russian_roulette_odds.ipynb

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        "# **Simulação de apostas numa Roleta Russa: análise de probabilidades e dos retornos esperados**\n",
        "\n",
        "### **Este código pode ser usado para**:\n",
        "\n",
        "* **Comparar estratégias de jogos de roleta**: avaliar o impacto das regras (bolsos adicionais) nos retornos médios, demonstrando como diferentes regras (roletas justas, europeias e americanas) impactam os retornos esperados.\n",
        "\n",
        "* **Simular estratégias de apostas**: testar diferentes abordagens em cenários controlados. Demonstrar as limitações e riscos da estratégia Martingale em jogos de azar.\n",
        "\n",
        "* **Ensino de simulações probabilísticas**: análise de resultados estatísticos, isto é, demonstrar conceitos como variabilidade e médias esperadas, avaliar médias e dispersões em experimentos simulados. Ilustrar conceitos como independência de eventos, risco e variância em experimentos probabilísticos.\n",
        "\n",
        "* **Demonstrar os retornos esperados para 95% de confiança**: mostrar como aumentos no número de giros reduzem a incerteza (intervalos menores)."
      ],
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      "source": [
        "import random, pylab"
      ]
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        "## **Inicialização da Roleta Justa (`FairRoulette`)**\n",
        "\n",
        "A classe `FairRoulette` simula uma roleta russa justa com 36 bolsos (*pockets*) numerados de 1 a 36, possuindo métodos para determinar a cor do bolso onde a bola caiu (preto/vermelho) e calcular retornos de apostas.\n",
        "Funções principais:\n",
        "\n",
        "* `spin`: gira a roleta e posiciona a bola em um bolso aleatório.\n",
        "* `isBlack` e `isRed`: identificam a cor do bolso.\n",
        "* `betBlack`, `betRed`, `betPocket`: calculam ganhos/perdas para diferentes tipos de apostas."
      ],
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        "class FairRoulette():\n",
        "    def __init__(self):\n",
        "        \"\"\"\n",
        "        Inicializa a roleta justa:\n",
        "        - Define os bolsos numerados de 1 a 36.\n",
        "        - Inicializa a bola como `None` (não foi girada ainda).\n",
        "        - Define as probabilidades para cores (preto/vermelho) como 1.0.\n",
        "        - Define a probabilidade de um número específico (pocketOdds).\n",
        "        \"\"\"\n",
        "        self.pockets = []  # Lista de bolsos disponíveis\n",
        "        for i in range(1, 37):  # Números de 1 a 36\n",
        "            self.pockets.append(i)\n",
        "        self.ball = None  # Representa o bolso onde a bola para após o giro\n",
        "        self.blackOdds, self.redOdds = 1.0, 1.0  # Probabilidades para preto e vermelho\n",
        "        self.pocketOdds = len(self.pockets) - 1.0  # Probabilidade de acertar um número específico\n",
        "\n",
        "    def spin(self):\n",
        "        \"\"\"\n",
        "        Simula o giro da roleta:\n",
        "        - Escolhe aleatoriamente um bolso onde a bola irá parar.\n",
        "        \"\"\"\n",
        "        self.ball = random.choice(self.pockets)\n",
        "\n",
        "    def isBlack(self):\n",
        "        \"\"\"\n",
        "        Determina se o bolso onde a bola caiu é preto:\n",
        "        - Verifica a numeração e regras específicas dos bolsos pretos.\n",
        "        - Retorna True se for preto, False caso contrário.\n",
        "        \"\"\"\n",
        "        if type(self.ball) != int:  # Verifica se a bola caiu em um bolso válido\n",
        "            return False\n",
        "        if ((self.ball > 0 and self.ball < 10) or  # Bolsos 1-9\n",
        "            (self.ball > 18 and self.ball < 28)):  # Bolsos 19-27\n",
        "            return self.ball % 2 == 0  # Números pares são pretos nesses intervalos\n",
        "        else:\n",
        "            return self.ball % 2 == 1  # Números ímpares são pretos fora desses intervalos\n",
        "\n",
        "    def isRed(self):\n",
        "        \"\"\"\n",
        "        Determina se o bolso onde a bola caiu é vermelho:\n",
        "        - Retorna True se for vermelho (não preto e válido), False caso contrário.\n",
        "        \"\"\"\n",
        "        return type(self.ball) == int and not self.isBlack()\n",
        "\n",
        "    def betBlack(self, amt):\n",
        "        \"\"\"\n",
        "        Calcula o retorno de uma aposta na cor preta:\n",
        "        - `amt`: valor apostado.\n",
        "        - Retorna um valor positivo proporcional à aposta se for preto, negativo caso contrário.\n",
        "        \"\"\"\n",
        "        if self.isBlack():\n",
        "            return amt * self.blackOdds\n",
        "        else:\n",
        "            return -amt\n",
        "\n",
        "    def betRed(self, amt):\n",
        "        \"\"\"\n",
        "        Calcula o retorno de uma aposta na cor vermelha:\n",
        "        - `amt`: valor apostado.\n",
        "        - Retorna um valor positivo proporcional à aposta se for vermelho, negativo caso contrário.\n",
        "        \"\"\"\n",
        "        if self.isRed():\n",
        "            return amt * self.redOdds\n",
        "        else:\n",
        "            return -amt\n",
        "\n",
        "    def betPocket(self, pocket, amt):\n",
        "        \"\"\"\n",
        "        Calcula o retorno de uma aposta em um número específico (bolso):\n",
        "        - `pocket`: número do bolso apostado.\n",
        "        - `amt`: valor apostado.\n",
        "        - Retorna um valor positivo proporcional às probabilidades se a bola cair no número apostado, negativo caso contrário.\n",
        "        \"\"\"\n",
        "        if str(pocket) == str(self.ball):  # Verifica se o bolso corresponde ao número apostado\n",
        "            return amt * self.pocketOdds\n",
        "        else:\n",
        "            return -amt\n",
        "\n",
        "    def __str__(self):\n",
        "        \"\"\"\n",
        "        Representação textual da classe:\n",
        "        - Retorna 'Fair Roulette'.\n",
        "        \"\"\"\n",
        "        return 'Fair Roulette'"
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        "## **Simulação do Jogo de Azar: \"Roleta Russa Justa\"**\n",
        "\n",
        "A função `playRoulette` é responsável por simular apostas repetidas numa roleta, acumulando os retornos médios para os diferentes tipos de apostas (vermelho, preto e um número específico).\n",
        "\n",
        "**Parâmetros:**\n",
        "\n",
        "* `game`: um objeto que representa o jogo de roleta, instanciado a partir da classe `FairRoulette` ou suas variações posteriores.\n",
        "* `numSpins`: quantidade de giros da roleta a serem simulados.\n",
        "* `toPrint`: `Flag` que indica se os resultados devem ser exibidos no console.\n",
        "\n",
        "**Lógica Principal:**\n",
        "\n",
        "Define um número da sorte (`luckyNumber`) para apostas específicas.\n",
        "Gira a roleta `numSpins` vezes e registra o retorno de apostas em vermelho, preto e no número da sorte. Se `toPrint` for verdadeiro, exibe os retornos médios esperados. Retorna uma tupla com os retornos médios esperados para cada tipo de aposta."
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        "def playRoulette(game, numSpins, toPrint=True):\n",
        "    \"\"\"\n",
        "    Simula um número especificado de rodadas de apostas em uma roleta.\n",
        "\n",
        "    Parâmetros:\n",
        "    - game: Objeto da classe FairRoulette ou suas subclasses.\n",
        "    - numSpins: Número de giros da roleta a serem simulados.\n",
        "    - toPrint: Indica se os resultados devem ser impressos no console (True por padrão).\n",
        "\n",
        "    Retorna:\n",
        "    - Uma tupla contendo os retornos médios esperados para:\n",
        "        1. Aposta na cor vermelha.\n",
        "        2. Aposta na cor preta.\n",
        "        3. Aposta em um número específico (\"luckyNumber\").\n",
        "    \"\"\"\n",
        "    luckyNumber = '2'  # Número da sorte para apostas específicas\n",
        "    bet = 1  # Valor fixo de cada aposta\n",
        "    totRed, totBlack, totPocket = 0.0, 0.0, 0.0  # Acumuladores para retornos\n",
        "\n",
        "    # Realiza as rodadas de apostas\n",
        "    for i in range(numSpins):\n",
        "        game.spin()  # Gira a roleta\n",
        "        totRed += game.betRed(bet)  # Calcula o retorno de uma aposta em vermelho\n",
        "        totBlack += game.betBlack(bet)  # Calcula o retorno de uma aposta em preto\n",
        "        totPocket += game.betPocket(luckyNumber, bet)  # Calcula o retorno de uma aposta no número da sorte\n",
        "\n",
        "    # Exibe os resultados, se solicitado\n",
        "    if toPrint:\n",
        "        print(numSpins, 'rodadas de', game)\n",
        "        print('Retorno esperado, apostando no vermelho =', str(100 * totRed / numSpins) + '%')\n",
        "        print('Retorno esperado, apostando no preto =', str(100 * totBlack / numSpins) + '%')\n",
        "        print('Apostas de retorno esperado', luckyNumber, '=', str(100 * totPocket / numSpins) + '%\\n')\n",
        "\n",
        "    # Retorna os retornos médios esperados\n",
        "    return (totRed / numSpins, totBlack / numSpins, totPocket / numSpins)\n",
        "\n",
        "\n",
        "# Configuração e execução da simulação\n",
        "numSpins = 1000000  # Número de giros da roleta\n",
        "game = FairRoulette()  # Instancia um jogo de roleta justa\n",
        "playRoulette(game, numSpins)  # Executa a simulação\n"
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            "1000000 rodadas de Fair Roulette\n",
            "Retorno esperado, apostando no vermelho = 11.3638%\n",
            "Retorno esperado, apostando no preto = -11.3638%\n",
            "Apostas de retorno esperado 2 = -0.9064%\n",
            "\n"
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              "(0.113638, -0.113638, -0.009064)"
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      "source": [
        "A saída acima mostra os retornos médios esperados para cada tipo de aposta após 1.000.000 de giros da roleta justa."
      ],
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      "source": [
        "## **Simulação com as roletas Europeia e Americana**\n",
        "\n",
        "A classe `EuRoulette` é uma subclasse de `FairRoulette` e representa a roleta europeia, que adiciona um bolso verde adicional (0) ao jogo, favorecendo assim ao cassino.\n",
        "\n",
        "A classe `AmRoulette`, uma subclasse de `EuRoulette`, representa a roleta americana, que adiciona mais outro bolso verde (00), tornando o jogo ainda mais favorável ao cassino.\n",
        "\n",
        "Ambas as classes utilizam o método `__str__` para retornar uma representação textual de suas instâncias.\n",
        "\n",
        "A função `findPocketReturn` simula apostas repetidas em um número específico (*pocket*) para diferentes configurações de giros e experimentos. A lógica consiste em executat `numTrials` experimentos independentes, cada um com `trialSize` giros da roleta. O código coleta os retornos médios de apostas no número da sorte de cada experimento e retorna uma lista contendo os retornos de cada experimento.\n"
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        "class EuRoulette(FairRoulette):\n",
        "    \"\"\"\n",
        "    Classe que representa a roleta europeia, uma subclass de FairRoulette.\n",
        "    Adiciona um bolso extra (0) à lista de bolsos, favorecendo a casa.\n",
        "    \"\"\"\n",
        "    def __init__(self):\n",
        "        super().__init__()  # Inicializa a roleta justa\n",
        "        self.pockets.append('0')  # Adiciona o bolso 0\n",
        "\n",
        "    def __str__(self):\n",
        "        \"\"\"\n",
        "        Representação textual da classe.\n",
        "        Retorna 'European Roulette'.\n",
        "        \"\"\"\n",
        "        return 'European Roulette'\n",
        "\n",
        "class AmRoulette(EuRoulette):\n",
        "    \"\"\"\n",
        "    Classe que representa a roleta americana, uma subclass de EuRoulette.\n",
        "    Adiciona um bolso extra (00), tornando a roleta ainda mais favorável à casa.\n",
        "    \"\"\"\n",
        "    def __init__(self):\n",
        "        super().__init__()  # Inicializa a roleta europeia\n",
        "        self.pockets.append('00')  # Adiciona o bolso 00\n",
        "\n",
        "    def __str__(self):\n",
        "        \"\"\"\n",
        "        Representação textual da classe.\n",
        "        Retorna 'American Roulette'.\n",
        "        \"\"\"\n",
        "        return 'American Roulette'\n",
        "\n",
        "def findPocketReturn(game, numTrials, trialSize, toPrint):\n",
        "    \"\"\"\n",
        "    Calcula os retornos médios de apostas em um número específico (pocket)\n",
        "    para um determinado número de rodadas.\n",
        "\n",
        "    Parâmetros:\n",
        "    - game: Objeto da classe FairRoulette, EuRoulette ou AmRoulette.\n",
        "    - numTrials: Número de experimentos independentes.\n",
        "    - trialSize: Número de giros por experimento.\n",
        "    - toPrint: Indica se os resultados intermediários devem ser impressos.\n",
        "\n",
        "    Retorna:\n",
        "    - Uma lista com os retornos para apostas em um número específico em cada experimento.\n",
        "    \"\"\"\n",
        "    pocketReturns = []\n",
        "    for t in range(numTrials):\n",
        "        trialVals = playRoulette(game, trialSize, toPrint)\n",
        "        pocketReturns.append(trialVals[2])  # Coleta o retorno de apostas no número da sorte\n",
        "    return pocketReturns\n",
        "\n",
        "# Configuração inicial da simulação\n",
        "random.seed(0)  # Define uma semente para resultados reproduzíveis\n",
        "numTrials = 20  # Número de experimentos independentes\n",
        "resultDict = {}  # Dicionário para armazenar os resultados\n",
        "games = (FairRoulette, EuRoulette, AmRoulette)  # Diferentes tipos de roleta\n",
        "\n",
        "# Simulação\n",
        "for G in games:\n",
        "    resultDict[G().__str__()] = []  # Inicializa a lista de resultados para cada tipo de roleta\n",
        "    for numSpins in (100, 1000, 10000, 100000):  # Diferentes tamanhos de giros\n",
        "        print('\\nSimulação de aposta num pocket por', numTrials,\n",
        "              'tentativas de', numSpins, 'giros cada.')\n",
        "        pocketReturns = findPocketReturn(G(), numTrials, numSpins, False)  # Executa a simulação\n",
        "        # Calcula o retorno médio e exibe\n",
        "        print('Retorno esperado para', G(), '=',\n",
        "              str(100 * sum(pocketReturns) / float(len(pocketReturns))) + '%')\n"
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            "\n",
            "Simulação de aposta num pocket por 20 tentativas de 100 giros cada.\n",
            "Retorno esperado para Fair Roulette = 6.199999999999998%\n",
            "\n",
            "Simulação de aposta num pocket por 20 tentativas de 1000 giros cada.\n",
            "Retorno esperado para Fair Roulette = 5.840000000000001%\n",
            "\n",
            "Simulação de aposta num pocket por 20 tentativas de 10000 giros cada.\n",
            "Retorno esperado para Fair Roulette = -1.846%\n",
            "\n",
            "Simulação de aposta num pocket por 20 tentativas de 100000 giros cada.\n",
            "Retorno esperado para Fair Roulette = 0.6002000000000001%\n",
            "\n",
            "Simulação de aposta num pocket por 20 tentativas de 100 giros cada.\n",
            "Retorno esperado para European Roulette = 8.0%\n",
            "\n",
            "Simulação de aposta num pocket por 20 tentativas de 1000 giros cada.\n",
            "Retorno esperado para European Roulette = -6.039999999999998%\n",
            "\n",
            "Simulação de aposta num pocket por 20 tentativas de 10000 giros cada.\n",
            "Retorno esperado para European Roulette = -3.196%\n",
            "\n",
            "Simulação de aposta num pocket por 20 tentativas de 100000 giros cada.\n",
            "Retorno esperado para European Roulette = -2.4076%\n",
            "\n",
            "Simulação de aposta num pocket por 20 tentativas de 100 giros cada.\n",
            "Retorno esperado para American Roulette = 2.5999999999999988%\n",
            "\n",
            "Simulação de aposta num pocket por 20 tentativas de 1000 giros cada.\n",
            "Retorno esperado para American Roulette = -9.099999999999998%\n",
            "\n",
            "Simulação de aposta num pocket por 20 tentativas de 10000 giros cada.\n",
            "Retorno esperado para American Roulette = -5.878%\n",
            "\n",
            "Simulação de aposta num pocket por 20 tentativas de 100000 giros cada.\n",
            "Retorno esperado para American Roulette = -5.129199999999999%\n"
          ]
        }
      ]
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      "source": [
        "## **Avaliação das médias e dispersões dos experimentos simulados**\n",
        "\n",
        "A função `getMeanAndStd` calcula a média e o desvio padrão de uma lista de valores, fornecendo informações estatísticas para análise de resultados de simulações:\n",
        "\n",
        "* Calcula a **média** (μ) como a soma dos valores dividida pelo tamanho da lista.\n",
        "* Para cada elemento, calcula o quadrado da diferença em relação à média e soma esses valores.\n",
        "* Calcula o **desvio padrão** (σ) como a raiz quadrada da soma das diferenças ao quadrado dividida pelo tamanho da lista.\n",
        "\n",
        "**Intervalo de 95% de Confiança**\n",
        "\n",
        "O intervalo de confiança de 95% é calculado usando o desvio padrão:\n",
        "𝐼𝐶 = média ± 1.96 * desvio padrão.\n",
        "Isso significa que o retorno verdadeiro estará dentro do intervalo calculado.\n"
      ],
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        "def getMeanAndStd(X):\n",
        "    \"\"\"\n",
        "    Calcula a média e o desvio padrão de uma lista de valores.\n",
        "\n",
        "    Parâmetros:\n",
        "    - X: Lista ou array de números.\n",
        "\n",
        "    Retorna:\n",
        "    - Uma tupla contendo:\n",
        "        1. A média dos valores.\n",
        "        2. O desvio padrão dos valores.\n",
        "    \"\"\"\n",
        "    mean = sum(X) / float(len(X))  # Calcula a média\n",
        "    tot = 0.0\n",
        "    for x in X:\n",
        "        tot += (x - mean) ** 2  # Soma dos quadrados das diferenças em relação à média\n",
        "    std = (tot / len(X)) ** 0.5  # Calcula o desvio padrão\n",
        "    return mean, std\n",
        "\n",
        "\n",
        "# Configuração inicial da simulação\n",
        "random.seed(0)  # Define uma semente para resultados reproduzíveis\n",
        "numTrials = 20  # Número de experimentos independentes\n",
        "resultDict = {}  # Dicionário para armazenar os resultados\n",
        "games = (FairRoulette, EuRoulette, AmRoulette)  # Tipos de roletas\n",
        "\n",
        "# Simulação\n",
        "for G in games:\n",
        "    resultDict[G().__str__()] = []  # Inicializa os resultados para cada tipo de roleta\n",
        "    for numSpins in (100, 1000, 10000):  # Diferentes tamanhos de giros\n",
        "        print('\\nSimulação de uma aposta num pocket por', numTrials,\n",
        "              'tentativas de', numSpins, 'giros cada.')\n",
        "\n",
        "        # Calcula os retornos para apostas em um número específico\n",
        "        pocketReturns = findPocketReturn(G(), numTrials, numSpins, False)\n",
        "        mean, std = getMeanAndStd(pocketReturns)  # Calcula a média e o desvio padrão\n",
        "        resultDict[G().__str__()].append((numSpins, 100 * mean, 100 * std))\n",
        "\n",
        "        # Imprime os resultados com intervalo de confiança de 95%\n",
        "        print('Retorno esperado para', G(), '=',\n",
        "              str(round(100 * mean, 3)) + '%, +/- ' +\n",
        "              str(round(100 * 1.96 * std, 3)) +\n",
        "              '% com 95% confiança')\n"
      ],
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        "outputId": "0b8d8613-ed0a-4ea3-d37d-3119af505195"
      },
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "Simulação de uma aposta num pocket por 20 tentativas de 100 giros cada.\n",
            "Retorno esperado para Fair Roulette = 6.2%, +/- 152.114% com 95% confiança\n",
            "\n",
            "Simulação de uma aposta num pocket por 20 tentativas de 1000 giros cada.\n",
            "Retorno esperado para Fair Roulette = 5.84%, +/- 39.752% com 95% confiança\n",
            "\n",
            "Simulação de uma aposta num pocket por 20 tentativas de 10000 giros cada.\n",
            "Retorno esperado para Fair Roulette = -1.846%, +/- 10.556% com 95% confiança\n",
            "\n",
            "Simulação de uma aposta num pocket por 20 tentativas de 100 giros cada.\n",
            "Retorno esperado para European Roulette = 13.4%, +/- 145.078% com 95% confiança\n",
            "\n",
            "Simulação de uma aposta num pocket por 20 tentativas de 1000 giros cada.\n",
            "Retorno esperado para European Roulette = -1.72%, +/- 40.046% com 95% confiança\n",
            "\n",
            "Simulação de uma aposta num pocket por 20 tentativas de 10000 giros cada.\n",
            "Retorno esperado para European Roulette = -4.384%, +/- 10.952% com 95% confiança\n",
            "\n",
            "Simulação de uma aposta num pocket por 20 tentativas de 100 giros cada.\n",
            "Retorno esperado para American Roulette = 8.0%, +/- 126.222% com 95% confiança\n",
            "\n",
            "Simulação de uma aposta num pocket por 20 tentativas de 1000 giros cada.\n",
            "Retorno esperado para American Roulette = -5.68%, +/- 28.012% com 95% confiança\n",
            "\n",
            "Simulação de uma aposta num pocket por 20 tentativas de 10000 giros cada.\n",
            "Retorno esperado para American Roulette = -5.698%, +/- 11.12% com 95% confiança\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **Análise Comparativa: impacto das regras de diferentes roletas nos retornos esperados**\n",
        "\n",
        "A função `plotReturn` tem por objetivo criar um gráfico de barras de erro que representa os retornos esperados em diferentes tipos de roletas com base em experimentos simulados, tendo em vista visualizar:\n",
        "\n",
        "* O comportamento dos retornos esperados em função do número de giros.\n",
        "* A comparação entre diferentes tipos de roletas.\n",
        "\n",
        "Cada tipo de roleta (Fair, European, American) apresenta uma curva específica  para comparação visual.\n",
        "* O eixo x representa o número de giros por tentativa (em escala logarítmica).\n",
        "* O eixo y representa os retornos esperados em porcentagem.\n",
        "* As barras de erro indicam a variabilidade dos retornos (desvios padrão).\n"
      ],
      "metadata": {
        "id": "Q86P-HjeMuMe"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def plotReturn(resultDict):\n",
        "    \"\"\"\n",
        "    Gera um gráfico que visualiza os retornos esperados em diferentes tipos de roleta,\n",
        "    com base nos dados fornecidos em `resultDict`.\n",
        "\n",
        "    Parâmetros:\n",
        "    - resultDict: Dicionário onde cada chave é o nome de um tipo de roleta\n",
        "      e o valor é uma lista de tuplas contendo:\n",
        "        1. Número de giros (spins) por experimento.\n",
        "        2. Retorno médio esperado em porcentagem.\n",
        "        3. Desvio padrão em porcentagem.\n",
        "\n",
        "    Retorno:\n",
        "    - Nenhum. Exibe um gráfico diretamente.\n",
        "    \"\"\"\n",
        "    for k in resultDict:  # Itera sobre os diferentes tipos de roleta\n",
        "        xVals, yVals, eVals = [], [], []  # Listas para armazenar dados do eixo x, y e erros\n",
        "        for trial in resultDict[k]:  # Para cada experimento realizado\n",
        "            xVals.append(trial[0])  # Número de giros por experimento\n",
        "            yVals.append(trial[1])  # Retorno médio esperado\n",
        "            eVals.append(trial[2])  # Desvio padrão\n",
        "\n",
        "        # Adiciona uma barra de erro para os dados\n",
        "        pylab.errorbar(xVals, yVals, yerr=eVals, label=k, marker='o')\n",
        "\n",
        "    # Configuração do gráfico\n",
        "    pylab.legend()  # Adiciona uma legenda\n",
        "    pylab.xlabel('Giros por tenativa', fontsize='x-large')  # Rótulo do eixo x\n",
        "    pylab.ylabel('Retorno percentual esperado', fontsize='x-large')  # Rótulo do eixo y\n",
        "    pylab.title('Retorno esperado de uma aposta num Pocket', fontsize='x-large')  # Título do gráfico\n",
        "    pylab.semilogx()  # Escala logarítmica para o eixo x\n",
        "\n",
        "    # Ajusta os limites do eixo x\n",
        "    minX, maxX = pylab.xlim()\n",
        "    pylab.xlim(1, maxX + 100000)  # Define o limite superior como 100.000 giros além do máximo\n",
        "\n",
        "# Imprime a função\n",
        "plotReturn(resultDict)\n",
        "\n",
        "# Linha para depuração\n",
        "# assert False"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 482
        },
        "id": "jEf9V4x3MHrP",
        "outputId": "03a401fe-f42c-4dc6-aec4-d65e2d19c2df"
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **Histograma da distribuição dos valores individuais de um dado contínuo e das médias de 50 lançamentos**\n",
        "\n",
        "A função `plotMeans` simula o lançamento de \"dados contínuos\" (ou seja, números aleatórios entre 0 e 5) e calcula as médias dos valores obtidos. Os resultados são apresentados no histograma abaixo, que exibe a distribuição das médias.\n",
        "\n",
        "1. **Primeira simulação**:\n",
        "\n",
        "* **Configuração**: 1 dado, 100.000 lançamentos.\n",
        "O histograma mostra a distribuição dos valores individuais de um dado contínuo, a média e o desvio padrão.\n",
        "\n",
        "2. **Segunda simulação**:\n",
        "\n",
        "* **Configuração**: 50 dados lançados simultaneamente, 100.000 lançamentos no total. O histograma mostra a distribuição das médias de 50 lançamentos, a média e o desvio padrão."
      ],
      "metadata": {
        "id": "12Kx6m83OVnO"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def plotMeans(numDice, numRolls, numBins, legend, color, style):\n",
        "    \"\"\"\n",
        "    Calcula as médias de valores obtidos ao lançar múltiplos \"dados contínuos\"\n",
        "    várias vezes e gera um histograma dessas médias.\n",
        "\n",
        "    Parâmetros:\n",
        "    - numDice: Número de \"dados contínuos\" lançados em cada iteração.\n",
        "    - numRolls: Número total de lançamentos realizados.\n",
        "    - numBins: Número de intervalos (bins) no histograma.\n",
        "    - legend: Rótulo para a legenda do histograma.\n",
        "    - color: Cor usada no histograma.\n",
        "    - style: Estilo do preenchimento do histograma (hatch).\n",
        "\n",
        "    Retorna:\n",
        "    - Uma tupla contendo:\n",
        "        1. A média das médias calculadas.\n",
        "        2. O desvio padrão das médias calculadas.\n",
        "    \"\"\"\n",
        "    means = []  # Lista para armazenar as médias dos valores dos lançamentos\n",
        "\n",
        "    for i in range(numRolls // numDice):  # Número de rodadas\n",
        "        vals = 0\n",
        "        for j in range(numDice):  # Simula o lançamento de `numDice` dados\n",
        "            vals += 5 * random.random()  # Valor aleatório entre 0 e 5\n",
        "        means.append(vals / float(numDice))  # Calcula a média e armazena\n",
        "\n",
        "    # Criação do histograma\n",
        "    pylab.hist(means, numBins, color=color, label=legend,\n",
        "               weights=pylab.array(len(means) * [1.0]) / len(means),\n",
        "               hatch=style, alpha=0.5, edgecolor='black') # adicionando transparência e bordas\n",
        "\n",
        "    return pylab.mean(means), pylab.std(means)  # Retorna a média e o desvio padrão das médias\n",
        "\n",
        "# Simulação e visualização\n",
        "mean, std = plotMeans(1, 100000, 11, '1 dado', 'blue', '*')\n",
        "print('Média de 1 dado =', mean, 'Desvio Padrão =', std)\n",
        "\n",
        "mean, std = plotMeans(50, 100000, 11, 'Média de 50 dados', 'red', '//')\n",
        "print('Média de 50 dados =', mean, 'Desvio Padrão =', std)\n",
        "\n",
        "# Configuração do gráfico\n",
        "pylab.title('Lançamento de Dados Contínuos')  # Título do gráfico em português\n",
        "pylab.xlabel('Valor')  # Rótulo do eixo x em português\n",
        "pylab.ylabel('Probabilidade')  # Rótulo do eixo y em português\n",
        "pylab.legend()  # Adiciona a legenda\n",
        "pylab.grid(True) # adicionando grid\n",
        "pylab.tight_layout() # ajustando o layout para evitar sobreposição de elementos\n",
        "pylab.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 524
        },
        "id": "IqS7kV1iWGnp",
        "outputId": "22cb83fc-9ec6-47be-c58a-4b059c5fd828"
      },
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Média de 1 dado = 2.495633755957571 Desvio Padrão = 1.4430163217178154\n",
            "Média de 50 dados = 2.498897433270734 Desvio Padrão = 0.20708713919719593\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "* O histograma da primeira simulação (1 dado) apresenta uma distribuição uniforme entre 0 e 5.\n",
        "* O histograma da segunda simulação (50 dados) tem uma distribuição mais estreita (desvio padrão menor), centrada em 2.5."
      ],
      "metadata": {
        "id": "ujKpNJ63ZX0e"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **Implementando a estratégia de apostas Martingale**\n",
        "\n",
        "A função `leaveAhead` implementa uma estratégia de apostas, conhecida como *Martingale*, onde o jogador dobra a aposta após cada perda, com o objetivo de recuperar as perdas anteriores e ainda obter lucro. O objetivo é determinar a probabilidade de o jogador terminar com um saldo maior que o inicial (`stake`) após um número definido de simulações (`numTrials`).\n",
        "\n",
        "**Lógica da Estratégia**:\n",
        "\n",
        "1. O jogador começa com um saldo inicial (`stake`) e uma aposta inicial (`bet`), a cada rodada:\n",
        "* O jogador aposta no preto (`betBlack`).\n",
        "* Se perder, dobra o valor da aposta para tentar recuperar a perda anterior.\n",
        "* Se ganhar, o saldo (`bankRoll`) é atualizado e a aposta é redefinida.\n",
        "2. O jogador continua apostando até:\n",
        "* Perder todo o dinheiro.\n",
        "* Dobrar o saldo inicial (condição de sucesso).\n"
      ],
      "metadata": {
        "id": "hfo-Rx75QeMz"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def leaveAhead(game, stake, bet, numTrials):\n",
        "    \"\"\"\n",
        "    Simula uma estratégia de apostas onde o jogador tenta dobrar seu capital inicial\n",
        "    (stake) e avalia a probabilidade de sair ganhando.\n",
        "\n",
        "    Parâmetros:\n",
        "    - game: Objeto do jogo de roleta (ex.: AmRoulette).\n",
        "    - stake: Quantidade inicial de dinheiro do jogador.\n",
        "    - bet: Valor inicial de cada aposta.\n",
        "    - numTrials: Número de simulações a serem realizadas.\n",
        "\n",
        "    Retorna:\n",
        "    - A probabilidade de o jogador sair ganhando ao final das simulações.\n",
        "    \"\"\"\n",
        "    numAhead = 0.0  # Contador de sucessos (jogador sai com lucro)\n",
        "\n",
        "    for t in range(numTrials):  # Realiza as simulações\n",
        "        bankRoll = stake  # Define o saldo inicial\n",
        "        curBet = bet  # Define o valor inicial da aposta\n",
        "\n",
        "        # Enquanto o jogador ainda tiver dinheiro e o saldo for menor que o dobro do stake\n",
        "        while bankRoll > 0 and bankRoll <= 2 * stake:\n",
        "            game.spin()  # Gira a roleta\n",
        "            outcome = game.betBlack(curBet)  # Resultado da aposta no preto\n",
        "            bankRoll += outcome  # Atualiza o saldo do jogador\n",
        "\n",
        "            # Se perder a aposta, dobra o valor da próxima (estratégia tipo Martingale)\n",
        "            if outcome < 0:\n",
        "                curBet = min(2 * curBet, bankRoll)  # Garante que não aposte mais do que possui\n",
        "\n",
        "        # Se o saldo final for maior que o stake inicial, conta como sucesso\n",
        "        if bankRoll > stake:\n",
        "            numAhead += 1\n",
        "\n",
        "    return numAhead / numTrials  # Calcula a probabilidade de sucesso\n",
        "\n",
        "# Configuração inicial da simulação\n",
        "stake = 1  # Capital inicial do jogador\n",
        "bet = 1  # Valor da aposta inicial\n",
        "numTrials = 100000  # Número de simulações\n",
        "successProb, stakes = [], []  # Listas para armazenar probabilidades e stakes\n",
        "\n",
        "# Realiza as simulações para diferentes valores de stake\n",
        "for i in range(10):\n",
        "    stakes.append(10 ** i)  # Varia o stake de 1 a 10^9\n",
        "    successProb.append(leaveAhead(AmRoulette(), 10 ** i, bet, numTrials))\n",
        "\n",
        "# Gera o gráfico com os resultados\n",
        "pylab.plot(stakes, successProb)  # Plota probabilidade de ganhar vs stake\n",
        "pylab.xlabel('Saldo (\"Bankroll\")')  # Rótulo do eixo x\n",
        "pylab.ylabel('Probabilidade de ganhar')  # Rótulo do eixo y\n",
        "pylab.semilogx()  # Usa escala logarítmica no eixo x\n",
        "pylab.show()  # Exibe o gráfico\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 454
        },
        "id": "iiwWHi5eQKv1",
        "outputId": "b69bee02-3c75-4a41-ed00-70ab9331aeab"
      },
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "O gráfico gerado mostra a probabilidade de sucesso (eixo y) em função do capital inicial (`stake`, eixo x) em escala logarítmica. Para apostas (`stakes`) pequenas, a probabilidade de sucesso é relativamente alta (mais próxima de 1). À medida que a aposta aumenta, a probabilidade de sucesso diminui rapidamente, pois o jogador enfrenta o risco de perder tudo antes de atingir o dobro do capital inicial."
      ],
      "metadata": {
        "id": "2LoFMkd7aYt1"
      }
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "jumRPDS0RIuS"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}