{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "82bf6bda-c640-4c26-9b71-f87f04b75ba7",
   "metadata": {},
   "source": [
    "# Add injury to insult\n",
    "*A case study of murdering someone with the right choice of words.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5d47a62d-23f9-4230-9750-faa3ec1707b8",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Install in JupyterLite\n",
    "%pip install -q pathfinder2e-stats\n",
    "\n",
    "import matplotlib as mpl  # noqa: F401  # Needed by JupyterLite\n",
    "import numpy as np\n",
    "import xarray\n",
    "\n",
    "import pathfinder2e_stats as pf2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9144b37a-3e64-4ab5-aeb9-ed64bfa38bf3",
   "metadata": {},
   "source": [
    "## Attacker\n",
    "Nyah, level 5 witch (The Resentment)\n",
    "**Skills** Diplomacy +14 (Bon Mot)\n",
    "\n",
    "**Occult Spells** DC 21; **3rd** Paralyze, Biting Words; **2nd** Blistering Invective; **1st** Sure Strike; **Cantrips (3rd)** Evil Eye, Guidance\n",
    "\n",
    "## Attack routine\n",
    "1. Bon Mot ➡ Blistering Invective\n",
    "2. Paralyze ➡ Evil Eye\n",
    "3. Evil Eye ➡ Biting Words\n",
    "4. Evil Eye ➡ Sure Strike ➡ Biting Words attack\n",
    "5. Evil Eye ➡ Guidance ➡ Biting Words attack\n",
    "\n",
    "## Assumptions\n",
    "- The target attempts to clear neither Bon Mot nor Sickened\n",
    "- No movement is needed; the target remains within 30ft at all times\n",
    "- Spellcasting is not disrupted or obstructed in any way\n",
    "- Ignoring damage dealt to other creatures by casting heightened blistering invective"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ee0024ad-5f26-4ce4-aeb9-020adc16587c",
   "metadata": {},
   "outputs": [],
   "source": [
    "level = 5\n",
    "\n",
    "diplomacy = (\n",
    "    (\n",
    "        pf2.tables.PC.level\n",
    "        + pf2.tables.PC.skill_proficiency.others.sel(priority=1)\n",
    "        + pf2.tables.PC.ability_bonus.boosts.sel(initial=3)\n",
    "        + pf2.tables.PC.skill_item_bonus.diplomacy\n",
    "    )\n",
    "    .sel(level=level)\n",
    "    .item()\n",
    ")\n",
    "\n",
    "spell_DC = pf2.tables.SIMPLE_PC.spell_DC.witch.sum(\"component\").sel(level=level).item()\n",
    "\n",
    "print(f\"{diplomacy=} {spell_DC=}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b7874760-1960-49f9-843a-db8a7a012941",
   "metadata": {},
   "outputs": [],
   "source": [
    "# You can change any of these to upcast or downcast them;\n",
    "# damage and incapacitation trait are adjusted automatically\n",
    "blistering_invective_rank = 2\n",
    "paralyze_rank = 3\n",
    "biting_words_rank = 3"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c4a1a3a1-68c5-46f6-b7a3-649bb91c10ea",
   "metadata": {},
   "source": [
    "## Targets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cd2630cf-e49e-48e7-965c-df82d79703ca",
   "metadata": {},
   "outputs": [],
   "source": [
    "targets = xarray.Dataset(\n",
    "    {\n",
    "        \"target\": [\n",
    "            \"The Stag Lord\",\n",
    "            \"Ettin\",\n",
    "            \"Vampire Count\",\n",
    "            \"Hill Giant\",\n",
    "            \"Dweomercat\",\n",
    "            \"Sphinx\",\n",
    "        ],\n",
    "        \"level\": (\"target\", [6, 6, 6, 7, 7, 8]),\n",
    "        \"HP\": (\"target\", [110, 110, 65, 140, 100, 135]),\n",
    "        \"AC\": (\"target\", [23, 21, 24, 24, 25, 27]),\n",
    "        \"Will\": (\"target\", [9, 12, 17, 13, 17, 19]),\n",
    "        \"bonus_save_vs_magic\": (\"target\", [0, 0, 0, 0, 1, 0]),\n",
    "        \"sickened\": (\"target\", [1, 0, 0, 0, 0, 0]),\n",
    "    }\n",
    ")\n",
    "targets[\"rank\"] = pf2.level2rank(targets.level)\n",
    "targets.to_pandas()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3e365d6f-5fa4-4243-9717-87bf53fd587f",
   "metadata": {},
   "source": [
    "As this is a what-if analysis, roll a single d20 and compare it against different targets.\n",
    "We don't want to repeat `dependent_dims=[\"target\"]` for every call of check() and damage(); so we're going to set it as thread-wide configuration. As we're going to analyse multiple rounds and we're going to use a ``round`` independent dimension later, let's take the opportunity to configure it now too."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d22d8a0c-1bc7-4ce4-8a5f-866d22d73b88",
   "metadata": {},
   "outputs": [],
   "source": [
    "pf2.set_config(\n",
    "    check_independent_dims=[\"round\"],\n",
    "    check_dependent_dims=[\"target\"],\n",
    "    damage_independent_dims=[\"round\"],\n",
    "    damage_dependent_dims=[\"target\"],\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2343a359-2bd0-4316-9963-bebca28d28c5",
   "metadata": {},
   "source": [
    "## Attack routine\n",
    "### Round 1: Bon Mot ➡ Blistering Invective"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "242db822-3827-4fd3-9d3e-2bf6757c6b1e",
   "metadata": {},
   "outputs": [],
   "source": [
    "bon_mot = pf2.check(\n",
    "    diplomacy,\n",
    "    DC=targets.Will + 10 - targets.sickened,\n",
    ")\n",
    "bon_mot[\"Will_penalty\"] = pf2.map_outcome(\n",
    "    bon_mot.outcome,\n",
    "    {pf2.DoS.success: 2, pf2.DoS.critical_success: 3},\n",
    ")\n",
    "\n",
    "sickened = [targets.sickened]\n",
    "will = [\n",
    "    pf2.sum_bonuses(\n",
    "        (\"untyped\", targets.Will),\n",
    "        (\"status\", targets.bonus_save_vs_magic),\n",
    "        (\"status\", -targets.sickened),\n",
    "        (\"status\", -bon_mot.Will_penalty),\n",
    "    )\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "03a31c1f-3f9d-4e8a-8592-a3176a15195c",
   "metadata": {},
   "outputs": [],
   "source": [
    "blistering_invective_spec = pf2.armory.spells.blistering_invective(\n",
    "    blistering_invective_rank\n",
    ")\n",
    "blistering_invective_spec"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9010ef00-0eed-42c3-a93f-9ab4db5b09f8",
   "metadata": {},
   "outputs": [],
   "source": [
    "blistering_invective = pf2.damage(\n",
    "    pf2.check(will[0], DC=spell_DC),\n",
    "    blistering_invective_spec,\n",
    "    persistent_damage_rounds=5,\n",
    ").rename({\"persistent_round\": \"round\"})\n",
    "\n",
    "blistering_invective_damage = (\n",
    "    blistering_invective[\"persistent_damage\"]\n",
    "    .where(blistering_invective[\"apply_persistent_damage\"], 0)\n",
    "    .sum(\"damage_type\")\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8c0f9b0-3a7a-4ba1-bb8a-e10fb548eab6",
   "metadata": {},
   "source": [
    "Probability of being on fire, by target by round"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "700bacd9-8206-4f3f-8f60-3b461579066f",
   "metadata": {},
   "outputs": [],
   "source": [
    "(blistering_invective_damage > 0).mean(\"roll\").round(2).to_pandas()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f2d5c287-19e7-4f20-b6c2-945b05509dde",
   "metadata": {},
   "source": [
    "Mean damage of Blistering Invective every round (assuming no actions are spent putting the fire out)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "75cb2313-befc-4734-9f68-7bbe8bd3fb52",
   "metadata": {},
   "outputs": [],
   "source": [
    "blistering_invective_damage.mean(\"roll\").round(2).to_pandas()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b1db4fea-1333-4811-989d-e7bd8ff70ba3",
   "metadata": {},
   "outputs": [],
   "source": [
    "frightened = pf2.map_outcome(\n",
    "    blistering_invective[\"outcome\"],\n",
    "    {pf2.DoS.failure: 1, pf2.DoS.critical_failure: 2},\n",
    ")\n",
    "# The frightened condition decays with every round that passes\n",
    "frightened = np.maximum(0, frightened - blistering_invective[\"round\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9d78f700-ca6f-4a9f-995b-99423e6115bf",
   "metadata": {},
   "outputs": [],
   "source": [
    "roll_with_high_frightened = np.unique(\n",
    "    frightened,\n",
    "    return_index=True,\n",
    "    axis=frightened.dims.index(\"roll\"),\n",
    ")[1][-2]\n",
    "frightened.isel(roll=roll_with_high_frightened).to_pandas()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f4e2d5be-fd8b-4aa4-8ba9-f1cc790581f4",
   "metadata": {},
   "source": [
    "### Round 2: Paralyze ➡ Evil Eye"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "915619b3-9deb-459d-bf02-ee998d4499b5",
   "metadata": {},
   "outputs": [],
   "source": [
    "will.append(\n",
    "    pf2.sum_bonuses(\n",
    "        (\"untyped\", targets.Will),\n",
    "        (\"status\", targets.bonus_save_vs_magic),\n",
    "        (\"status\", -sickened[-1]),\n",
    "        (\"status\", -bon_mot.Will_penalty),\n",
    "        (\"status\", -frightened.isel(round=1, drop=True)),\n",
    "    )\n",
    ")\n",
    "paralyze = pf2.check(\n",
    "    bonus=will[-1],\n",
    "    DC=spell_DC,\n",
    "    incapacitation=targets[\"rank\"] > paralyze_rank,\n",
    ")\n",
    "\n",
    "# In case of failure, we use Evil Eye to extend the paralysis for the whole combat\n",
    "paralyze[\"need_evil_eye\"] = paralyze.outcome <= pf2.DoS.failure\n",
    "paralyze[\"off_guard\"] = paralyze.outcome <= pf2.DoS.failure"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c3fcbd43-d30a-4064-8621-226d570e4a61",
   "metadata": {},
   "source": [
    "Probability of the target being paralyzed, as well as of needing to cast Evil Eye every round in order to maintain the condition for the whole fight.\n",
    "\n",
    "**FIXME:** a critical failure on the initial saving throw followed by a critical success on any of the consecutive rounds will cause the target to snap out of paralysis early. This is not modelled here yet."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f6266502-7bea-4825-8555-f1bc292a4d57",
   "metadata": {},
   "outputs": [],
   "source": [
    "paralyze[\"need_evil_eye\"].mean(\"roll\").round(2).to_pandas().to_frame(\"% paralyzed\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "598280de-cdb5-4131-aa01-25a3d33a426d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def evil_eye(will_bonus, spell_DC):\n",
    "    c = pf2.check(will_bonus, DC=spell_DC).outcome\n",
    "    return pf2.map_outcome(c, {pf2.DoS.critical_failure: 2, pf2.DoS.failure: 1})\n",
    "\n",
    "\n",
    "sickened.append(np.maximum(sickened[-1], evil_eye(will[-1], spell_DC)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a97dac9-2bc9-4a64-b93b-b0a6e478956e",
   "metadata": {},
   "source": [
    "### Round 3: Evil Eye ➡ Biting Words\n",
    "If the target scored a simple failure vs. Paralyze in round 2, extend its duration with Evil Eye.\n",
    "Then, cast Biting Words.\n",
    "### Round 4: Evil Eye ➡ Sure Strike ➡ Biting Words attack\n",
    "### Round 5: Evil Eye ➡ Guidance ➡ Biting Words attack"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d4fcaf4a-9895-4fdf-902c-ad0daeb3786e",
   "metadata": {},
   "outputs": [],
   "source": [
    "for _round in range(2, 5):\n",
    "    will.append(\n",
    "        pf2.sum_bonuses(\n",
    "            (\"untyped\", targets.Will),\n",
    "            (\"status\", targets.bonus_save_vs_magic),\n",
    "            (\"status\", -sickened[-1]),\n",
    "            (\"status\", -bon_mot.Will_penalty),\n",
    "        )\n",
    "    )\n",
    "    sickened.append(np.maximum(sickened[-1], evil_eye(will[-1], spell_DC)))\n",
    "\n",
    "assert len(will) == 5\n",
    "assert len(sickened) == 5\n",
    "\n",
    "will = xarray.concat(will, dim=\"round\")\n",
    "sickened = xarray.concat(sickened, dim=\"round\")\n",
    "sure_strike = xarray.DataArray([False, False, False, True, False], dims=[\"round\"])\n",
    "guidance = xarray.DataArray([False, False, False, False, True], dims=[\"round\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e30cf6d-51ed-4a79-958f-52aac06e2770",
   "metadata": {},
   "source": [
    "Mean Will saves debuff by target and round"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "78d7ed3a-ca46-4f8e-bb70-b234aec93344",
   "metadata": {},
   "outputs": [],
   "source": [
    "(will - targets.Will).mean(\"roll\").round(2).T.to_pandas()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "32c36db4-8219-4ca8-aec4-1c9c44908b73",
   "metadata": {},
   "outputs": [],
   "source": [
    "off_guard = xarray.concat(\n",
    "    [\n",
    "        xarray.DataArray(False),\n",
    "        paralyze.off_guard.expand_dims(round=4),\n",
    "    ],\n",
    "    dim=\"round\",\n",
    ")\n",
    "AC = pf2.sum_bonuses(\n",
    "    (\"untyped\", targets.AC),\n",
    "    (\"status\", -frightened),\n",
    "    (\"status\", -sickened),\n",
    "    (\"circumstance\", off_guard.astype(int) * -2),\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5efe611c-07b5-477e-9157-11ac16400291",
   "metadata": {},
   "source": [
    "Mean Armor Class debuff by target and round"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fa833fe2-6290-43c2-ba77-12ca1f8ef245",
   "metadata": {},
   "outputs": [],
   "source": [
    "(AC - targets.AC).mean(\"roll\").round(2).sel(drop=True).to_pandas()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8010d78c-d606-46fb-91b6-299ba09c7e5c",
   "metadata": {},
   "source": [
    "In round 3, we use Sure Strike only if we don't need to extend the duration of paralyze.\n",
    "In round 4 and 5, we always use Sure Strike."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "edcca9de-1703-4ced-844a-9364cd832be0",
   "metadata": {},
   "outputs": [],
   "source": [
    "biting_words_check = pf2.check(\n",
    "    spell_DC - 10 + guidance,\n",
    "    DC=AC,\n",
    "    fortune=sure_strike,\n",
    ")\n",
    "biting_words_check[\"outcome\"] = biting_words_check[\"outcome\"].where(\n",
    "    AC[\"round\"] >= 2, pf2.DoS.no_roll\n",
    ")\n",
    "\n",
    "biting_words_damage = pf2.damage(\n",
    "    biting_words_check,\n",
    "    pf2.armory.spells.biting_words(biting_words_rank),\n",
    ").total_damage"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "57c9b85d-7736-46d5-94ec-8cea6f5d616a",
   "metadata": {},
   "source": [
    "Mean damage of Biting Words by target and round"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9c2f3708-6c4b-4d6d-ba41-7db6a2adfcb3",
   "metadata": {},
   "outputs": [],
   "source": [
    "(biting_words_damage.mean(\"roll\").round(2).to_pandas())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "42c3e885-be0b-4c70-a44a-7afacfa79e0e",
   "metadata": {},
   "source": [
    "## Put it all together"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "57d9947b-3922-4815-82eb-3436e09ec3c5",
   "metadata": {},
   "outputs": [],
   "source": [
    "final = xarray.Dataset(\n",
    "    {\n",
    "        \"AC\": AC,\n",
    "        \"Will\": will,\n",
    "        \"off_guard\": paralyze.off_guard,\n",
    "        \"need_evil_eye\": paralyze.need_evil_eye,\n",
    "        \"blistering_invective\": blistering_invective_damage,\n",
    "        \"biting_words\": biting_words_damage,\n",
    "        \"total_damage\": blistering_invective_damage + biting_words_damage,\n",
    "    }\n",
    ").transpose(\"target\", \"roll\", \"round\")\n",
    "final[\"harmed\"] = final.total_damage.sum(\"round\") > 0\n",
    "final[\"bloodied\"] = final.total_damage.sum(\"round\") > targets.HP // 2\n",
    "final[\"killed\"] = final.total_damage.sum(\"round\") >= targets.HP\n",
    "final"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "da162a65-2559-4fb2-8e37-7bde09415721",
   "metadata": {},
   "source": [
    "## Let's analyse our results!\n",
    "### Mean cumulative damage by the end of the attack routine"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "69d45f7b-6634-4486-81f4-d61eec4ff43e",
   "metadata": {},
   "outputs": [],
   "source": [
    "(\n",
    "    final[[\"blistering_invective\", \"biting_words\", \"total_damage\"]]\n",
    "    .mean(\"roll\")\n",
    "    .sum(\"round\")\n",
    "    .round(2)\n",
    "    .to_pandas()\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7bdfbff6-4fa1-4f70-8392-ca0496e44314",
   "metadata": {},
   "source": [
    "### Various probabilities\n",
    "\n",
    "- Probability of dealing any HP damage at all\n",
    "- Probability of dealing more than 50% HP damage\n",
    "- Probability of solo killing the target\n",
    "- Probability of paralyzing the target in round 2\n",
    "- Probability of needing to spam evil eye every round to keep the target paralyzed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "927bfc4e-527e-4914-9a6a-1c6f52b47d41",
   "metadata": {},
   "outputs": [],
   "source": [
    "(\n",
    "    final[[\"harmed\", \"bloodied\", \"killed\", \"off_guard\", \"need_evil_eye\"]]\n",
    "    .mean(\"roll\")\n",
    "    .round(2)\n",
    "    .to_pandas()\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "176f0f15-0ba3-4856-ab19-59b013f3017e",
   "metadata": {},
   "source": [
    "### Damage distribution, normalized by target's Hit Points total"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4a157fb7-8dcb-4f60-9a98-611646b0c0dc",
   "metadata": {},
   "outputs": [],
   "source": [
    "_ = (\n",
    "    (final[\"total_damage\"].sum(\"round\") / targets.HP)\n",
    "    .to_pandas()\n",
    "    .T.describe()\n",
    "    .T.plot(\n",
    "        kind=\"barh\",\n",
    "        y=\"mean\",\n",
    "        xerr=\"std\",\n",
    "        legend=False,\n",
    "        title=\"Damage as % of total HP after round 5; mean+stddev\",\n",
    "    )\n",
    ")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
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