2_hsr_gacha_system.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Gacha System Explained\n",
    "> Credits to [KokomiClan](https://www.youtube.com/watch?v=gZGW190E3ok) for the wonderful explanation\n",
    "\n",
    "## How to get 5 star?\n",
    "\n",
    "We will get a 5 star if we have a random number <= pull rate given by the banner. Random number is generated on the server evenly between 0 and 1. Below is the algorithm:\n",
    "\n",
    "```py\n",
    "def get_rate(warp):\n",
    "    # base rate same until we reach 74th pull\n",
    "    if warp < 74:\n",
    "        return 0.06\n",
    "    \n",
    "    # after 73th pull, the rate increase 6% per pull until 90 pull\n",
    "    elif warp < 90 and warp >= 74:\n",
    "        return (warp - 73) * 0.06 + 0.006\n",
    "    \n",
    "    else:\n",
    "        return 1.00\n",
    "```\n",
    "\n",
    "## The Distribution of Successful Pull\n",
    "\n",
    "### For warp < 74\n",
    "It is just geometric distribution:\n",
    "\n",
    "```\n",
    "warp < 74\n",
    "\n",
    "prob(5_star in X wrap) = 1 - (prob(no 5_star))^warp\n",
    "             = 1 - (1 - 0.006)^warp\n",
    "\n",
    "prob(X < 40) = 1 - (1 - 0.006)^40 = 0.2139\n",
    "```\n",
    "\n",
    "If we want to know the probability of getting 5-star in the 40 pull:\n",
    "\n",
    "```\n",
    "prob(X = 40) = prob(X < 40) - prob(X < 39)\n",
    "```\n",
    "\n",
    "### For warp >= 74\n",
    "The rate will change with warp, taking the previous rate into consideration:\n",
    "\n",
    "```\n",
    "P(X < 74) = P(X < 73) + (1 - P(X < 73)) * get_rate(74)\n",
    "P(X < 75) = (1 - P(X < 73)) * get_rate_mult(75) * get_rate(75) + P(X < 74)\n",
    "P(X < 76) = (1 - P(X < 73)) * get_rate_mult(76) * get_rate(76) + P(X < 75) + P(X < 74)\n",
    "\n",
    "...\n",
    "\n",
    "```\n",
    "\n",
    "Recursive rate algorithm:\n",
    "\n",
    "```py\n",
    "def get_rate_mult(warp):\n",
    "    if warp == 75:\n",
    "        return 1 - get_rate(74)\n",
    "    \n",
    "    else:\n",
    "        return (1 - get_rate(warp - 1)) * get_rate_mult(warp - 1)\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# pull rate graph visualization\n",
    "\n",
    "# function to get rate\n",
    "def get_rate(warp):\n",
    "    # base rate same until we reach 74th pull\n",
    "    if warp < 74:\n",
    "        return 0.06\n",
    "    \n",
    "    # after 73th pull, the rate increase 6% per pull until 90 pull\n",
    "    elif warp < 90 and warp >= 74:\n",
    "        return (warp - 73) * 0.06 + 0.006\n",
    "    \n",
    "    else:\n",
    "        return 1.00\n",
    "\n",
    "# test\n",
    "x = []\n",
    "for i in range(1,91):\n",
    "    x.append(get_rate(i))\n",
    "    \n",
    "# plot\n",
    "import matplotlib.pyplot as plt\n",
    "plt.plot(x)\n",
    "plt.xlabel('pull')\n",
    "plt.ylabel('rate')\n",
    "plt.plot(x, 'ro')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the rate increases significantly after 74 pull which leads us to a higher chance of getting 5 star. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average pull for a 5 star including guarantee: 62.310438\n",
      "Consolidated probability rate: 1.6%\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x1200 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# warp simulation\n",
    "\n",
    "\n",
    "import numpy as np\n",
    "from numba import jit\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import geom\n",
    "\n",
    "# plot setting\n",
    "plt.rcParams['figure.figsize'] = [10, 12]\n",
    "\n",
    "N = 1000000\n",
    "\n",
    "\n",
    "@jit(nopython=True, parallel=True)\n",
    "def simulate():\n",
    "    # Pre-allocate the array\n",
    "    five_star = np.zeros((N,))\n",
    "\n",
    "    # Simulate random uniform numbers\n",
    "    random_numbers = np.random.uniform(0, 1, N * 90) # We use N * 90 since hard pity is at 90 pulls, i.e. upper bound\n",
    "\n",
    "    for i in range(N):\n",
    "        for j in range(1, 91):\n",
    "            if random_numbers[i * 90 + j] <= get_rate(j):\n",
    "                five_star[i] = j\n",
    "                break\n",
    "\n",
    "    return five_star\n",
    "\n",
    "\n",
    "# Define the pull rate function\n",
    "@jit(nopython=True)\n",
    "def get_rate(x: float):\n",
    "    # Normal pulls\n",
    "    if x < 74:\n",
    "        return 0.006\n",
    "    # Soft pity -> Hard Pity Ramp\n",
    "    elif 74 <= x < 90:\n",
    "        return (x - 73) * 0.06 + 0.006\n",
    "    else:\n",
    "        return 1.0\n",
    "\n",
    "\n",
    "# For the soft pity, we need to add this to the probabilities - recursive function since it depends on the previous\n",
    "def get_rate_mult(x: float):\n",
    "    if x == 75:\n",
    "        return 1 - get_rate(74)\n",
    "    else:\n",
    "        return (1 - get_rate(x - 1)) * get_rate_mult(x - 1)\n",
    "\n",
    "\n",
    "# Define a probability function\n",
    "def prob(x, cumulative=False, rate=False):\n",
    "    # Pre-allocate the array\n",
    "    output = np.zeros((x.size, ))\n",
    "\n",
    "    # Cumulative Probabilities above 75 need to be calculated differently using recursion\n",
    "    plus_75 = [(1 - geom.cdf(73, 0.006)) * get_rate_mult(i) * get_rate(i) for i in range(75, 90)]\n",
    "    plus_75 = np.cumsum(plus_75) + geom.cdf(73, 0.006) + (1 - geom.cdf(73, 0.006)) * get_rate(74)\n",
    "\n",
    "    # Calculate cumulative probabilities\n",
    "    for ii in range(x.size):\n",
    "        if x[ii] < 74:\n",
    "        # In simple english: 1 - (1 - 0.006) ^ ii, or 1 - probability of not getting a 5 star in ii pulls\n",
    "            output[ii] = geom.cdf(x[ii], 0.006)\n",
    "        elif x[ii] == 74:\n",
    "            # In simple english: Probability of getting it in 73 pulls, then getting it on the 74th pull which is\n",
    "            # the rate of getting it multiplied by the probability of not getting it in 73 pulls\n",
    "            output[ii] = geom.cdf(73, 0.006) + (1 - geom.cdf(73, 0.006)) * get_rate(74)\n",
    "        elif 75 <= x[ii] < 90:\n",
    "            # Some recursive magic xD.\n",
    "            output[ii] = plus_75[int(x[ii]) - 75]\n",
    "        else:\n",
    "            output[ii] = 1\n",
    "\n",
    "        if rate:\n",
    "            output[ii] = get_rate(x[ii])\n",
    "\n",
    "    if not cumulative:\n",
    "        output = np.insert(np.diff(output), 0, 0.006)\n",
    "\n",
    "    return output\n",
    "\n",
    "\n",
    "\n",
    "results = simulate()\n",
    "\n",
    "# Print the output\n",
    "print(\"Average pull for a 5 star including guarantee: {}\".format(results.mean()))\n",
    "\n",
    "# Plot the histogram of the results\n",
    "ax, fig = plt.subplots(3, 1)\n",
    "plt.subplot(3, 1, 1)\n",
    "plt.hist(results, bins=45, density='True')\n",
    "\n",
    "# Get the probability distribution, cumulative distribution and pull rates\n",
    "x = np.linspace(1, 90, 90, dtype=float)\n",
    "y_prob = prob(x)\n",
    "y_cum_prob = prob(x, cumulative=True)\n",
    "y_rate = [get_rate(x) for x in range(1, 91)]\n",
    "\n",
    "# Plot the results of probability distribution\n",
    "plt.plot(x, y_prob, 'r')\n",
    "plt.title(\"Probability distribution of 5 star pulls\")\n",
    "\n",
    "# Cumulative rates\n",
    "plt.subplot(3, 1, 2)\n",
    "plt.title(\"Cumulative probability distribution of 5 star pulls\")\n",
    "plt.plot(x, y_cum_prob, 'b')\n",
    "plt.grid()\n",
    "\n",
    "# Pull rates\n",
    "plt.subplot(3, 1, 3)\n",
    "plt.title(\"Pull rates of 5 star pulls\")\n",
    "plt.plot(x, y_rate, 'b')\n",
    "\n",
    "# Finally, working out the consolidated probability rate:\n",
    "print(\"Consolidated probability rate: {:.2}%\".format((1 / (y_prob @ np.arange(1, 91))) * 100))\n",
    "\n",
    "# Save the output\n",
    "np.savetxt(\"data/y_prob.csv\", y_prob, delimiter=',')\n",
    "np.savetxt(\"data/y_cum_prob.csv\", y_cum_prob, delimiter=',')\n",
    "np.savetxt(\"data/y_rate.csv\", y_rate, delimiter=',')\n",
    "\n",
    "\n",
    "# save the image plot\n",
    "plt.savefig('image/image1.png')"
   ]
  }
 ],
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