Ark Mutation Chances

Ark Mutations.ipynb

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   "source": [
    "# Ark Mutation Chances\n",
    "\n",
    "Calculates, and then simulates, the chances of a given number of mutations occurring in Ark.\n",
    "\n",
    "Assumes BOTH parents can contribute mutations (i.e. both are <20 mutations).\n",
    "\n",
    "If only one parent can contribute mutations, all chances are halved."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "C = 0.025    # Chance to mutate on each roll\n",
    "rolls = 3    # There are three chances to mutate each time"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculate the chances using the list of possible outcomes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Outcome chances:\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[(0.975, 0.975, 0.975),\n",
       " (0.975, 0.975, 0.025),\n",
       " (0.975, 0.025, 0.975),\n",
       " (0.975, 0.025, 0.025),\n",
       " (0.025, 0.975, 0.975),\n",
       " (0.025, 0.975, 0.025),\n",
       " (0.025, 0.025, 0.975),\n",
       " (0.025, 0.025, 0.025)]"
      ]
     },
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     "name": "stdout",
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     "text": [
      "Chance of exact number of mutations:\n",
      "  0: 92.685937%\n",
      "  1:  7.129687%\n",
      "  2:  0.182813%\n",
      "  3:  0.001563%\n",
      "\n",
      "Total: 0.9999999999999999 (should ~= 1)\n",
      "  (floating point accuracy makes this unlikely to be exact)\n",
      "\n",
      "Chance of 'at least N' mutations:\n",
      "  1:  7.314063%\n",
      "  2:  0.184375%\n",
      "  3:  0.001563%\n"
     ]
    }
   ],
   "source": [
    "from itertools import product\n",
    "from functools import reduce\n",
    "from operator import mul\n",
    "\n",
    "# Gather a list of possible outcomes\n",
    "outcomes = list(product((1-C, C), repeat=rolls))\n",
    "print(\"Outcome chances:\")\n",
    "display(outcomes)\n",
    "\n",
    "# Add up chances for number of mutations in each outcome\n",
    "mut_count_chances = {n: 0 for n in range(rolls+1)}\n",
    "for outcome in outcomes:\n",
    "    muts = sum(1 for chance in outcome if chance == C)\n",
    "    outcome_chance = reduce(mul, outcome, 1)\n",
    "    mut_count_chances[muts] += outcome_chance\n",
    "    \n",
    "print(\"Chance of exact number of mutations:\")\n",
    "for muts,chance in mut_count_chances.items():\n",
    "    print(f\"  {muts}: {chance*100:9.6f}%\")\n",
    "\n",
    "print(f\"\\nTotal: {sum(mut_count_chances.values())} (should ~= 1)\")\n",
    "print(\"  (floating point accuracy makes this unlikely to be exact)\\n\")\n",
    "\n",
    "# Add chance of greater mutations for 'at least N mutations'\n",
    "at_least_chances = dict()\n",
    "for muts in range(1, rolls+1):\n",
    "    at_least_chances[muts] = sum(mut_count_chances[n] for n in range(muts, rolls+1))\n",
    "    \n",
    "print(\"Chance of 'at least N' mutations:\")\n",
    "for muts,chance in at_least_chances.items():\n",
    "    print(f\"  {muts}: {chance*100:9.6f}%\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulate 10 million runs to verify"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mutations in simulation:\n",
      "  0: 92.686610%\n",
      "  1:  7.128360%\n",
      "  2:  0.183400%\n",
      "  3:  0.001630%\n"
     ]
    }
   ],
   "source": [
    "from collections import Counter\n",
    "from random import random\n",
    "\n",
    "counter = Counter()\n",
    "\n",
    "runs = 10_000_000\n",
    "for i in range(runs):\n",
    "    muts = sum(random() <= C for roll in range(rolls))\n",
    "    counter.update({muts: 1})\n",
    "    \n",
    "print(\"Mutations in simulation:\")\n",
    "for roll in range(rolls+1):\n",
    "    print(f\"  {roll}: {counter[roll]/runs*100:9.6f}%\")"
   ]
  }
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