Calculate chance of success in an Arkham attack roll using brute force

Arkham Successes.ipynb

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   "source": [
    "# Arkham Successes\n",
    "_Calculate chance of success in an Arkham attack roll using brute force._"
   ]
  },
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     "text": [
      "  [- CURSED -]   |   [- NORMAL -]   |  [- BLESSED -]\n",
      "                 |                  |\n",
      "      successes  |       successes  |       successes\n",
      "dice  1   2   3  | dice  1   2   3  | dice  1   2   3\n",
      "  1  17%  -   -  |   1  33%  -   -  |   1  50%  -   - \n",
      "  2  31%  3%  -  |   2  56% 11%  -  |   2  75% 25%  - \n",
      "  3  42%  7%  0% |   3  70% 26%  4% |   3  88% 50% 12%\n",
      "  4  52% 13%  2% |   4  80% 41% 11% |   4  94% 69% 31%\n",
      "  5  60% 20%  4% |   5  87% 54% 21% |   5  97% 81% 50%\n",
      "  6  67% 26%  6% |   6  91% 65% 32% |   6  98% 89% 66%\n"
     ]
    }
   ],
   "source": [
    "from itertools import product\n",
    "\n",
    "# the most concurrent successes required in the game\n",
    "MAX_SUCCESSES_NEEDED = 3\n",
    "\n",
    "# table headers\n",
    "print(\"  [- CURSED -]   |   [- NORMAL -]   |  [- BLESSED -]\")\n",
    "print(\"                 |                  |\")\n",
    "print(\"      successes  |       successes  |       successes\")\n",
    "print(\"dice  1   2   3  | dice  1   2   3  | dice  1   2   3\")\n",
    "\n",
    "for n_dice in range(1, 7):\n",
    "    total = 0\n",
    "    \n",
    "    # used to count number of wins at various difficulties\n",
    "    # incrementing value at i means: we've won a roll where i successes are required\n",
    "    cursed_wins = [0] * (MAX_SUCCESSES_NEEDED + 1)\n",
    "    normal_wins = [0] * (MAX_SUCCESSES_NEEDED + 1)\n",
    "    blessed_wins = [0] * (MAX_SUCCESSES_NEEDED + 1)\n",
    "\n",
    "    # roll n_dice number of d6\n",
    "    for roll in product(range(1, 7), repeat=n_dice):\n",
    "        total += 1\n",
    "\n",
    "        # count how many of each value we got\n",
    "        counts = [0] * 7\n",
    "        for die in roll:\n",
    "            counts[die] += 1\n",
    "\n",
    "        # see how many successes we got\n",
    "        for successes_needed in range(1, MAX_SUCCESSES_NEEDED + 1):\n",
    "            if counts[6] >= successes_needed:\n",
    "                cursed_wins[successes_needed] += 1\n",
    "            if sum(counts[5:]) >= successes_needed:\n",
    "                normal_wins[successes_needed] += 1\n",
    "            if sum(counts[4:]) >= successes_needed:\n",
    "                blessed_wins[successes_needed] += 1\n",
    "\n",
    "    # print table\n",
    "    for i, wins in enumerate((cursed_wins, normal_wins, blessed_wins)):\n",
    "        if i != 0:\n",
    "            print(' | ', end='')\n",
    "        print(' ', n_dice, ' ', end='')\n",
    "        print(*(' - ' if x == 0 else \"{:3.0%}\".format(x / total) for x in wins[1:]), end='')\n",
    "    print()"
   ]
  }
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Github will display the interpreted Jupyter notebook on the desktop site. For mobile and noscript users, here's the output:

  [- CURSED -]   |   [- NORMAL -]   |  [- BLESSED -]
                 |                  |
      successes  |       successes  |       successes
dice  1   2   3  | dice  1   2   3  | dice  1   2   3
  1  17%  -   -  |   1  33%  -   -  |   1  50%  -   - 
  2  31%  3%  -  |   2  56% 11%  -  |   2  75% 25%  - 
  3  42%  7%  0% |   3  70% 26%  4% |   3  88% 50% 12%
  4  52% 13%  2% |   4  80% 41% 11% |   4  94% 69% 31%
  5  60% 20%  4% |   5  87% 54% 21% |   5  97% 81% 50%
  6  67% 26%  6% |   6  91% 65% 32% |   6  98% 89% 66%