lmoureaux/freeciv-combat.ipynb

## freeciv-combat.ipynb
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import random as rnd\n",
    "import scipy as sp\n",
    "from scipy.special import binom"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ruleset definitions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "veteran_raise_chance = [50, 45, 40, 35, 30, 25, 20, 15, 10, 0]\n",
    "veteran_power_factor = [100, 150, 175, 200, 225, 250, 275, 300, 325, 350]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Units"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "# strength (excl. level), hp, firepower, level\n",
    "trireme = (1, 10, 1, 0)\n",
    "\n",
    "cannon = (8, 20, 2, 0)\n",
    "vcannon = (8, 20, 2, 1)\n",
    "vvcannon = (8, 20, 2, 2)\n",
    "\n",
    "vcavalery = (8, 20, 1, 1)\n",
    "vvcavalery = (8, 20, 1, 2)\n",
    "vvvcavalery = (8, 20, 1, 3)\n",
    "\n",
    "vfanatics = (18, 20, 1, 1)\n",
    "vvfanatics = (18, 20, 1, 2)\n",
    "vvvfanatics = (18, 20, 1, 3)\n",
    "\n",
    "riflemen = (2.5*4*1.25*1.25, 20, 1, 0)\n",
    "vriflemen = (2.5*4*1.25*1.25, 20, 1, 1)\n",
    "vvriflemen = (2.5*4*1.25*1.25, 20, 1, 2)\n",
    "vvvriflemen = (2.5*4*1.25*1.25, 20, 1, 3)\n",
    "\n",
    "\n",
    "vvriflemen = (3*4*1.25*1.25, 20, 1, 2)\n",
    "\n",
    "musketeer = (2.5*3*1.25*1.25, 20, 1, 0)\n",
    "vmusketeer = (2.5*3*1.25*1.25, 20, 1, 1)\n",
    "vvmusketeer = (2.5*3*1.25*1.25, 20, 1, 2)\n",
    "\n",
    "attackers = [ trireme ] \n",
    "defenders = [ (2, 5, 1, 1), (2, 5, 1, 2), (2, 4, 1, 2) ]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Combat simulator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "def unit_strength(unit):\n",
    "    return unit[0] * veteran_power_factor[unit[3]] / 100.\n",
    "\n",
    "def unit_eff_strength(unit):\n",
    "    return unit_strength(unit) * unit[1] * unit[2]\n",
    "\n",
    "def simulate_combat(attacker, defender):\n",
    "    astrength, alife, afp, alevel = attacker\n",
    "    dstrength, dlife, dfp, dlevel = defender\n",
    "    astrength = unit_strength(attacker)\n",
    "    dstrength = unit_strength(defender)\n",
    "    while alife > 0 and dlife > 0:\n",
    "        if rnd.uniform(0, astrength + dstrength) > astrength:\n",
    "            # Defender wins the round\n",
    "            alife -= dfp\n",
    "        else:\n",
    "            # Attacker wins\n",
    "            dlife -= afp\n",
    "    if alife <= 0:\n",
    "        # Defender wins\n",
    "        alife = 0\n",
    "        raise_chance = veteran_raise_chance[dlevel]\n",
    "        if rnd.uniform(0, 100) < raise_chance:\n",
    "            dlevel += 1\n",
    "    else:\n",
    "        # Attacker wins\n",
    "        dlife = 0\n",
    "        raise_chance = veteran_raise_chance[alevel]\n",
    "        if rnd.uniform(0, 100) <= raise_chance:\n",
    "            alevel += 1\n",
    "    return (attacker[0], alife, afp, alevel), (defender[0], dlife, dfp, dlevel)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "combats_count = int(50000)\n",
    "cities_emptied = 0\n",
    "stacks_killed  = 0\n",
    "def_hp_left = np.zeros((len(defenders), defenders[0][1] + 1))\n",
    "\n",
    "for combat in range(combats_count):\n",
    "    dcopy = defenders[:]\n",
    "    for iatt in range(len(attackers)):\n",
    "        # Choose the best defender\n",
    "        defender = dcopy[0]\n",
    "        defender_strength = unit_eff_strength(defender)\n",
    "        idef = 0\n",
    "        for i in range(len(dcopy)):\n",
    "            if unit_eff_strength(dcopy[i]) > defender_strength:\n",
    "                defender = dcopy[i]\n",
    "                defender_strength = unit_eff_strength(dcopy[i])\n",
    "                idef = i\n",
    "        # Attack\n",
    "        attacker = attackers[iatt]\n",
    "        updated_attacker, updated_defender = simulate_combat(attacker, defender)\n",
    "        dcopy[idef] = updated_defender\n",
    "    # Harvest\n",
    "    all_def_dead = True\n",
    "    any_def_dead = False\n",
    "    for idef in range(len(dcopy)):\n",
    "        def_hp_left[idef][dcopy[idef][1]] += 1\n",
    "        if dcopy[idef][1] > 0:\n",
    "            all_def_dead = False\n",
    "        else:\n",
    "            any_def_dead = True\n",
    "    if all_def_dead:\n",
    "        cities_emptied += 1\n",
    "    if any_def_dead:\n",
    "        stacks_killed += 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "City emptying probability: 0.000000\n",
      "Stack kill probability: 0.181520\n"
     ]
    }
   ],
   "source": [
    "print(\"City emptying probability: %f\" % (cities_emptied / combats_count))\n",
    "print(\"Stack kill probability: %f\" % (stacks_killed / combats_count))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7efbd7eec5c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7efc1132c9e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7efbd7c4f908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def_hp_left_err = np.sqrt(def_hp_left) / combats_count\n",
    "\n",
    "for idef in range(len(defenders)):\n",
    "    plt.bar(np.arange(len(def_hp_left[idef])),\n",
    "            def_hp_left[idef] / combats_count,\n",
    "            yerr=def_hp_left_err[idef], \n",
    "            align='center',\n",
    "            alpha=0.5)\n",
    "    plt.ylim(0, 1)\n",
    "    plt.xlim(-0.5, defenders[0][1] + 0.5)\n",
    "    plt.title(\"HP of defender #%d\" % idef)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}