Grüfello - Alles wird gut

alles_wird_gut.ipynb

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    "# Grüffelo - Alles wird gut\n",
    "* See this link for the actual game: [Schmidt Spiele](https://www.schmidtspiele-shop.de/der-grueffelo-alles-wird-gut)\n",
    "* This script calculates the chances to win - you'll win in exactly 8 of 9 games."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
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   "source": [
    "from dataclasses import dataclass\n",
    "from typing import Tuple, MutableSet\n",
    "from queue import LifoQueue\n",
    "\n",
    "\n",
    "@dataclass(frozen=True)\n",
    "class State:\n",
    "    position: int  # position of the mouse\n",
    "    predators: Tuple[int]  # uncovered pieces per predator"
   ]
  },
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   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
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     "name": "stdout",
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     "text": [
      "Chance to win is 88.8889 %\n"
     ]
    }
   ],
   "source": [
    "open_states: LifoQueue[State] = LifoQueue()\n",
    "open_states.put(State(position=0, predators=(0, 0, 0)))\n",
    "\n",
    "visited_states: MutableSet[State] = set()\n",
    "\n",
    "wins, losses = 0, 0\n",
    "\n",
    "while not open_states.empty():\n",
    "    state = open_states.get()\n",
    "\n",
    "    if state in visited_states:\n",
    "        # preventing loops by storing already visited states\n",
    "        # loops in gameplay are possible (reaching same state after some dice rolls)\n",
    "        continue\n",
    "    \n",
    "    visited_states.add(state)\n",
    "\n",
    "    for dice in range(1, 7):\n",
    "\n",
    "        if dice <= 3:\n",
    "            # corresponds to going 1, 2 or 3 steps with the mouse\n",
    "            if state.position + dice >= 31:\n",
    "                wins += 1\n",
    "            else:\n",
    "                open_states.put(State(state.position + dice, state.predators))\n",
    "\n",
    "        elif state.predators[dice - 4] < 4:\n",
    "            # for predetor 0, 1 or 2 check if not all 4 pieces are uncovered\n",
    "            predators = list(state.predators)\n",
    "            predators[dice - 4] += 1\n",
    "\n",
    "            if predators == [4, 4, 4]:\n",
    "                losses += 1\n",
    "            else:\n",
    "                open_states.put(State(state.position, tuple(predators)))\n",
    "\n",
    "        elif state.position not in (0, 4, 7, 12, 14, 17, 21, 24, 27):\n",
    "            # if a predator piece is already fully uncovered, go one step back if possible\n",
    "            open_states.put(State(state.position - 1, state.predators))\n",
    "\n",
    "print(f'Chance to win is {wins / (wins + losses) * 100:.3f} %')"
   ]
  }
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