bjml-4.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "4ae50727-fca7-47e9-b3dc-c9ce572a6cf2",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import random\n",
    "import torch.nn as nn\n",
    "import matplotlib.pyplot as plt\n",
    "from itertools import chain\n",
    "from collections import Counter"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "749783bc-ba99-47db-9d36-8b73ab86d60c",
   "metadata": {},
   "source": [
    "### new strategy: generate a crap ton of random rounds and recalibrate after. better accounts for stochasticity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "50e90f74-9edd-4f73-bf4e-d45515a5b348",
   "metadata": {},
   "outputs": [],
   "source": [
    "class Blackjack:\n",
    "    def __init__(self):\n",
    "        self.reset()\n",
    "\n",
    "        self.trajectories = []\n",
    "\n",
    "        self.terminal_states = {} # dictionary of dictionaries\n",
    "        self.non_terminal_states = {} # dictionary of tuples\n",
    "\n",
    "        self.Q = {}\n",
    "\n",
    "    def init_q(self):\n",
    "        for x in self.trajectories:\n",
    "            J = len(x) - 1\n",
    "\n",
    "            for j in range(J):\n",
    "                self.Q[x[j]] = 0.\n",
    "\n",
    "    def calibrate_q(self):\n",
    "        for x in self.Q.keys():\n",
    "            numerator = 0.\n",
    "            denominator = 0.\n",
    "\n",
    "            if x in self.terminal_states.keys():\n",
    "                numerator += self.terminal_states[x][0]\n",
    "                denominator += self.terminal_states[x][1]\n",
    "\n",
    "                #print(x, numerator, denominator)\n",
    "\n",
    "            if x in self.non_terminal_states.keys():\n",
    "                \n",
    "                for y, n in self.non_terminal_states[x].items():\n",
    "\n",
    "                    other_y_options = [(*y[:-1], i) for i in range(4)]\n",
    "\n",
    "                    best_mean = -100.\n",
    "                    best_bottom = 0.\n",
    "                    \n",
    "                    for yi in other_y_options:\n",
    "                        if yi not in self.Q.keys():\n",
    "                            continue\n",
    "\n",
    "                        if self.Q[yi] > best_mean:\n",
    "                            best_mean = self.Q[yi]\n",
    "                            best_bottom = n\n",
    "\n",
    "                    numerator += best_mean * n\n",
    "                    denominator += n\n",
    "\n",
    "                #print(x, numerator, denominator)\n",
    "\n",
    "            self.Q[x] = numerator / denominator\n",
    "\n",
    "\n",
    "    def recalibrate_aux(self):\n",
    "        for x in self.trajectories:\n",
    "\n",
    "            # non terminal states\n",
    "            J = len(x) - 2\n",
    "\n",
    "            for j in range(J):\n",
    "                if x[j] not in self.non_terminal_states.keys():\n",
    "                    sub_dict = {x[j+1]: 1}\n",
    "                    self.non_terminal_states[x[j]] = sub_dict\n",
    "\n",
    "                else:\n",
    "                    if x[j+1] not in self.non_terminal_states[x[j]].keys():\n",
    "                        self.non_terminal_states[x[j]][x[j+1]] = 1\n",
    "                        \n",
    "                    else:\n",
    "                        self.non_terminal_states[x[j]][x[j+1]] += 1\n",
    "\n",
    "            # terminal state\n",
    "            if x[-2] not in self.terminal_states.keys():\n",
    "                count_and_reward = [x[-1], 1]\n",
    "                self.terminal_states[x[-2]] = count_and_reward\n",
    "\n",
    "            else:\n",
    "                self.terminal_states[x[-2]][0] += x[-1]\n",
    "                self.terminal_states[x[-2]][1] += 1\n",
    "\n",
    "            \n",
    "    def reset(self):\n",
    "        self.deck = 4 * (list(range(2, 12)) + [10, 10, 10])\n",
    "        self.shoe = 8 * self.deck\n",
    "        random.shuffle(self.shoe)\n",
    "\n",
    "        self.policy = None\n",
    "        self.value = None\n",
    "\n",
    "        self.running_count = 0.\n",
    "\n",
    "    def get_multiplier(self):\n",
    "        return 1. + (1. * max(0, self.get_capped_true_count()))\n",
    "\n",
    "    def is_soft(self, c1, c2):\n",
    "        return c1 == 11 or c2 == 11\n",
    "\n",
    "    def get_score(self, hand, c, soft):\n",
    "        \"\"\"returns the score and its softness given the existing hand and a new card\"\"\"\n",
    "        if c != 11 and not soft:\n",
    "            return False, hand + c\n",
    "    \n",
    "        if c == 11 and not soft: # if valid with 1 or 11, then is still soft (and add 11). else add 1 only\n",
    "            if hand + 11 <= 21: # and by extension vaild with hand + 1\n",
    "                return True, hand + 11\n",
    "    \n",
    "            return False, hand + 1\n",
    "    \n",
    "        if c != 11 and soft: # if total > 21, then subtract 10 and it's no longer soft. else, add the card and it's still soft \n",
    "            if hand + c > 21:\n",
    "                return False, hand + c - 10\n",
    "    \n",
    "            return True, hand + c\n",
    "    \n",
    "        # else c == 11 and it's soft\n",
    "        # my argument: we add one and it remains soft since by construction, a hand cannot be soft\n",
    "        # unless it is of total at least 11\n",
    "        return True, hand + 1\n",
    "\n",
    "    def get_true_count(self):\n",
    "        \"\"\"returns the true count exactly based on the running count and length of the shoe\"\"\"\n",
    "        return round(self.running_count / round(len(self.shoe) / 52))\n",
    "\n",
    "    def get_capped_true_count(self):\n",
    "        return max(min(self.get_true_count(), 2), -2)\n",
    "\n",
    "    def deal_card(self, hidden = False):\n",
    "        card = self.shoe.pop(0)\n",
    "\n",
    "        if not hidden:\n",
    "            self.unhide(card)\n",
    "    \n",
    "        return card\n",
    "\n",
    "    def unhide(self, card):\n",
    "        if card <= 6:\n",
    "            self.running_count += 1\n",
    "        elif card >= 10:\n",
    "            self.running_count -= 1\n",
    "\n",
    "    def blackjack(self, c1, c2):\n",
    "        return (c1 == 11 and c2 == 10) or (c1 == 10 and c2 == 11)\n",
    "\n",
    "    def get_action(self, doublable, splittable):\n",
    "        p = 0.3 if doublable else 0.1\n",
    "        q = 0.3 if splittable else 0.1\n",
    "        \n",
    "        probabilities = torch.tensor([(1 - p - q) / 2, (1 - p - q) / 2, p, q])\n",
    "        return torch.distributions.Categorical(probabilities).sample().item()\n",
    "\n",
    "    def get_trained_action(self, y):\n",
    "        other_y_options = [(*y[:-1], i) for i in range(4)]\n",
    "\n",
    "        best_option = 0\n",
    "        value = -1e10\n",
    "        \n",
    "        for yi in other_y_options:\n",
    "            if yi in bj.Q.keys():\n",
    "                if bj.Q[yi] > value:\n",
    "                    best_option = yi[-1]\n",
    "                    value = bj.Q[yi]\n",
    "                    \n",
    "        return best_option\n",
    "\n",
    "\n",
    "    def evaluate_player_hand(self, c1, c2, d1, eval = False):\n",
    "        \"\"\"two cards plus the dealer upcard\"\"\"\n",
    "        \n",
    "        doublable = True\n",
    "        is_second = False\n",
    "        first = False\n",
    "        \n",
    "        if c2 == None:\n",
    "            c2 = self.deal_card()\n",
    "            splittable = False\n",
    "            hand = 1\n",
    "\n",
    "        else:\n",
    "            splittable = c1 == c2\n",
    "            hand = 0\n",
    "\n",
    "        player = 0.\n",
    "        is_second = False\n",
    "        multiplier = 1.\n",
    "\n",
    "        soft, player = self.get_score(player, c1, False)\n",
    "        soft, player = self.get_score(player, c2, soft)\n",
    "\n",
    "            \n",
    "        while player < 21:\n",
    "\n",
    "            if not eval:\n",
    "                action = self.get_action(doublable, splittable)\n",
    "                self.trajectory.append((soft, player, doublable, splittable, self.get_capped_true_count(), hand, is_second, d1, action))\n",
    "                \n",
    "            else:\n",
    "                action = self.get_trained_action((soft, player, doublable, splittable, self.get_capped_true_count(), hand, is_second, d1, None))\n",
    "\n",
    "\n",
    "            #print('State:', 'soft' if soft else '', player, 'on', d1, '| Action:', action)\n",
    "            \n",
    "            if action == 0: # stand\n",
    "                break\n",
    "\n",
    "            elif action == 1: # hit\n",
    "                c = self.deal_card()\n",
    "                soft, player = self.get_score(player, c, soft)\n",
    "\n",
    "                doublable = False\n",
    "                splittable = False\n",
    "\n",
    "            elif action == 2: # double\n",
    "                \n",
    "                # punish if not allowed\n",
    "                if not doublable:\n",
    "                    return _, _, _, True\n",
    "                \n",
    "                multiplier = 2.\n",
    "\n",
    "                c = self.deal_card()\n",
    "                soft, player = self.get_score(player, c, soft)\n",
    "                \n",
    "                break\n",
    "                \n",
    "            else: # split\n",
    "\n",
    "                # punish if not allowed\n",
    "                if not splittable:\n",
    "                    return _, _, _, True\n",
    "\n",
    "                cnew = self.deal_card()\n",
    "                is_second = True\n",
    "\n",
    "                # now reset everything\n",
    "                player = 0.\n",
    "\n",
    "                soft, player = self.get_score(player, c1, False)\n",
    "                soft, player = self.get_score(player, cnew, soft)\n",
    "\n",
    "                splittable = False\n",
    "\n",
    "        #print('Exiting with', player)\n",
    "                \n",
    "        return player, is_second, multiplier, False\n",
    "\n",
    "    def evaluate_dealer_hand(self, d1, d2):\n",
    "        dealer = 0.\n",
    "        self.unhide(d2)\n",
    "\n",
    "        soft, dealer = self.get_score(dealer, d1, False)\n",
    "        soft, dealer = self.get_score(dealer, d2, soft)\n",
    "\n",
    "        while dealer < 17:\n",
    "            d = self.deal_card()\n",
    "            soft, dealer = self.get_score(dealer, d, soft)\n",
    "\n",
    "        return dealer\n",
    "\n",
    "    def blackjack_round(self, eval):\n",
    "        # deal player cards\n",
    "        c1 = self.deal_card()\n",
    "        c2 = self.deal_card()\n",
    "\n",
    "        d1 = self.deal_card()\n",
    "        d2 = self.deal_card(hidden = True)\n",
    "\n",
    "        player_natural = self.blackjack(c1, c2)\n",
    "        dealer_natural = self.blackjack(d1, d2)\n",
    "\n",
    "        if dealer_natural:\n",
    "            \n",
    "            self.unhide(d2)\n",
    "            if not player_natural:\n",
    "                return -1. # dealer blackjack\n",
    "\n",
    "            return 0. # tie\n",
    "\n",
    "        if player_natural:\n",
    "            return 1.5 # player blackjack\n",
    "            \n",
    "\n",
    "        # evaluate player hand\n",
    "        player, is_second, multiplier, did_illegal_move = self.evaluate_player_hand(c1, c2, d1, eval)\n",
    "        \n",
    "        if did_illegal_move:\n",
    "            return -33.\n",
    "\n",
    "        # if there's a second then do the second\n",
    "        if is_second:\n",
    "            player2, _, multiplier2, did_illegal_move = self.evaluate_player_hand(c2, None, d1, eval)\n",
    "\n",
    "            if did_illegal_move:\n",
    "                return -33.    \n",
    "        \n",
    "        # if both busted then we're done\n",
    "        if player > 21 and not is_second:\n",
    "            self.unhide(d2)\n",
    "            return -1. * multiplier\n",
    "\n",
    "        if player > 21 and is_second and player2 > 21:\n",
    "            self.unhide(d2)\n",
    "            return -1. * (multiplier + multiplier2)\n",
    "            \n",
    "        # if not then process dealer hand\n",
    "        dealer = self.evaluate_dealer_hand(d1, d2)\n",
    "\n",
    "        #if is_second:\n",
    "        #    print('At this point we have player', player, 'and second player', player2, 'and dealer', dealer)\n",
    "        #print('Dealer hit to', dealer)\n",
    "\n",
    "        if not is_second:\n",
    "            if dealer > 21:\n",
    "                return 1 * multiplier\n",
    "\n",
    "            elif player > dealer:\n",
    "                return 1 * multiplier\n",
    "\n",
    "            elif player < dealer:\n",
    "                return -1 * multiplier\n",
    "\n",
    "            return 0\n",
    "\n",
    "        else: # then there is a second\n",
    "            final_return = 0.\n",
    "\n",
    "            # first hand\n",
    "            if player > 21: \n",
    "                final_return -= multiplier\n",
    "                \n",
    "            elif dealer > 21:\n",
    "                final_return += multiplier\n",
    "\n",
    "            elif player > dealer:\n",
    "                final_return += multiplier\n",
    "\n",
    "            elif player < dealer:\n",
    "                final_return -= multiplier\n",
    "                \n",
    "            # second hand\n",
    "            if player2 > 21: \n",
    "                final_return -= multiplier2\n",
    "                \n",
    "            elif dealer > 21:\n",
    "                final_return += multiplier2\n",
    "\n",
    "            elif player2 > dealer:\n",
    "                final_return += multiplier2\n",
    "\n",
    "            elif player2 < dealer:\n",
    "                final_return -= multiplier2\n",
    "\n",
    "            return final_return\n",
    "\n",
    "\n",
    "    def do_game(self, eval):\n",
    "\n",
    "        winnings = 0.\n",
    "        hands = 0.\n",
    "        \n",
    "        while len(self.shoe) > 60:\n",
    "\n",
    "            self.trajectory = []\n",
    "\n",
    "            multiplier = self.get_multiplier()\n",
    "            w = self.blackjack_round(eval)\n",
    "\n",
    "            winnings += (multiplier * 10 * w)\n",
    "            hands += 1\n",
    "\n",
    "            if len(self.trajectory) == 0:\n",
    "                continue # skip if it's a blackjack, no processing to do\n",
    "                \n",
    "            self.trajectory.append(w)\n",
    "            self.trajectories.append(self.trajectory)\n",
    "\n",
    "            #print('Won', w)\n",
    "            #print()\n",
    "\n",
    "        return winnings / hands\n",
    "\n",
    "    def do_games(self, n_games, eval = False):\n",
    "\n",
    "        winnings = []\n",
    "        \n",
    "        for n in range(n_games):\n",
    "            self.reset() # reset everything\n",
    "            \n",
    "            w = self.do_game(eval)\n",
    "            winnings.append(w)\n",
    "\n",
    "            if n % 2500 == 0:\n",
    "\n",
    "                state_action_pairs = [x[:-1] for x in bj.trajectories]\n",
    "                state_action_pairs = list(chain.from_iterable(state_action_pairs))\n",
    "\n",
    "                table = Counter(state_action_pairs)\n",
    "                total_hands = table.keys().__len__()\n",
    "\n",
    "                detail_hands = torch.tensor(list(table.values())) > 40\n",
    "                \n",
    "                print('=== Game', n, ',', total_hands, '(', 100 * total_hands / (5912 * 5),'% ) different state-actions observed, ', \\\n",
    "                      100 * torch.mean(1. * detail_hands).item(),'% in detail ===')\n",
    "\n",
    "        return winnings\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "58fca4b2-ad4d-4de0-b51a-de73a38828fa",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== Game 0 , 67 ( 0.22665764546684708 % ) different state-actions observed,  0.0 % in detail ===\n",
      "=== Game 2500 , 15222 ( 51.495263870094725 % ) different state-actions observed,  8.284062892198563 % in detail ===\n",
      "=== Game 5000 , 17917 ( 60.61231393775372 % ) different state-actions observed,  14.438800513744354 % in detail ===\n",
      "=== Game 7500 , 19443 ( 65.7746955345061 % ) different state-actions observed,  17.80589371919632 % in detail ===\n",
      "=== Game 10000 , 20565 ( 69.5703653585927 % ) different state-actions observed,  20.875273644924164 % in detail ===\n",
      "=== Game 12500 , 21412 ( 72.43572395128552 % ) different state-actions observed,  23.18326234817505 % in detail ===\n",
      "=== Game 15000 , 22053 ( 74.6041948579161 % ) different state-actions observed,  24.99433159828186 % in detail ===\n",
      "=== Game 17500 , 22630 ( 76.55615696887686 % ) different state-actions observed,  26.60185694694519 % in detail ===\n",
      "=== Game 20000 , 23066 ( 78.03112313937754 % ) different state-actions observed,  27.97624170780182 % in detail ===\n",
      "=== Game 22500 , 23451 ( 79.33355886332882 % ) different state-actions observed,  28.988102078437805 % in detail ===\n",
      "=== Game 25000 , 23785 ( 80.46346414073072 % ) different state-actions observed,  30.460375547409058 % in detail ===\n",
      "=== Game 27500 , 24063 ( 81.40392422192151 % ) different state-actions observed,  31.700119376182556 % in detail ===\n",
      "=== Game 30000 , 24323 ( 82.28349120433018 % ) different state-actions observed,  32.90301263332367 % in detail ===\n",
      "=== Game 32500 , 24581 ( 83.15629228687415 % ) different state-actions observed,  34.2866450548172 % in detail ===\n",
      "=== Game 35000 , 24806 ( 83.91745602165088 % ) different state-actions observed,  35.44707000255585 % in detail ===\n",
      "=== Game 37500 , 25008 ( 84.60081190798377 % ) different state-actions observed,  36.704254150390625 % in detail ===\n",
      "=== Game 40000 , 25184 ( 85.19621109607577 % ) different state-actions observed,  37.69854009151459 % in detail ===\n",
      "=== Game 42500 , 25337 ( 85.71380243572395 % ) different state-actions observed,  38.722026348114014 % in detail ===\n",
      "=== Game 45000 , 25492 ( 86.2381596752368 % ) different state-actions observed,  39.52612578868866 % in detail ===\n",
      "=== Game 47500 , 25628 ( 86.69824086603518 % ) different state-actions observed,  40.14749526977539 % in detail ===\n",
      "=== Game 50000 , 25776 ( 87.19891745602165 % ) different state-actions observed,  40.77436327934265 % in detail ===\n",
      "=== Game 52500 , 25885 ( 87.56765899864682 % ) different state-actions observed,  41.456443071365356 % in detail ===\n",
      "=== Game 55000 , 26019 ( 88.02097428958051 % ) different state-actions observed,  42.003920674324036 % in detail ===\n",
      "=== Game 57500 , 26129 ( 88.39309878213803 % ) different state-actions observed,  42.41264462471008 % in detail ===\n",
      "=== Game 60000 , 26212 ( 88.67388362652233 % ) different state-actions observed,  42.884936928749084 % in detail ===\n",
      "=== Game 62500 , 26327 ( 89.06292286874154 % ) different state-actions observed,  43.33953857421875 % in detail ===\n",
      "=== Game 65000 , 26425 ( 89.39445196211096 % ) different state-actions observed,  43.746453523635864 % in detail ===\n",
      "=== Game 67500 , 26506 ( 89.66847090663059 % ) different state-actions observed,  44.08435821533203 % in detail ===\n",
      "=== Game 70000 , 26590 ( 89.95263870094723 % ) different state-actions observed,  44.47536766529083 % in detail ===\n",
      "=== Game 72500 , 26645 ( 90.13870094722598 % ) different state-actions observed,  44.74760890007019 % in detail ===\n",
      "=== Game 75000 , 26708 ( 90.35182679296346 % ) different state-actions observed,  44.93035674095154 % in detail ===\n",
      "=== Game 77500 , 26769 ( 90.55818673883627 % ) different state-actions observed,  45.17912566661835 % in detail ===\n",
      "=== Game 80000 , 26848 ( 90.8254397834912 % ) different state-actions observed,  45.407480001449585 % in detail ===\n",
      "=== Game 82500 , 26907 ( 91.02503382949932 % ) different state-actions observed,  45.58665156364441 % in detail ===\n",
      "=== Game 85000 , 26962 ( 91.21109607577807 % ) different state-actions observed,  45.76441049575806 % in detail ===\n",
      "=== Game 87500 , 27025 ( 91.42422192151557 % ) different state-actions observed,  45.95744609832764 % in detail ===\n",
      "=== Game 90000 , 27091 ( 91.64749661705007 % ) different state-actions observed,  46.144476532936096 % in detail ===\n",
      "=== Game 92500 , 27149 ( 91.84370771312585 % ) different state-actions observed,  46.347931027412415 % in detail ===\n",
      "=== Game 95000 , 27187 ( 91.9722598105548 % ) different state-actions observed,  46.58108651638031 % in detail ===\n",
      "=== Game 97500 , 27236 ( 92.13802435723952 % ) different state-actions observed,  46.761637926101685 % in detail ===\n",
      "=== Game 100000 , 27274 ( 92.26657645466847 % ) different state-actions observed,  46.93847596645355 % in detail ===\n",
      "=== Game 102500 , 27325 ( 92.43910690121787 % ) different state-actions observed,  47.15096056461334 % in detail ===\n",
      "=== Game 105000 , 27370 ( 92.5913396481732 % ) different state-actions observed,  47.402265667915344 % in detail ===\n",
      "=== Game 107500 , 27413 ( 92.73680649526386 % ) different state-actions observed,  47.62338995933533 % in detail ===\n",
      "=== Game 110000 , 27443 ( 92.8382949932341 % ) different state-actions observed,  47.80089557170868 % in detail ===\n",
      "=== Game 112500 , 27480 ( 92.96346414073072 % ) different state-actions observed,  48.04949164390564 % in detail ===\n",
      "=== Game 115000 , 27525 ( 93.11569688768606 % ) different state-actions observed,  48.22888374328613 % in detail ===\n",
      "=== Game 117500 , 27558 ( 93.22733423545331 % ) different state-actions observed,  48.43602478504181 % in detail ===\n",
      "=== Game 120000 , 27607 ( 93.39309878213803 % ) different state-actions observed,  48.62172603607178 % in detail ===\n",
      "=== Game 122500 , 27633 ( 93.48105548037888 % ) different state-actions observed,  48.847392201423645 % in detail ===\n",
      "=== Game 125000 , 27666 ( 93.59269282814614 % ) different state-actions observed,  49.06744658946991 % in detail ===\n",
      "=== Game 127500 , 27697 ( 93.69756427604871 % ) different state-actions observed,  49.2508202791214 % in detail ===\n",
      "=== Game 130000 , 27732 ( 93.81596752368065 % ) different state-actions observed,  49.44829046726227 % in detail ===\n",
      "=== Game 132500 , 27751 ( 93.88024357239513 % ) different state-actions observed,  49.691903591156006 % in detail ===\n",
      "=== Game 135000 , 27779 ( 93.97496617050068 % ) different state-actions observed,  49.883005023002625 % in detail ===\n",
      "=== Game 137500 , 27805 ( 94.06292286874154 % ) different state-actions observed,  50.113290548324585 % in detail ===\n",
      "=== Game 140000 , 27838 ( 94.1745602165088 % ) different state-actions observed,  50.323301553726196 % in detail ===\n",
      "=== Game 142500 , 27861 ( 94.25236806495263 % ) different state-actions observed,  50.5294144153595 % in detail ===\n",
      "=== Game 145000 , 27890 ( 94.35047361299053 % ) different state-actions observed,  50.77088475227356 % in detail ===\n",
      "=== Game 147500 , 27922 ( 94.45872801082544 % ) different state-actions observed,  50.89176893234253 % in detail ===\n",
      "=== Game 150000 , 27948 ( 94.54668470906631 % ) different state-actions observed,  51.09131336212158 % in detail ===\n",
      "=== Game 152500 , 27974 ( 94.63464140730717 % ) different state-actions observed,  51.27261281013489 % in detail ===\n",
      "=== Game 155000 , 28003 ( 94.73274695534506 % ) different state-actions observed,  51.49090886116028 % in detail ===\n",
      "=== Game 157500 , 28025 ( 94.80717185385656 % ) different state-actions observed,  51.703834533691406 % in detail ===\n",
      "=== Game 160000 , 28049 ( 94.88836265223274 % ) different state-actions observed,  51.91985368728638 % in detail ===\n",
      "=== Game 162500 , 28067 ( 94.94925575101489 % ) different state-actions observed,  52.096766233444214 % in detail ===\n",
      "=== Game 165000 , 28094 ( 95.04059539918809 % ) different state-actions observed,  52.27094888687134 % in detail ===\n",
      "=== Game 167500 , 28112 ( 95.10148849797022 % ) different state-actions observed,  52.397555112838745 % in detail ===\n",
      "=== Game 170000 , 28130 ( 95.16238159675237 % ) different state-actions observed,  52.60576009750366 % in detail ===\n",
      "=== Game 172500 , 28158 ( 95.25710419485792 % ) different state-actions observed,  52.7807354927063 % in detail ===\n",
      "=== Game 175000 , 28176 ( 95.31799729364005 % ) different state-actions observed,  52.98480987548828 % in detail ===\n",
      "=== Game 177500 , 28201 ( 95.40257104194858 % ) different state-actions observed,  53.13286781311035 % in detail ===\n",
      "=== Game 180000 , 28221 ( 95.4702300405954 % ) different state-actions observed,  53.2794713973999 % in detail ===\n",
      "=== Game 182500 , 28237 ( 95.52435723951285 % ) different state-actions observed,  53.433436155319214 % in detail ===\n",
      "=== Game 185000 , 28254 ( 95.58186738836265 % ) different state-actions observed,  53.58533263206482 % in detail ===\n",
      "=== Game 187500 , 28269 ( 95.63261163734776 % ) different state-actions observed,  53.76560688018799 % in detail ===\n",
      "=== Game 190000 , 28289 ( 95.70027063599458 % ) different state-actions observed,  53.97858023643494 % in detail ===\n",
      "=== Game 192500 , 28317 ( 95.79499323410013 % ) different state-actions observed,  54.09471392631531 % in detail ===\n",
      "=== Game 195000 , 28336 ( 95.85926928281461 % ) different state-actions observed,  54.252541065216064 % in detail ===\n",
      "=== Game 197500 , 28352 ( 95.91339648173206 % ) different state-actions observed,  54.39828038215637 % in detail ===\n",
      "=== Game 200000 , 28373 ( 95.98443843031123 % ) different state-actions observed,  54.55538630485535 % in detail ===\n",
      "=== Game 202500 , 28397 ( 96.06562922868741 % ) different state-actions observed,  54.67126965522766 % in detail ===\n",
      "=== Game 205000 , 28411 ( 96.1129905277402 % ) different state-actions observed,  54.8484742641449 % in detail ===\n",
      "=== Game 207500 , 28436 ( 96.19756427604871 % ) different state-actions observed,  54.965537786483765 % in detail ===\n",
      "=== Game 210000 , 28451 ( 96.24830852503383 % ) different state-actions observed,  55.077147483825684 % in detail ===\n",
      "=== Game 212500 , 28473 ( 96.32273342354533 % ) different state-actions observed,  55.23478388786316 % in detail ===\n",
      "=== Game 215000 , 28489 ( 96.37686062246279 % ) different state-actions observed,  55.35469651222229 % in detail ===\n",
      "=== Game 217500 , 28506 ( 96.43437077131259 % ) different state-actions observed,  55.45849800109863 % in detail ===\n",
      "=== Game 220000 , 28522 ( 96.48849797023004 % ) different state-actions observed,  55.57814836502075 % in detail ===\n",
      "=== Game 222500 , 28544 ( 96.56292286874154 % ) different state-actions observed,  55.720990896224976 % in detail ===\n",
      "=== Game 225000 , 28567 ( 96.64073071718539 % ) different state-actions observed,  55.837154388427734 % in detail ===\n",
      "=== Game 227500 , 28574 ( 96.66441136671178 % ) different state-actions observed,  55.96696138381958 % in detail ===\n",
      "=== Game 230000 , 28589 ( 96.71515561569689 % ) different state-actions observed,  56.136977672576904 % in detail ===\n",
      "=== Game 232500 , 28605 ( 96.76928281461434 % ) different state-actions observed,  56.24890923500061 % in detail ===\n",
      "=== Game 235000 , 28622 ( 96.82679296346414 % ) different state-actions observed,  56.34477138519287 % in detail ===\n",
      "=== Game 237500 , 28631 ( 96.85723951285522 % ) different state-actions observed,  56.44581317901611 % in detail ===\n",
      "=== Game 240000 , 28645 ( 96.90460081190798 % ) different state-actions observed,  56.55088424682617 % in detail ===\n",
      "=== Game 242500 , 28654 ( 96.93504736129906 % ) different state-actions observed,  56.620365381240845 % in detail ===\n",
      "=== Game 245000 , 28662 ( 96.96211096075778 % ) different state-actions observed,  56.73365592956543 % in detail ===\n",
      "=== Game 247500 , 28676 ( 97.00947225981055 % ) different state-actions observed,  56.848931312561035 % in detail ===\n",
      "=== Game 250000 , 28684 ( 97.03653585926928 % ) different state-actions observed,  56.982988119125366 % in detail ===\n"
     ]
    }
   ],
   "source": [
    "bj = Blackjack()\n",
    "w = bj.do_games(250_001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "b3a14f53-8a15-49fe-8329-c655cc9a492f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([2.0000e+00, 1.0000e+00, 1.0000e+00, 7.0000e+00, 7.0000e+00,\n",
       "        1.0000e+01, 2.6000e+01, 5.1000e+01, 8.6000e+01, 1.8300e+02,\n",
       "        2.6700e+02, 5.3100e+02, 8.2300e+02, 1.2900e+03, 1.9560e+03,\n",
       "        2.9810e+03, 4.3940e+03, 5.8190e+03, 7.9810e+03, 1.0585e+04,\n",
       "        1.3705e+04, 1.7523e+04, 2.2612e+04, 2.9864e+04, 3.8008e+04,\n",
       "        4.0713e+04, 3.1715e+04, 1.4917e+04, 3.6630e+03, 2.8000e+02]),\n",
       " array([-287.24637681, -277.71837258, -268.19036836, -258.66236413,\n",
       "        -249.1343599 , -239.60635568, -230.07835145, -220.55034722,\n",
       "        -211.022343  , -201.49433877, -191.96633454, -182.43833031,\n",
       "        -172.91032609, -163.38232186, -153.85431763, -144.32631341,\n",
       "        -134.79830918, -125.27030495, -115.74230072, -106.2142965 ,\n",
       "         -96.68629227,  -87.15828804,  -77.63028382,  -68.10227959,\n",
       "         -58.57427536,  -49.04627114,  -39.51826691,  -29.99026268,\n",
       "         -20.46225845,  -10.93425423,   -1.40625   ]),\n",
       " <BarContainer object of 30 artists>)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(w, bins = 30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "def7ebdc-a52d-46f6-b94f-07878ed09e38",
   "metadata": {},
   "outputs": [],
   "source": [
    "bj.init_q()\n",
    "bj.recalibrate_aux()\n",
    "\n",
    "for _ in range(50):\n",
    "    bj.calibrate_q()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "86b56c15-21b8-48e5-9b14-f2fcfbfd728e",
   "metadata": {},
   "source": [
    "## distribution of average loss per hand (based on 10.0 scale)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b9a59d81-b4f7-4463-97c8-f143735a74a0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== Game 0 , 28684 ( 97.03653585926928 % ) different state-actions observed,  56.982988119125366 % in detail ===\n",
      "0.03970206273531555\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(array([  1.,   3.,   0.,   3.,  12.,  11.,  17.,  27.,  48.,  57.,  84.,\n",
       "        122., 171., 191., 215., 273., 199., 169., 127.,  87.,  61.,  32.,\n",
       "         35.,  21.,   9.,  12.,   4.,   2.,   3.,   4.]),\n",
       " array([-9.46969697e+00, -8.83865579e+00, -8.20761461e+00, -7.57657343e+00,\n",
       "        -6.94553225e+00, -6.31449106e+00, -5.68344988e+00, -5.05240870e+00,\n",
       "        -4.42136752e+00, -3.79032634e+00, -3.15928516e+00, -2.52824398e+00,\n",
       "        -1.89720280e+00, -1.26616162e+00, -6.35120435e-01, -4.07925408e-03,\n",
       "         6.26961927e-01,  1.25800311e+00,  1.88904429e+00,  2.52008547e+00,\n",
       "         3.15112665e+00,  3.78216783e+00,  4.41320901e+00,  5.04425019e+00,\n",
       "         5.67529138e+00,  6.30633256e+00,  6.93737374e+00,  7.56841492e+00,\n",
       "         8.19945610e+00,  8.83049728e+00,  9.46153846e+00]),\n",
       " <BarContainer object of 30 artists>)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "w = bj.do_games(2000, eval = True) # keep in mind the above must be done first to populate the Q\n",
    "print(sum(w) / len(w))\n",
    "plt.hist(w, bins = 30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ffbadd08-69d0-46a6-a3ef-4b60d1d198c8",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "c6d6bedd-19d8-43f3-9861-392ee518e6e1",
   "metadata": {},
   "source": [
    "## best hands by payout (1.0 scale)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "034ba157-f36e-4dd4-8f06-3c0f1cd556e9",
   "metadata": {},
   "outputs": [],
   "source": [
    "for k, v in bj.Q.items():\n",
    "    if v > 2.0:\n",
    "        print(k, v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f12c3860-f0e9-477b-8860-cee911ca7d49",
   "metadata": {},
   "outputs": [],
   "source": [
    "y = (True, 20.0, True, False, 0, 0, True, 2, 2)\n",
    "other_y_options = [(*y[:-1], i) for i in range(4)]\n",
    "\n",
    "for yi in other_y_options:\n",
    "    if yi in bj.Q.keys():\n",
    "        print(yi, bj.Q[yi])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "af0bb6d9-6914-4cbb-8400-b575a74cce77",
   "metadata": {},
   "outputs": [],
   "source": [
    "# soft, player, doublable, splittable, self.get_capped_true_count(), hand, is_second, d1, action\n",
    "y = (False, 20.0, True, True, 0, 0, False, 6, 2)\n",
    "other_y_options = [(*y[:-1], i) for i in range(4)]\n",
    "\n",
    "for yi in other_y_options:\n",
    "    if yi in bj.Q.keys():\n",
    "        print(yi, bj.Q[yi])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "99ea3335-691d-4d6c-9264-ab9ddbd82440",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "980df200-020b-4ae8-b160-abc1bfa7cb76",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9e329c15-caea-408f-a47b-e9bf0c8fdf91",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "14e84d3d-d7a0-43ce-bc71-1de17b652a8f",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "950367a5-2bbc-4638-8d5f-9d5ef62b7587",
   "metadata": {},
   "source": [
    "## how many hands"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 325,
   "id": "49e655af-08ab-42b6-882b-70f45c5e6734",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "351941"
      ]
     },
     "execution_count": 325,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "state_action_pairs = [x[:-1] for x in bj.trajectories]\n",
    "state_action_pairs = list(chain.from_iterable(state_action_pairs))\n",
    "len(state_action_pairs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 326,
   "id": "cfffa782-20ed-46b4-bd5a-9241a2f89b5c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "17451"
      ]
     },
     "execution_count": 326,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table = Counter(state_action_pairs)\n",
    "table.keys().__len__()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 327,
   "id": "8cd26f68-0b1d-4dfd-a1ce-e41b5a0c3357",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 5912 (this might be it -- in fact im convinced since i seen it twice)\n",
    "# 5912 * 5 = 29560"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "62025d47-7539-42e6-9466-87d7393dfd83",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0725a2c7-6d74-4101-9162-fcdde4f6a2a3",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2701a11c-8680-4733-a4f3-218deba67484",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d7062f83-8d47-483a-8cb3-119090bffc5e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ca99abbf-cbbc-4a47-a1e1-1bab07e245e6",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "40a95fa1-c4cd-4c7d-9ae5-70e550272160",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "763b7e22-b538-4f3d-b4ce-4826a85261bc",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "62bfdf07-ff31-4f9e-9bce-34e7c8926193",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "77320af7-08d0-42a0-9d0e-3bc28d3c2a49",
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