state $S$ should be the same as the value of the best possible action in that next state $S'$. \n",
    "<br/>\n",
    "This is seen as being a bit too optimistic, so we want to actually say something more like: The value of doing action $A$ in state $S$ should be *almost* as good as the value of the best possible action in that next state $S'$. I.e. we need to apply a discount to that value. This will also reflect the fact that the longer back an action was in time, the less crucial it likely was for the end result. We achieve this by multiplying with a discount value $\\gamma$ with $ 0 < \\gamma < 1 $: \n",
    "\n",
    "$$ Q(S,A) = \\gamma * max_a Q(S', a)$$\n",
    "\n",
    "Finally we don't want to completely replace the old Q-value of our action with each update. What if we just got lucky and out opponent made a mistake, i.e. we won, but the action wasn't actually that good? In order to account for this, we set the new Q value to a value somewhere between the old Q value and the potential new Q value. We use an additional parameter, the learning rate $\\alpha$ to set how much the new value will change the old value and get the final formula as above:\n",
    "\n",
    "$$ Q(S,A) = (1-\\alpha) * Q(S,A) + \\alpha * \\gamma * max_a Q(S', a)$$\n",
    "\n",
    "</div>\n",
    "\n",
    "By repeatedly playing game after game and updating the Q values after each game, the Q function will converge to the true Q values for Tic Tac Toe.\n",
    "\n",
    "### How to initialize the Q Table?\n",
    "The one thing we haven't discussed yet is what value we chose to initialize the Q table with. This value does actually matter. \n",
    "\n",
    "If we initialize  all values with 0, the player will be very \"pessimistic\", i.e. it will assume every move leads to a loss, and is likely to settle for anything that is better than losing. E.g. if the player achieves a draw before its first win, it will increase the values of the moves that lead to the draw while all other move values will still be 0. In subsequent games it will favor using those moves again over trying something new with the potential chance of actually winning.\n",
    "\n",
    "On the other hand, if we initialize the values to 1, the player will be very optimistic and expect every move to lead to victory. The player is thus less likely to settle for a draw as best possible outcome and will actively explore other options first. The downside however is that it will learn quite slowly as it will exhaust any other option before settling on a strategy that leads to a draw.\n",
    "\n",
    "Feel encouraged to try different values in the code below and compare performance. By default the player will initialize the values with 0.6, i.e. be slightly optimistic but not take too long to be dissuaded from a bad choice.  In practice, as we know a draw is the best outcome one can expect, a value of 0 should converge fastest."
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    "## Putting it all together\n",
    "The class [TQPlayer](https://github.com/fcarsten/tic-tac-toe/blob/master/tic_tac_toe/TabularQPlayer.py) implements an agent playing Tic Tac Toe and learning its Q function on the way. Let's pit it against some of the players we have previously created and see how it goes. We will have it play several battles of 100 games against the same player and see how its performance improves.\n",
    "\n",
    "First we define a new utility function `eval_players` which takes 2 players and the number of battles as input, then executes the battles and prints a plot of the results. You can also optionally pass the number of games per battle."
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    "%matplotlib inline\n",
    "\n",
    "import matplotlib\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from tic_tac_toe.Board import Board, GameResult, CROSS, NAUGHT, EMPTY\n",
    "from tic_tac_toe.Player import Player\n",
    "from tic_tac_toe.RandomPlayer import RandomPlayer\n",
    "from tic_tac_toe.MinMaxAgent import MinMaxAgent\n",
    "from tic_tac_toe.RndMinMaxAgent import RndMinMaxAgent\n",
    "from tic_tac_toe.TabularQPlayer import TQPlayer\n",
    "\n",
    "from tic_tac_toe.Board import Board, GameResult, CROSS, NAUGHT, EMPTY\n",
    "from util import battle\n",
    "\n",
    "def eval_players(p1 : Player, p2 : Player, num_battles : int, games_per_battle = 100, loc='best'):\n",
    "    p1_wins = []\n",
    "    p2_wins = []\n",
    "    draws = []\n",
    "    count = []    \n",
    "\n",
    "    for i in range(num_battles):\n",
    "        p1win, p2win, draw = battle(p1, p2, games_per_battle, True)\n",
    "        p1_wins.append(p1win*100.0/games_per_battle)\n",
    "        p2_wins.append(p2win*100.0/games_per_battle)\n",
    "        draws.append(draw*100.0/games_per_battle)\n",
    "        count.append(i*games_per_battle)\n",
    "        p1_wins.append(p1win*100.0/games_per_battle)\n",
    "        p2_wins.append(p2win*100.0/games_per_battle)\n",
    "        draws.append(draw*100.0/games_per_battle)\n",
    "        count.append((i+1)*games_per_battle)\n",
    "\n",
    "    plt.ylabel('Game outcomes in %')\n",
    "    plt.xlabel('Game number')\n",
    "\n",
    "    plt.plot(count, draws, 'r-', label='Draw')\n",
    "    plt.plot(count, p1_wins, 'g-', label='Player 1 wins')\n",
    "    plt.plot(count, p2_wins, 'b-', label='Player 2 wins')\n",
    "    plt.legend(loc=loc, shadow=True, fancybox=True, framealpha =0.7)"
   ]
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    "First we let it play against the deterministic Min Max player. The Min Max player will get first move."
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P1zPPPKNNmzbpiSeekJeXl/r06aP09HRJktVqdTjOarXat13MmDFjNHz4cPtydna2fbQKAFA2DMNQZmamKlSoIKvVKg8PbgjGpRmGobNnz+rkyZOSpLCwsFK35XTYmT59umrVqqWjR49qypQpCggIkCQdP35cAwcOLHUhF1NcXKyWLVvqpZdekiS1aNFCu3fv1pw5c9SnT59St+vt7S1vb29XlQkAKIGioiKdPXtWVqtVvr6+KigokM1mU3FxsbtLQzlVoUIF+fr6KiMjQ76+vgoMDCxVO06HHU9PT40cOfKC9cOGDStVAZdTvXp1xcTEOKxr1KiR/vvf/0qSqlWrJknKyMhQ9erV7ftkZGSoefPmLq8HAFB6f0x18PT0lM1mU0ZGhmw22xVdnoD5FRYWKisrS19//bVuv/12BQUFOd2G02FHkj744AO9+eab+umnn5SWlqaaNWvq1VdfVXR0tH2isCu0bt1a+/fvd1j3ww8/qGbNmpLOT1auVq2aUlJS7OEmOztbGzZs0OOPP+6yOgAArlNcXKyTJ0/KZrPJ19eXsIPLKiwslKenp44cOaJly5bp/vvvd/oSqNMXTP+YQ9OpUyedPn3antRDQkL06quvOtvcZQ0bNkzr16/XSy+9pIMHD2r+/Pl66623NGjQIEmSxWLR0KFD9eKLL+qzzz7Trl271Lt3b4WHh6tr164urQUA4BqFhYU6d+6cfHx8CDooEYvFokqVKunEiRPKy8tz+ninw87rr7+ut99+W88++6zD7WAtW7bUrl27nC7gcm644QYtWbJECxYsUJMmTTRx4kS9+uqrSkxMtO8zatQoDRkyRP3799cNN9yg3NxcJScny8fHx6W1AABcwzAMGYZB0IFTKlSooMLCQhUUFDh9rNOXsQ4dOqQWLVpcsN7b21tnzpxxuoC/c9ddd+muu+665HaLxaIXXnhBL7zwgsu/GwAAXPucHtmJjo7W9u3bL1ifnJysRo0auaImAADKjWHDhikiIkIRERGqVauWmjdvrgceeEALFy7kTrJrhNMjO8OHD9egQYOUn58vwzC0ceNGLViwQElJSXrnnXfKokYAANyqXbt2mjZtmoqKivTbb79p9erVGj9+vL788kvNnTtXFSte+HNaUFAgT09PN1SLv3I67DzyyCPy9fXVc889p7y8PPXq1Uvh4eF67bXXLvnEYgAALmAYspw9656v9vWVnJgz5O3tbX+oXfXq1dW0aVNdd9116tGjhxYvXqxevXopIiJCL730klatWqV169bpscce09ChQzVq1Ch99913yszMVI0aNdS7d2898sgjkqR9+/apQ4cO2r59uypXrqzff/9dzZo1091336033nhDkvTaa69p9erVWrJkies74h+iVLeeJyYmKjExUXl5ecrNzb2ipxoCAP6ZLGfPKrxBA7d8968//CDDz++K2mjdurViYmK0bNky9erVS5I0bdo0jRkzRhMmTFDFihVVXFys6tWra86cOapUqZI2b96sp59+WlarVXfffbcaNGigSpUqKS0tTXfddZc2btyoSpUqaf369fbvWb9+veLj46+o1n+6K3pWt5+fH0EHAPCPVbduXf3yyy/25a5du6pHjx6qWbOmatSoYX8Qb2xsrKKionTvvfeqe/fu+vzzzyWdv8nmj/c5SlJaWpq6d+8um82mgwcPqqCgQJs3b1arVq3ccn5m4fTIzsmTJzVu3DitWrVKmZmZF0zOOnXqlMuKAwCYl+Hrq19/+MFt3+2Sdv5yC32zZs0u2GfevHlatGiRjh07pvz8fBUUFDi8HaBVq1aaP3++pPOjOE8//bQOHTqktLQ0nT59WoWFhbrhhhtcUu8/ldNh59///rcOHjyofv36yWq18pwEAEDpWCxXfCnJ3Q4cOODwImm/v5zP//73P02cOFHjxo3T9ddfL39/f82ZM0fbtm2z7xMfH68JEybop59+0oEDB3TjjTfqxx9/VFpamrKystSsWTP5uiic/VM5HXbWrl2rdevWKTY2tizqAQDgmvDtt99q3759evTRRy+5z6ZNm9SyZUuHl1f//PPPDvs0atRIwcHBmjFjhmJiYuTv76/4+Hi98cYbysrKYr6OCzg9Z6dhw4Y666bZ8wAAuIPNZlNmZqaOHz+uXbt26fXXX1ffvn2VkJCg++6775LHRUdHa+fOnVq9erV++uknvfLKK9qxY4fDPn/M21myZIk92DRq1Eg2m03r1q1jvo4LOB123njjDT377LNKTU3VyZMnlZ2d7fABAMBsVq9ereuuu07x8fF68MEH9d133+mFF17Qu+++6/DqpL968MEH1alTJw0cOFB33323fv/9d/Xu3fuC/eLj41VUVGQPOx4eHmrVqpUsFgvzdVzAYhiG4cwBBw4cUK9evbR161aH9X9M0vrjxaDXkuzsbAUHBysrK6tUr46H+5z5PVMBM6ySpNwnMuRfibsDgfLKZrPp6NGjqlq1qk6cOMGLQFEihYWFysjI0L59+3Tq1Cn16dNHlSpVklTy32+n5+wkJibK09NT8+fPZ4IyAAAo95wOO7t379a2bdvUwE0PggIAAHCG03N2WrZsqaNHj5ZFLQAAAC7n9MjOkCFD9OSTT+qpp55S06ZNL3jJ2cUeqAQAAOAuToedHj16SJL69u1rX2exWK7pCcoAAMC8nA47hw4dKos6AAAAyoTTYadmzZplUQcAAECZcDrsSNKPP/6oV199VXv37pUkxcTE6Mknn1SdOnVcWhwAAMCVcvpurK+//loxMTHauHGjmjVrpmbNmmnDhg1q3Lixli9fXhY1AgAAlJrTYWf06NEaNmyYNmzYoGnTpmnatGnasGGDhg4dqqeffrosagQAoNxavHixYmJi3F2G21wL5+902Nm7d6/69et3wfq+ffvq+++/d0lRAACUF8OGDVNERIQiIiIUHR2t1q1ba/r06SosLHR3aSXy4Ycf6r777lPDhg0VERGhrKwsl7Z/9913a82aNS5t09WcDjtVq1bV9u3bL1i/fft2hYXxXiIAgPm0a9dOW7du1dq1azVgwABNmzZNc+bMcXdZDgoKCi66Pj8/X+3atdPgwYPL5Ht9fX1VpUqVMmnbVZwOO48++qj69++vyZMna+3atVq7dq1efvllDRgwQI8++mhZ1AgAMCHDMJRXkOeWj5PvwJa3t7fCwsIUERGh3r17q23btvrmm28uuu/hw4fVt29fNW/eXPXr11fnzp21du1a+/bp06erffv2Fxx3++2365VXXrEvz58/X+3atVOdOnV0yy236L333rNvO3r0qCIiIvTZZ5+pW7duqlOnjpYsWXLReh555BENHjxY1113XYnOdcWKFYqJibE/N2/Pnj2KiIjQSy+9ZN9n5MiRGjJkiKQLL2NNnTpVt99+uz755BO1atVKjRo10sCBA5Wbm2vf54svvlD79u1Vp04dNWnSRD179lReXl6J6isNp+/GGjt2rAIDAzV16lSNGTNGkhQeHq4JEyboiSeecHmBAABzOlt4Vg3ed897Fn/o84P8PP1KfbyPj49+//33i27Ly8vTbbfdplGjRsnLy0v//e9/9dBDD2nNmjWqUaOGevTooenTp2v79u1q3ry5pPPvndy7d6/efvttSdKnn36qqVOnauLEiWrSpIl2796tUaNGyc/PT/fff7/9u5KSkjR27Fg1adJE3t7epT6fP7vxxhuVm5ur3bt3KzY2VmlpaQoNDVVaWpp9n/Xr12vgwIGXbOPnn3/W119/rXnz5ikrK0uPP/64Zs2apaeffloZGRkaPHiwnn32Wd1xxx3Kzc3Vxo0bnQ6gznA67FgsFg0bNkzDhg1TTk6OJCkwMNDlhQEAUN4YhqF169YpNTVVDz300EX3iYmJcRjpeOqpp5ScnKxvvvlGDz/8sMLDw3XLLbdo8eLF9rCzaNEitWrVyv4su6lTp2rs2LG68847JUlRUVE6cOCAPvzwQ4ew069fP/s+rhIUFKTGjRsrLS3NHnYeffRRTZ8+XWfOnFF2drYOHz6sVq1aXbKN4uJiTZ8+XQEBAZKke++9V+vWrdPTTz+tzMxMFRYWqlOnToqIiJAkNWrUyKXn8FeleoJyYWGh6tWr5xByDhw4IE9PT9WqVcuV9QEATMq3oq9+6POD277bGStWrFD9+vVVWFio4uJide3aVSNGjLjovmfOnNG0adOUkpJi/2HPz8/XsWPH7Pv06tVLI0eO1Lhx4+Th4aGlS5dq/Pjxks6PDP38888aOXKkRo0aZT+mqKjogsGF2NhYp86jpFq1aqW0tDQNGDBAGzdu1JgxY/T5559r48aNOn36tKxWq2rXrn3J4yMjI+1BR5KsVqtOnjwp6XwYbNOmjRISEnTLLbfo5ptvVufOnRUSElIm5yKVIuw89NBD6tu3r+rVq+ewfsOGDXrnnXe0evVqV9UGADAxi8VyRZeSrqabbrpJL730kry8vGS1WlWx4qV/PidOnKi1a9fqueeeU61ateTj46MBAwY4TCDu0KGDvLy8lJycLE9PTxUWFqpz586SzoclSZoyZYpatGjh0HaFChUclv38yqb/4uPjtWjRIn3//ffy9PRU3bp1FR8fr7S0NGVlZV12VEfSBf1jsVhUXFws6fw5LFiwQJs3b1Zqaqrmzp2rKVOm6PPPP1dUVFSZnI/TE5S3bdum1q1bX7C+VatWF71LCwCAa52fn5+io6NVo0aNywYdSdq0aZPuv/9+derUSY0aNVJYWJh++eUXh30qVqyo++67T4sXL9bixYt1zz33yNf3/GhT1apVZbVadeTIEUVHRzt8yioM/NUf83befvtte7D5I+ykpaUpPj7+itq3WCy64YYbNHLkSH399dfy9PRUcnKyK0q/qFLN2fljrs6fZWVl8cZzAMA/XnR0tJYtW6YOHTrIYrHolVdesY9q/NkDDzygW2+9VZIuuJNqxIgRGjdunAIDA3XrrbfKZrNp586dysrKUv/+/Z2qJzMzUydOnNDhw4clSfv27VNAQIDCw8NVqVKlix4TEhKiRo0aacmSJXrxxRclSXFxcXr88cdVUFBwRWFn69at+vbbb3XzzTerSpUq2rZtm06dOqW6deuWus2/43TYufnmm5WUlKQFCxbYh9OKioqUlJSkNm3auLxAAACuJePHj9eIESPUpUsXhYaGauDAgRcdJKhdu7Zatmyp06dPX3BbeK9eveTr66s5c+Zo0qRJ8vX1VcOGDfXII484Xc8HH3yg6dOn25e7desmSZo2bZq6d+9+yeNatWqlPXv22INNpUqVVK9ePf32229X9C7MwMBArV+/Xu+8845yc3NVo0YNjR07Vrfddlup2/w7FsPJe7327NmjW265RSEhIWrbtq0kae3atcrOztbKlSvVpEmTMim0LGVnZys4OFhZWVkKCgpydzlwwpnfMxUwwypJyn0iQ/6VeLAlUF7ZbDYdPXpUVatW1YkTJ+Tj4yOLxeLustzGMAy1adNGffr0cXq05p+ksLBQGRkZ2rdvn06dOqU+ffrYR6RK+vvt9Jydxo0ba+fOnerevbsyMzOVk5Oj3r17a9++fddk0AEA4Go7efKk5s6dqxMnTlx2dAWu4fRlrCNHjigyMtLhSYp/3na1Jk8BAHCtio2NVWhoqCZPnlymt1zjPKfDTnR0tI4fP37Be7BOnjyp6OhoJikDAPA3/np3FsqW05exDMO46DXW3Nxc+fj4uKQoAAAAVynxyM7w4cMlnb/1fOzYsQ4PMioqKtKGDRvsj70GAAAoL0ocdrZt2ybp/MjOrl275OXlZd/m5eWl2NhYjRw50vUVAgAAXIESh51Vq1ZJkh5++GG99tpr3KINAACuCU5PUJ47d25Z1AEAAFAmnA47f/eEw5UrV5a6GAAAAFdz+m6s2NhYh09MTIzOnTunrVu3qmnTpmVRIwAA5dbixYsVExPj7jLcZurUqbr99tvdXcZlOT2y8+f3a/zZhAkTlJube8UFAQBQngwbNkwff/yxJMnT01Ph4eG67777NGTIkL99A7q7/f7775o6darWrFmjY8eOqXLlyurYsaOeeuopl829feyxx9S3b1+XtFVWnB7ZuZQHH3xQ7777rquaAwCg3GjXrp22bt2qtWvXasCAAZo2bZrmzJnj7rIcFBQUXLAuIyNDGRkZGjt2rFJSUjR9+nStXr3apXdP+/v7X/Lt6eWFy8JOWloaDxUEAJSYYUh5eRa3fJx7Bbbk7e2tsLAwRUREqHfv3mrbtq2++eabi+57+PBh9e3bV82bN1f9+vXVuXNnrV271r59+vTpat++/QXH3X777XrllVfsy/Pnz1e7du1Up04d3XLLLXrvvffs244ePaqIiAh99tln6tatm+rUqaMlS5Zc0GbDhg319ttvq0OHDqpVq5Zat26tp59+WitWrFBhYeFF6587d65DfcnJyYqIiNAHH3xgX9ezZ09NmTJF0oWXsYYNG6Z+/fppzpw5uu6669SkSRM9++yzDmHsvffeU5s2bVSnTh01b968zF+E6vT427333uuwbBiGjh8/rs2bN2vs2LEuKwwAYG5nz1rUoEG4W777hx9+lZ+fk4nnT3x8fPT7779fdFteXp5uu+02jRo1Sl5eXvrvf/+rhx56SGvWrFGNGjXUo0cPTZ8+Xdu3b7c/jHf37t3au3ev3n77bUnSp59+qqlTp2rixIlq0qSJdu/erVGjRsnPz0/333+//buSkpI0duxYNWnSRN7e3iWqPTs7WwEBAZe8BNeqVSuNGzdOJ0+eVOXKlbV+/XqFhoYqLS1N//73v1VQUKAtW7Zo0KBBl/yO7777TmFhYVq8eLEOHz6sxx9/XDExMUpMTNSOHTs0btw4vfbaa2rZsqVOnz6tDRs2lKj20nI67AQHBzsse3h4qEGDBnrhhRfK/QQlAACuhGEYWrdunVJTU/XQQw9ddJ+YmBiHCctPPfWUkpOT9c033+jhhx9WeHi4brnlFi1evNgedhYtWqRWrVqpZs2aks6PlowdO1Z33nmnJCkqKkoHDhzQhx9+6BB2+vXrZ9+nJE6dOqXXXntNiYmJl9ynYcOGCgkJUVpamu666y6lpaWpf//+9qkq27dvV2FhoVq2bHnJNoKDg/Xiiy+qQoUKqlu3rtq3b69vv/1WiYmJOnbsmPz8/JSQkKCAgABFRESoSZMmJT6H0uA5OwAAt/D1NfTDD7+67budsWLFCtWvX1+FhYUqLi5W165dNWLEiIvue+bMGU2bNk0pKSnKzMxUYWGh8vPzdezYMfs+vXr10siRIzVu3Dh5eHho6dKlGj9+vKTzI0M///yzRo4cqVGjRtmPKSoqUmBgoMN3xcbGlvgccnJy1Lt3b9WrV8/+CqiLsVgsiouLU1pamtq2basDBw6oT58+mj17tg4ePKj169crNjZWvr6+l2yjfv36qlChgn05LCxM+/btkyTdfPPNqlGjhm666Sa1a9dO7dq1U6dOnS7b3pUq9TTyLVu2aO/evZKkxo0bq0WLFi4rCgBgfhaLruhS0tV000036aWXXpKXl5esVutl78KaOHGi1q5dq+eee061atWSj4+PBgwY4DBnpUOHDvLy8lJycrI8PT1VWFiozp07SzofliRpypQpF/y2/jlASHJ4T+Xl5Obm6sEHH1RAQIDeeecdeXp6Xnb/+Ph4zZ8/Xxs3blTjxo0VGBioVq1aKS0tTevXr1erVq0ue/xf27dYLCouLpYkBQQEKDk5WWlpaUpNTdXUqVM1bdo0ffnllxdcPXIVp8NOZmamevbsqdWrVyskJESSdPr0ad16661auHChqlat6uoaAQBwKz8/P0VHR5do302bNun+++9Xp06dJJ0PL7/88ovDPhUrVtR9992nxYsXy9PTU/fcc499ZKNq1aqyWq06cuTIBfNkSyMnJ0eJiYny8vLS3LlzS3QzUXx8vCZMmKAvvvhC8fHx9nVr167Vpk2brnhCccWKFdW2bVu1bdtWw4cPV0xMjL799lunLsk59X3OHjBkyBDl5ORoz549atSokSTp+++/V58+ffTEE09owYIFLi8SAIBrRXR0tJYtW6YOHTrIYrHolVdesY9q/NkDDzygW2+9VZIuuJNqxIgRGjdunAIDA3XrrbfKZrNp586dysrKcipo5OTkqFevXjp79qxmzJihnJwc5eTkSJIqV658wUjRHxo1aqTg4GAtXbpU8+bNk3Q+7EycOFEWi0U33HBDiWv4qxUrVujnn39Wq1atFBwcrJUrV6q4uFh16tQpdZt/x+mwk5ycrBUrVtiDjnR+MtasWbOYoAwA+McbP368RowYoS5duig0NFQDBw60B4w/q127tv1upOuuu85hW69eveTr66s5c+Zo0qRJ8vX1VcOGDfXII484VcuuXbu0bds2SVKbNm0ctqWlpSkyMvKix/0xbyclJUU33nijpPMBKCAgQHXq1Cnx5bOLCQoK0rJlyzRt2jTZbDZFR0dr1qxZatCgQanb/DsWw3DuaQOBgYFau3atfQb5H7Zt26ZbbrlF2dnZrqzvqsjOzlZwcLCysrJ4m/s15szvmQqYYZUk5T6RIf9KYW6uCMCl2Gw2HT16VFWrVtWJEyfk4+Mji8Xi7rLcxjAMtWnTRn369Cnz58xcywoLC5WRkaF9+/bp1KlT6tOnj/0hhiX9/Xb6oYK33XabnnzySf366//NoD927JiGDRt20YckAQAARydPntTcuXN14sQJde/e3d3lmJ7Tl7Fmzpype+65R7Vq1bIPfx09elRNmjTRhx9+6PICAQAwm9jYWIWGhmry5Mn2m31QdpwOO5GRkdq6datWrFhhv2e+UaNGSkhIcHlxAACY0V/vzkLZKtW7sSwWizp06KAhQ4ZoyJAhVy3ovPzyy7JYLBo6dKh9XX5+vgYNGqTKlSsrICBA3bp1U0ZGxlWpBwAAlH8uexFoWdu0aZPefPNNNWvWzGH9sGHD9Pnnn+vjjz9Wamqqfv31V5c8lwAAUDacvC8GuGKlfoLy1ZSbm6vExES9/fbbevHFF+3rs7Ky9J///Efz58/XbbfdJun86ywaNWpUoic8AgCunooVK8pisSgrK0tFRUUqLCz8R9+Nhb9XXFysnJwc2Ww2nTt3rtTtXBNhZ9CgQercubMSEhIcws6WLVtUUFDgcBmtYcOGioqKUlpa2iXDjs1mk81msy9fi7fLA8C1pkKFCqpevboOHTqk33//XV5eXu4uCeXcH2Hn1KlTMgxDFotFHh7OX5Qq92Fn4cKF2rp1qzZt2nTBtvT0dHl5eV0wk91qtSo9Pf2SbSYlJen55593dakAgL/h5+enatWq6dtvv5Uk+/NSgIspKipScXGxDMOwP0vH39/f6XZKFXZ+/PFHzZ07Vz/++KNee+01hYWFadmyZYqKilLjxo1L0+RFHT16VE8++aSWL19eond5lNSYMWMc3vianZ19yadIAgBcKzQ0VC1atNDq1at1+vTpv30pJZCfny9/f3/dfPPNl30J66U4fURqaqo6deqk1q1ba82aNZo0aZLCwsK0Y8cO/ec//9Enn3zidBGXsmXLFmVmZjo8RruoqEhr1qzRzJkz9fXXX+vcuXM6ffq0w+hORkaGqlWrdsl2vb295e3t7bI6AQAlZ7FY1LJlS3l5eenw4cPKzc11d0koxywWi4KCgtSgQQPVq1evVG04HXZGjx6tF198UcOHD1dgYKB9/W233aaZM2eWqohLad++vXbt2uWw7uGHH1bDhg319NNPKzIyUp6enkpJSVG3bt0kSfv379eRI0fsb2kFAJQ/FotFsbGxio2NdXcp+AdwOuzs2rVL8+fPv2B9WFiYfvvtN5cU9YfAwEA1adLEYZ2/v78qV65sX9+vXz8NHz5coaGhCgoK0pAhQxQfH8+dWAAAQFIpwk5ISIiOHz+u6Ohoh/Xbtm1TjRo1XFZYSU2fPl0eHh7q1q2bbDabOnbsqDfeeOOq1wEAAMonp8NOz5499fTTT+vjjz+WxWJRcXGxvv32W40cOVK9e/cuixodrF692mHZx8dHs2bN0qxZs8r8uwEAwLXH6ZvVX3rpJTVs2FCRkZHKzc1VTEyMbr75Zt1000167rnnyqJGAACAUnN6ZMfLy0tvv/22xo4dq927dys3N1ctWrQo9QxpAACAslTqhwpGRUUpKirKlbUAAAC4nNNhxzAMffLJJ1q1apUyMzNVXFzssP3TTz91WXEAAABXyumwM3ToUL355pu69dZbZbVaeYkbAAAo15wOOx988IE+/fRT3XnnnWVRDwAAgEs5fTdWcHCwateuXRa1AAAAuJzTYWfChAl6/vnndfbs2bKoBwAAwKWcvozVvXt3LViwQGFhYapVq9YFb6vdunWry4oDAAC4Uk6HnT59+mjLli168MEHmaAMAADKPafDzpdffqmvv/5abdq0KYt6AAAAXMrpOTuRkZEKCgoqi1oAAABczumwM3XqVI0aNUqHDx8ug3IAAABcy+nLWA8++KDy8vJUp04d+fn5XTBB+dSpUy4rDgAA4Eo5HXZeffXVMigDAACgbJTqbiwAAIBrRanfei5J+fn5OnfunMM6Ji8DAIDyxOkJymfOnNHgwYMVFhYmf39/VapUyeEDAABQnjgddkaNGqWVK1dq9uzZ8vb21jvvvKPnn39e4eHhev/998uiRgAAgFJz+jLW559/rvfff1/t2rXTww8/rLZt26pu3bqqWbOmPvroIyUmJpZFnQAAAKXi9MjOqVOn7G89DwoKst9q3qZNG61Zs8a11QEAAFwhp8NO7dq1dejQIUlSw4YNtXjxYknnR3xCQkJcWhwAAMCVcjrsPPzww9qxY4ckafTo0Zo1a5Z8fHw0bNgwPfXUUy4vEAAA4Eo4PWdn2LBh9j8nJCRo37592rJli+rWratmzZq5tDgAAIArdUXP2ZGkmjVrqmbNmq6oBQAAwOVKHHbOnj2rlJQU3XXXXZKkMWPGyGaz2bdXqFBBEydOlI+Pj+urBAAAKKUSh5333ntPX375pT3szJw5U40bN5avr68kad++fQoPD3e4zAUAAOBuJZ6g/NFHH6l///4O6+bPn69Vq1Zp1apVeuWVV+x3ZgEAAJQXJQ47Bw8eVNOmTe3LPj4+8vD4v8NvvPFGff/9966tDgAA4AqV+DLW6dOnHebonDhxwmF7cXGxw3YAAIDyoMQjOxEREdq9e/clt+/cuVMREREuKQoAAMBVShx27rzzTo0bN075+fkXbDt79qyef/55de7c2aXFAQAAXKkSX8Z65plntHjxYjVo0ECDBw9W/fr1JUn79+/XzJkzVVhYqGeeeabMCgUAACiNEocdq9Wq7777To8//rhGjx4twzAkSRaLRR06dNAbb7whq9VaZoUCAACUhlNPUI6OjlZycrJOnTqlgwcPSpLq1q2r0NDQMikOAADgSpXqdRGhoaG68cYbXV0LAACAyzn91nMAAIBrCWEHAACYGmEHAACYGmEHAACYGmEHAACYGmEHAACYGmEHAACYGmEHAACYGmEHAACYGmEHAACYGmEHAACYGmEHAACYGmEHAACYGmEHAACYGmEHAACYGmEHAACYGmEHAACYGmEHAACYGmEHAACYGmEHAACYWrkOO0lJSbrhhhsUGBiosLAwde3aVfv373fYJz8/X4MGDVLlypUVEBCgbt26KSMjw00VAwCA8qZch53U1FQNGjRI69ev1/Lly1VQUKDbb79dZ86cse8zbNgwff755/r444+VmpqqX3/9Vffee68bqwYAAOWJxTAMw91FlNSJEycUFham1NRU3XzzzcrKylLVqlU1f/583XfffZKkffv2qVGjRkpLS1OrVq1K1G52draCg4OVlZWloKCgsjwFuNiZ3zMVMMMqScp9IkP+lcLcXBEA4Gop6e93uR7Z+ausrCxJUmhoqCRpy5YtKigoUEJCgn2fhg0bKioqSmlpaZdsx2azKTs72+EDAADM6ZoJO8XFxRo6dKhat26tJk2aSJLS09Pl5eWlkJAQh32tVqvS09Mv2VZSUpKCg4Ptn8jIyLIsHQAAuNE1E3YGDRqk3bt3a+HChVfc1pgxY5SVlWX/HD161AUVAgCA8qiiuwsoicGDB+uLL77QmjVrFBERYV9frVo1nTt3TqdPn3YY3cnIyFC1atUu2Z63t7e8vb3LsmQAAFBOlOuRHcMwNHjwYC1ZskQrV65UdHS0w/brr79enp6eSklJsa/bv3+/jhw5ovj4+KtdLgAAKIfK9cjOoEGDNH/+fP3vf/9TYGCgfR5OcHCwfH19FRwcrH79+mn48OEKDQ1VUFCQhgwZovj4+BLfiQUAAMytXIed2bNnS5LatWvnsH7u3Ll66KGHJEnTp0+Xh4eHunXrJpvNpo4dO+qNN964ypUCAIDyqlyHnZI8AsjHx0ezZs3SrFmzrkJFAADgWlOu5+wAAABcKcIOAAAwNcIOAAAwNcIOAAAwNcIOAAAwNcIOAAAwNcIOAAAwNcIOAAAwNcIOAAAwNcIOAAAwNcIOAAAwNcIOAAAwNcIOAAAwNcIOAAAwNcIOAAAwNcIOAAAwNcIOAAAwNcIOAAAwNcIOAAAwNcIOAAAwNcIOAAAwNcIOAAAwNcIOAAAwNcIOAAAwNcIOAAAwNcIOAAAwNcIOAAAwNcIOAAAwNcIOAAAwNcIOAAAwNcIOAAAwNcIOAAAwNcIOAAAwNcIOAAAwNcIOAAAwNcIOAAAwNcIOAAAwNcIOAAAwNcIOAAAwNcIOAAAwNcIOAAAwtYruLsC0DEPKy3N3FeaXd8bdFQAAyjnCTlnJy5MCAtxdhfl5SnrW3UUAAMozLmPBPPz83F0BAKAcYmSnrPj5Sbm57q7C/M6dkWZYz//ZYnFvLQCAcomwU1YsFsnf391VmJ+nuwsAAJR3XMYCAACmRtgBAACmRtgBAACmRtgBAACmRtgBAACmRtgBAACmRtgBAACmRtgBAACmRtgBAACmRtgBAACmZpqwM2vWLNWqVUs+Pj6Ki4vTxo0b3V0SAAAoB0wRdhYtWqThw4dr/Pjx2rp1q2JjY9WxY0dlZma6uzQAAOBmFsMwDHcXcaXi4uJ0ww03aObMmZKk4uJiRUZGasiQIRo9evTfHp+dna3g4GBlZWUpKCjIJTUZhpSX55KmcBlnzp2R9f8LkyT99OQh+Xvy8lUAKI+qBPvJw8Pi0jZL+vt9zb/1/Ny5c9qyZYvGjBljX+fh4aGEhASlpaVd9BibzSabzWZfzs7OdnldeXlSQIDLm8UF/CWdkSTVfsm9lQAALi3j1BmFVXLPf5Be85exfvvtNxUVFclqtTqst1qtSk9Pv+gxSUlJCg4Otn8iIyOvRqkAAMANrvmRndIYM2aMhg8fbl/Ozs52eeDx85Nyc13aJC7BMAzlFXDNEADKsyrBfm777ms+7FSpUkUVKlRQRkaGw/qMjAxVq1btosd4e3vL29u7TOuyWCR/po9cJRYFiM4GAFzcNX8Zy8vLS9dff71SUlLs64qLi5WSkqL4+Hg3VgYAAMqDa35kR5KGDx+uPn36qGXLlrrxxhv16quv6syZM3r44YfdXRoAAHAzU4SdHj166MSJExo3bpzS09PVvHlzJScnXzBpGQAA/POY4jk7V6osnrMDAADKVkl/v6/5OTsAAACXQ9gBAACmRtgBAACmRtgBAACmRtgBAACmRtgBAACmRtgBAACmRtgBAACmRtgBAACmZorXRVypPx4inZ2d7eZKAABASf3xu/13L4Mg7EjKycmRJEVGRrq5EgAA4KycnBwFBwdfcjvvxpJUXFysX3/9VYGBgbJYLC5rNzs7W5GRkTp69Cjv3CpD9PPVQ19fHfTz1UE/Xx1l2c+GYSgnJ0fh4eHy8Lj0zBxGdiR5eHgoIiKizNoPCgrif0hXAf189dDXVwf9fHXQz1dHWfXz5UZ0/sAEZQAAYGqEHQAAYGqEnTLk7e2t8ePHy9vb292lmBr9fPXQ11cH/Xx10M9XR3noZyYoAwAAU2NkBwAAmBphBwAAmBphBwAAmBphBwAAmBphpwzNmjVLtWrVko+Pj+Li4rRx40Z3l3RNWbNmje6++26Fh4fLYrFo6dKlDtsNw9C4ceNUvXp1+fr6KiEhQQcOHHDY59SpU0pMTFRQUJBCQkLUr18/5ebmXsWzKN+SkpJ0ww03KDAwUGFhYeratav279/vsE9+fr4GDRqkypUrKyAgQN26dVNGRobDPkeOHFHnzp3l5+ensLAwPfXUUyosLLyap1LuzZ49W82aNbM/WC0+Pl7Lli2zb6efXe/ll1+WxWLR0KFD7evoZ9eYMGGCLBaLw6dhw4b27eWunw2UiYULFxpeXl7Gu+++a+zZs8d49NFHjZCQECMjI8PdpV0zvvrqK+PZZ581Pv30U0OSsWTJEoftL7/8shEcHGwsXbrU2LFjh3HPPfcY0dHRxtmzZ+373HHHHUZsbKyxfv16Y+3atUbdunWNBx544CqfSfnVsWNHY+7cucbu3buN7du3G3feeacRFRVl5Obm2vd57LHHjMjISCMlJcXYvHmz0apVK+Omm26yby8sLDSaNGliJCQkGNu2bTO++uoro0qVKsaYMWPccUrl1meffWZ8+eWXxg8//GDs37/feOaZZwxPT09j9+7dhmHQz662ceNGo1atWkazZs2MJ5980r6efnaN8ePHG40bNzaOHz9u/5w4ccK+vbz1M2GnjNx4443GoEGD7MtFRUVGeHi4kZSU5Maqrl1/DTvFxcVGtWrVjFdeecW+7vTp04a3t7exYMECwzAM4/vvvzckGZs2bbLvs2zZMsNisRjHjh27arVfSzIzMw1JRmpqqmEY5/vU09PT+Pjjj+377N2715BkpKWlGYZxPpR6eHgY6enp9n1mz55tBAUFGTab7eqewDWmUqVKxjvvvEM/u1hOTo5Rr149Y/ny5cYtt9xiDzv0s+uMHz/eiI2Nvei28tjPXMYqA+fOndOWLVuUkJBgX+fh4aGEhASlpaW5sTLzOHTokNLT0x36ODg4WHFxcfY+TktLU0hIiFq2bGnfJyEhQR4eHtqwYcNVr/lakJWVJUkKDQ2VJG3ZskUFBQUO/dywYUNFRUU59HPTpk1ltVrt+3Ts2FHZ2dnas2fPVaz+2lFUVKSFCxfqzJkzio+Pp59dbNCgQercubNDf0r8e3a1AwcOKDw8XLVr11ZiYqKOHDkiqXz2My8CLQO//fabioqKHP4SJclqtWrfvn1uqspc0tPTJemiffzHtvT0dIWFhTlsr1ixokJDQ+374P8UFxdr6NChat26tZo0aSLpfB96eXkpJCTEYd+/9vPF/h7+2Ib/s2vXLsXHxys/P18BAQFasmSJYmJitH37dvrZRRYuXKitW7dq06ZNF2zj37PrxMXFad68eWrQoIGOHz+u559/Xm3bttXu3bvLZT8TdgBIOv9fw7t379a6devcXYppNWjQQNu3b1dWVpY++eQT9enTR6mpqe4uyzSOHj2qJ598UsuXL5ePj4+7yzG1Tp062f/crFkzxcXFqWbNmlq8eLF8fX3dWNnFcRmrDFSpUkUVKlS4YOZ5RkaGqlWr5qaqzOWPfrxcH1erVk2ZmZkO2wsLC3Xq1Cn+Hv5i8ODB+uKLL7Rq1SpFRETY11erVk3nzp3T6dOnHfb/az9f7O/hj234P15eXqpbt66uv/56JSUlKTY2Vq+99hr97CJbtmxRZmamrrvuOlWsWFEVK1ZUamqqZsyYoYoVK8pqtdLPZSQkJET169fXwYMHy+W/Z8JOGfDy8tL111+vlJQU+7ri4mKlpKQoPj7ejZWZR3R0tKpVq+bQx9nZ2dqwYYO9j+Pj43X69Glt2bLFvs/KlStVXFysuLi4q15zeWQYhgYPHqwlS5Zo5cqVio6Odth+/fXXy9PT06Gf9+/fryNHjjj0865duxyC5fLlyxUUFKSYmJircyLXqOLiYtlsNvrZRdq3b69du3Zp+/bt9k/Lli2VmJho/zP9XDZyc3P1448/qnr16uXz37PLpzzDMIzzt557e3sb8+bNM77//nujf//+RkhIiMPMc1xeTk6OsW3bNmPbtm2GJGPatGnGtm3bjJ9//tkwjPO3noeEhBj/+9//jJ07dxpdunS56K3nLVq0MDZs2GCsW7fOqFevHree/8njjz9uBAcHG6tXr3a4hTQvL8++z2OPPWZERUUZK1euNDZv3mzEx8cb8fHx9u1/3EJ6++23G9u3bzeSk5ONqlWrcqvuX4wePdpITU01Dh06ZOzcudMYPXq0YbFYjG+++cYwDPq5rPz5bizDoJ9dZcSIEcbq1auNQ4cOGd9++62RkJBgVKlSxcjMzDQMo/z1M2GnDL3++utGVFSU4eXlZdx4443G+vXr3V3SNWXVqlWGpAs+ffr0MQzj/O3nY8eONaxWq+Ht7W20b9/e2L9/v0MbJ0+eNB544AEjICDACAoKMh5++GEjJyfHDWdTPl2sfyUZc+fOte9z9uxZY+DAgUalSpUMPz8/41//+pdx/Phxh3YOHz5sdOrUyfD19TWqVKlijBgxwigoKLjKZ1O+9e3b16hZs6bh5eVlVK1a1Wjfvr096BgG/VxW/hp26GfX6NGjh1G9enXDy8vLqFGjhtGjRw/j4MGD9u3lrZ8thmEYrh8vAgAAKB+YswMAAEyNsAMAAEyNsAMAAEyNsAMAAEyNsAMAAEyNsAMAAEyNsAMAAEyNsAMAAEyNsAMALmaxWLR06VJ3lwHg/0fYAfC30tPT9eSTT6pu3bry8fGR1WpV69atNXv2bOXl5bm7PAC4rIruLgBA+fbTTz+pdevWCgkJ0UsvvaSmTZvK29tbu3bt0ltvvaUaNWronnvucXeZpnfu3Dl5eXm5uwzgmsTIDoDLGjhwoCpWrKjNmzere/fuatSokWrXrq0uXbroyy+/1N13323fd9q0aWratKn8/f0VGRmpgQMHKjc317593rx5CgkJ0RdffKEGDRrIz89P9913n/Ly8vTee++pVq1aqlSpkp544gkVFRXZj7PZbBo5cqRq1Kghf39/xcXFafXq1Zet22Kx6J133tG//vUv+fn5qV69evrss88uqOXPli5dKovFYl+eMGGCmjdvrnfffVdRUVEKCAjQwIEDVVRUpClTpqhatWoKCwvTpEmTLvj+48ePq1OnTvL19VXt2rX1ySefOGw/evSounfvrpCQEIWGhqpLly46fPiwfftDDz2krl27atKkSQoPD1eDBg0ue74ALo2wA+CSTp48qW+++UaDBg2Sv7//Rff5czjw8PDQjBkztGfPHr333ntauXKlRo0a5bB/Xl6eZsyYoYULFyo5OVmrV6/Wv/71L3311Vf66quv9MEHH+jNN990CAeDBw9WWlqaFi5cqJ07d+r+++/XHXfcoQMHDly2/ueff17du3fXzp07deeddyoxMVGnTp1yqg9+/PFHLVu2TMnJyVqwYIH+85//qHPnzvrll1+UmpqqyZMn67nnntOGDRscjhs7dqy6deumHTt2KDExUT179tTevXslSQUFBerYsaMCAwO1du1affvttwoICNAdd9yhc+fO2dtISUnR/v37tXz5cn3xxRdO1Q3gT8rkXeoATGH9+vWGJOPTTz91WF+5cmXD39/f8Pf3N0aNGnXJ4z/++GOjcuXK9uW5c+cakoyDBw/a1w0YMMDw8/MzcnJy7Os6duxoDBgwwDAMw/j555+NChUqGMeOHXNou3379saYMWMu+d2SjOeee86+nJuba0gyli1bZq8lODjY4ZglS5YYf/6/xfHjxxt+fn5Gdna2Q221atUyioqK7OsaNGhgJCUlOXz3Y4895tB2XFyc8fjjjxuGYRgffPCB0aBBA6O4uNi+3WazGb6+vsbXX39tGIZh9OnTx7BarYbNZrvkOQIoGebsAHDaxo0bVVxcrMTERNlsNvv6FStWKCkpSfv27VN2drYKCwuVn5+vvLw8+fn5SZL8/PxUp04d+zFWq1W1atVSQECAw7rMzExJ0q5du1RUVKT69es71GCz2VS5cuXL1tmsWTP7n/39/RUUFGRvt6Rq1aqlwMBAh9oqVKggDw8Ph3V/bTc+Pv6C5e3bt0uSduzYoYMHDzq0K0n5+fn68ccf7ctNmzZlng7gAoQdAJdUt25dWSwW7d+/32F97dq1JUm+vr72dYcPH9Zdd92lxx9/XJMmTVJoaKjWrVunfv366dy5c/aw4+np6dCWxWK56Lri4mJJUm5uripUqKAtW7aoQoUKDvv9OSBdzOXa9fDwkGEYDtsLCgpK1Mbl2i2J3NxcXX/99froo48u2Fa1alX7ny916RCAcwg7AC6pcuXK6tChg2bOnKkhQ4Zc9sd3y5YtKi4u1tSpU+2jHosXL77iGlq0aKGioiJlZmaqbdu2V9zeH6pWraqcnBydOXPGfl5/jLy4wvr169W7d2+H5RYtWkiSrrvuOi1atEhhYWEKCgpy2XcCuDgmKAO4rDfeeEOFhYVq2bKlFi1apL1792r//v368MMPtW/fPvtoS926dVVQUKDXX39dP/30kz744APNmTPnir+/fv36SkxMVO/evfXpp5/q0KFD2rhxo5KSkvTll1+Wut24uDj5+fnpmWee0Y8//qj58+dr3rx5V1zvHz7++GO9++67+uGHHzR+/Hht3LhRgwcPliQlJiaqSpUq6tKli9auXatDhw5p9erVeuKJJ/TLL7+4rAYA5xF2AFxWnTp1tG3bNiUkJGjMmDGKjY1Vy5Yt9frrr2vkyJGaOHGiJCk2NlbTpk3T5MmT1aRJE3300UdKSkpySQ1z585V7969NWLECDVo0EBdu3bVpk2bFBUVVeo2Q0ND9eGHH+qrr75S06ZNtWDBAk2YMMEl9Urn7wRbuHChmjVrpvfff18LFixQTEyMpPPzltasWaOoqCjde++9atSokfr166f8/HxGeoAyYDH+etEaAADARBjZAQAApkbYAQAApkbYAQAApkbYAQAApkbYAQAApkbYAQAApkbYAQAApkbYAQAApkbYAQAApkbYAQAApkbYAQAApvb/AND75HgPKVUmAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "player1 = MinMaxAgent()\n",
    "player2 = TQPlayer()\n",
    "eval_players(player1, player2, 5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Tabular Q-learning player learns to play optimally against the deterministic MinMax agent in less than 100 games. Let's see how it does against the non-deterministic Min Max Agent:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "player1 = RndMinMaxAgent()\n",
    "player2 = TQPlayer()\n",
    "eval_players(player1, player2, 100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is struggling quite a bit more now, needing about 6000 games to learn a close to perfect strategy. Let's see how the initial values of the Q function impact things. First, let's initialize with 1.0:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "player1 = RndMinMaxAgent()\n",
    "player2 = TQPlayer(q_init=1.0)\n",
    "eval_players(player1, player2, 100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Not actually much worse, but the learning progress does seem a little bit less smooth. Let's try initial values of close to 0 (setting it to 0 will not work with our current code as a loss would not decrease the value further, i.e. once it choses a losing strategy it will never play anything else):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "player1 = RndMinMaxAgent()\n",
    "player2 = TQPlayer(q_init=0.001)\n",
    "eval_players(player1, player2, 100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In contrast to the previous one, where the player was expecting to win and tried every possible way to achieve this, this time the player is quite happy to achieve a draw and settles for it much more quickly.\n",
    "\n",
    "Can the TQPlayer learn from a player that does not play well? Let's see how it does against itself:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "player1 = TQPlayer()\n",
    "player2 = TQPlayer()\n",
    "eval_players(player1, player2, 100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Yes, after about 7000 games, it seems it has found a strategy to not lose against itself. How does this trained player do against a Min Max?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "player1 = RndMinMaxAgent()\n",
    "\n",
    "eval_players(player1, player2, 100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Even against the Min Max player, which it has never played before, it does not lose any games. We created a player that can, just by playing against itself, learn how to play Tic Tac Toe perfectly against a Min Max opponent.\n",
    "\n",
    "Now, how does it perform against a RandomPlayer:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "player1 = RandomPlayer()\n",
    "\n",
    "eval_players(player1, player2, 100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, no losses. It actually wins quite a lot of games now. \n",
    "\n",
    "One last thing we'll try is training a new TQPlayer against a Random Player:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "player1 = RandomPlayer()\n",
    "player2 = TQPlayer()\n",
    "eval_players(player1, player2, 500)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now this is interesting! Even after 50,000 games, it still loses the odd game. However, it does seem to win more games against the Random Player based on this strategy than with the no-loss strategy from before. I'm not 100% sure what is going on there, but I suspect that it found a strategy that is a bit risky, but statiscally better than the conservative no-loss strategy. I.e. it found some situations where, when it plays a move that may cause it to lose the game, chances are that the Random Player will make a mistake and it will actually win. It seems to be inclined to take this risk in certain situations.\n",
    "\n",
    "## Conclusions TQPlayer vs Min Max\n",
    "\n",
    "Both players have a severe limitation: They are only feasible for games with a small number of states. The Min Max player needs to be able to traverse the tree of possible continuations which is not feasible if there are as many as there are in Chess or Go. The TQPlayer needs to store the Q values for every state, which is also not feasible for games like chess or go.\n",
    "\n",
    "The Min Max player has the advantage that it plays perfectly from the start. No need to learn anything. The TQPlayer on the other hand needs to play a lot of games to play well.\n",
    "\n",
    "The TQPlayer however is able to learn effective strategies against opponents which play less than perfect. Min Max always assumes the opponent will make the best possible move in every situation. If that's not the case, the Min Max player is not able to exploit this flaw in its opponent. The TQPlayer however is more flexible and can learn an optimal stragegy against any opponent.\n",
    "\n",
    "Feel encouraged to experiment yourself with various different settings and see how it goes!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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    "name": "ipython",
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   "file_extension": ".py",
   "mimetype": "text/x-python",
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   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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