hw10_Gamblers_ruin.ipynb

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     "text": [
      "Estimate: 2.40x10^-6 ± 0.17x10^-6\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "import math\n",
    "\n",
    "N = 3000\n",
    "K = 600\n",
    "p = 18/37\n",
    "q = 0.55\n",
    "\n",
    "def deter_win(Y,p,q):\n",
    "    money = 100\n",
    "    temp = 1\n",
    "    for idx in range(len(Y)):\n",
    "        if Y[idx] == 1:\n",
    "            money += 1\n",
    "            temp *= (p/q)\n",
    "        else :\n",
    "            money -= 1\n",
    "            temp *= ((1-p)/(1-q))\n",
    "\n",
    "        if money == 200 :\n",
    "            return 1 * temp\n",
    "        elif money == 0 :\n",
    "            return 0 * temp\n",
    "    return 0 * temp\n",
    "\n",
    "\n",
    "probability = q * torch.ones(K,1)\n",
    "temp = []\n",
    "for experiment in range(N):\n",
    "    Y = torch.bernoulli(probability)\n",
    "    temp.append(deter_win(Y,p,q))\n",
    "\n",
    "samp = torch.tensor(temp)\n",
    "Ihat,s = samp.mean(), samp.var()\n",
    "print(f\"Estimate: {Ihat*1000000:.2f}x10^-6 ± {math.sqrt(s/N)*1000000:.2f}x10^-6\")"
   ]
  },
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   "source": []
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