{
 "cells": [
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   "cell_type": "markdown",
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    }
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   "source": [
    "# Straight Shot Difficulty\n",
    "\n",
    "Consider a straight shot into a pocket where the cue ball (CB) is a total distance $D$ from the pocket. Which object ball (OB) position (distance $d$ from the CB) results in the most difficult pot?\n",
    "\n",
    "This question is posed by Dr. Dave Billiards in [this proof](https://billiards.colostate.edu/technical_proofs/TP_3-4.pdf) and based on the assumptions made, the answer is\n",
    "\n",
    "$$\n",
    "d = D/2\n",
    "$$\n",
    "\n",
    "In other words, the shot is made most difficult when the OB is placed equidistantly from both the pocket and the CB.\n",
    "\n",
    "In this example, we will directly simulate straight shots and determine under what circumstances this theory holds up."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d36cdb8d",
   "metadata": {},
   "source": [
    "## Setting up a system\n",
    "\n",
    "Let's set up a system where the OB is shot into a corner pocket _straight on_ (at an angle of 45 degrees from both the long cushion and short cushion).\n",
    "\n",
    "We'll begin by creating a big square [Table](../autoapi/pooltool/index.rst#pooltool.Table) that gives us plenty of space. There are many different parameters that can be passed to [PocketTableSpecs](../autoapi/pooltool/objects/index.rst#pooltool.objects.PocketTableSpecs) that influence the shape of the pockets (you can get a visual explanation of each parameter [here](../resources/table_specs.md)), but here we will keep the default values, which are modelled after my old 7-foot Showood table with pretty wide 5 inch pockets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e936c90f",
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    "execution": {
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     "shell.execute_reply": "2026-03-15T06:52:02.516891Z"
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   "source": [
    "import pooltool as pt\n",
    "import numpy as np\n",
    "\n",
    "np.random.seed(42)\n",
    "\n",
    "table_specs = pt.objects.PocketTableSpecs(l=10, w=10)\n",
    "table = pt.Table.from_table_specs(table_specs)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "800e6f5e",
   "metadata": {},
   "source": [
    "As a reminder, $D$ represents the distance of the CB to the pocket, but let's be a little more precise with what that means. From the CB, we will measure from the ball's center, and from the pocket we will measure from pocket's edge that's closest to the CB. So when $D$ is 0, the CB is teetering on the edge of the pocket.\n",
    "\n",
    "With that in mind, let's pick the bottom-left corner [Pocket](../autoapi/pooltool/objects/index.rst#pooltool.objects.Pocket) as our target and place a CB a distance $D$ away."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "1aff3ee3",
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2026-03-15T06:52:02.525326Z"
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The pocket point is [0.0143542676580869 0.0143542676580869]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "# lb stands for left-bottom\n",
    "pocket = table.pockets[\"lb\"]\n",
    "\n",
    "# The pocket's center is defined with 3D coordinates, but we'll just use X and Y\n",
    "center = pocket.center[:2]\n",
    "\n",
    "pocket_point = center + pocket.radius / np.sqrt(2)\n",
    "\n",
    "print(f\"The pocket point is {pocket_point}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ce62613",
   "metadata": {},
   "source": [
    "Now let's create a cue ball a distance $D$ away."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "15884154",
   "metadata": {
    "execution": {
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   "outputs": [],
   "source": [
    "D = 1.0\n",
    "\n",
    "def create_cue_ball(pocket_point, D):\n",
    "    cue_point = pocket_point + D / np.sqrt(2)\n",
    "    return pt.Ball.create(\"CB\", xy=cue_point)\n",
    "\n",
    "cue_ball = create_cue_ball(pocket_point, D)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "704f82e8",
   "metadata": {},
   "source": [
    "Let's create an object ball a distance $d$ from the cue ball. In order for the object ball to be between the cue and the pocket, $d$ is constrained by\n",
    "\n",
    "$$\n",
    "2 R \\lt d \\lt D\n",
    "$$\n",
    "\n",
    "where $R$ is the radius of the balls."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "9587ae3e",
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2026-03-15T06:52:02.738253Z"
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   "outputs": [],
   "source": [
    "def create_object_ball(cue_ball, d):\n",
    "    obj_point = cue_ball.xyz[:2] - d / np.sqrt(2)\n",
    "    return pt.Ball.create(\"OB\", xy=obj_point)\n",
    "\n",
    "d = 0.3\n",
    "\n",
    "obj_ball = create_object_ball(cue_ball, d)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "95351ff2",
   "metadata": {},
   "source": [
    "Let's go ahead and turn everything we've done into a function that takes $d$ and $D$ as parameters and returns a [System](../autoapi/pooltool/index.rst#pooltool.System)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "d6e40365",
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2026-03-15T06:52:02.745645Z"
    }
   },
   "outputs": [],
   "source": [
    "def create_system(d, D):\n",
    "    table_specs = pt.objects.PocketTableSpecs(l=10, w=10)\n",
    "    table = pt.Table.from_table_specs(table_specs)       \n",
    "    pocket = table.pockets[\"lb\"]\n",
    "    pocket_point = pocket.center[:2] + pocket.radius / np.sqrt(2)\n",
    "\n",
    "    cue_ball = create_cue_ball(pocket_point, D)\n",
    "    obj_ball = create_object_ball(cue_ball, d)\n",
    "\n",
    "    return pt.System(\n",
    "        cue=pt.Cue(cue_ball_id=\"CB\"),\n",
    "        balls=(cue_ball, obj_ball),\n",
    "        table=table,\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46a0670b",
   "metadata": {},
   "source": [
    "With this function, we can create a system:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "404172c2",
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2026-03-15T06:52:02.752272Z"
    }
   },
   "outputs": [],
   "source": [
    "system = create_system(d, D)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a42e69fe",
   "metadata": {},
   "source": [
    "If you have a graphics card, you can visualize the system in 3D with\n",
    "\n",
    "```python\n",
    "pt.show(system)\n",
    "```\n",
    "\n",
    "## Simulating a shot\n",
    "\n",
    "No energy has been imparted into the system so it's currently rather dull. Let's change that by striking the CB in the direction of the OB."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "58e960a9",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-15T06:52:02.755954Z",
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     "shell.execute_reply": "2026-03-15T06:52:02.842637Z"
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   "outputs": [],
   "source": [
    "# phi is the aiming direction\n",
    "phi = pt.aim.at_ball(cue_ball=system.balls[\"CB\"], object_ball=system.balls[\"OB\"], cut=0)\n",
    "\n",
    "# Based on the geometry, we know that phi is 225 degrees (towards the bottom-left pocket)\n",
    "assert phi == 225.0\n",
    "\n",
    "system.cue.set_state(V0=1, phi=phi, cue_ball_id=\"CB\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "29da653d",
   "metadata": {},
   "source": [
    "Since the pocket, OB, and CB are all lined up, this should lead to a successful pot. Let's check by simulating and filtering the system events according to our criteria."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "dd1cd57e",
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2026-03-15T06:52:03.118300Z"
    }
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pt.simulate(system, inplace=True)\n",
    "\n",
    "def successful_pot(system) -> bool:\n",
    "    # Find events that are ball-pocket events and involve the object ball\n",
    "    pocket_events = pt.events.filter_events(\n",
    "        system.events,\n",
    "        pt.events.by_type(pt.EventType.BALL_POCKET),\n",
    "        pt.events.by_ball(\"OB\"),\n",
    "    )\n",
    "    return bool(len(pocket_events))    \n",
    "\n",
    "successful_pot(system)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60ec5314",
   "metadata": {},
   "source": [
    "Great! As expected, it went straight in."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d31587ee",
   "metadata": {},
   "source": [
    "## Modeling imprecision\n",
    "\n",
    "Real pool players don't have perfect precision and we are going to emulate this by introducing uncertainty into the aiming angle $\\phi$. We'll call this uncertainty $d\\phi$.\n",
    "\n",
    "While we're at it, let's make a function that adds uncertainty not just to $\\phi$, but to the other cue striking parameters as well, that you can read about [here](../autoapi/pooltool/index.rst#pooltool.Cue)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "cd733141",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-15T06:52:03.122828Z",
     "iopub.status.busy": "2026-03-15T06:52:03.122544Z",
     "iopub.status.idle": "2026-03-15T06:52:03.128488Z",
     "shell.execute_reply": "2026-03-15T06:52:03.127207Z"
    }
   },
   "outputs": [],
   "source": [
    "def perturb(x, dx):\n",
    "    return x + dx * (2*np.random.rand() - 1)\n",
    "\n",
    "def strike(system, V0, a, phi, theta, dV0=0, da=0, dphi=0, dtheta=0):\n",
    "    system.cue.set_state(\n",
    "        cue_ball_id=\"CB\",\n",
    "        V0=perturb(V0, dV0),\n",
    "        a=perturb(a, da),\n",
    "        phi=perturb(phi, dphi),\n",
    "        theta=perturb(theta, dtheta),\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b1dad881",
   "metadata": {},
   "source": [
    "## Estimating Difficulty for a Given $d$\n",
    "\n",
    "To evaluate the difficulty level associated with shot where the OB is a distance $d$ from the CB, we will calculate the fraction of successful pots (successful shots) from a set of trials. In these trials, we will introduce random perturbations to the angle $\\phi$ for each shot. The perturbations are limited so that the angle $\\phi$ deviates by no more than a fixed amount $d\\phi$.\n",
    "\n",
    "This means that for each shot, the angle $\\phi$ is randomly adjusted within the range $[\\phi - d\\phi, \\phi + d\\phi]$. By observing how these perturbations affect the success rate, we can estimate the difficulty associated with the given $d$.\n",
    "\n",
    "Let's pick a $d\\phi$ and then simulate 100 shots."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "ee0d1e66",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-15T06:52:03.131413Z",
     "iopub.status.busy": "2026-03-15T06:52:03.131141Z",
     "iopub.status.idle": "2026-03-15T06:52:03.671586Z",
     "shell.execute_reply": "2026-03-15T06:52:03.670111Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The success rate is 41%.\n"
     ]
    }
   ],
   "source": [
    "dphi = 0.4  # Just 0.4 degrees!\n",
    "phi = 225.0\n",
    "V0 = 1.0  # 1 m/s cue-stick strike\n",
    "a = 0  # No sidespin\n",
    "theta = 0  # Level cue stick\n",
    "d = 0.6\n",
    "D = 2.0\n",
    "\n",
    "num_trials = 100\n",
    "successes = []\n",
    "for _ in range(num_trials):\n",
    "    system = create_system(d, D)\n",
    "    strike(system, V0, a, phi, theta, dphi=dphi)\n",
    "    pt.simulate(system, inplace=True)\n",
    "    success = successful_pot(system)\n",
    "    successes.append(success)\n",
    "\n",
    "pot_fraction = sum(successes) / len(successes)\n",
    "print(f\"The success rate is {pot_fraction*100:.0f}%.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "315fd227",
   "metadata": {},
   "source": [
    "## Which $d$ yields the most difficult shot?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1df8f50a",
   "metadata": {},
   "source": [
    "Great. Now, we can run the same experiment, but vary $d$ to determine which yields the most difficult shot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "3a989057",
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2026-03-15T06:52:24.626658Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For d = 0.06 m, the success rate is 100%.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For d = 0.23 m, the success rate is 100%.\n",
      "For d = 0.41 m, the success rate is 62%.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For d = 0.59 m, the success rate is 49%.\n",
      "For d = 0.76 m, the success rate is 39%.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For d = 0.94 m, the success rate is 40%.\n",
      "For d = 1.12 m, the success rate is 38%.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For d = 1.29 m, the success rate is 37%.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For d = 1.47 m, the success rate is 50%.\n",
      "For d = 1.65 m, the success rate is 66%.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For d = 1.82 m, the success rate is 100%.\n",
      "For d = 2.00 m, the success rate is 100%.\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Vary from 1mm separation between CB and OB to 1mm from pocket's edge\n",
    "d_values = np.linspace(2.001*cue_ball.params.R, D-0.001, 12)\n",
    "\n",
    "num_trials = 400\n",
    "pot_fractions = []\n",
    "\n",
    "for d in d_values:\n",
    "    successes = []\n",
    "    for _ in range(num_trials):\n",
    "        system = create_system(d, D)\n",
    "        strike(system, V0, a, phi, theta, dphi=dphi)\n",
    "        pt.simulate(system, inplace=True)\n",
    "        success = successful_pot(system)\n",
    "        successes.append(success)\n",
    "\n",
    "    pot_fraction = sum(successes) / len(successes)\n",
    "    pot_fractions.append(pot_fraction)\n",
    "    print(f\"For d = {d:.2f} m, the success rate is {pot_fraction*100:.0f}%.\")\n",
    "\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(d_values, pot_fractions, marker='o')\n",
    "plt.xlabel('Distance d (m)')\n",
    "plt.ylabel('Success Rate')\n",
    "plt.title('Success Rate vs. Distance d')\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c9119af",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    }
   },
   "source": [
    "Reading left to right, shot success starts high because the OB is close to the CB. But as the OB moves further away from the CB, the success rate decreases, reaching a minimum at around $D/2$. Past this point, the success rate starts to go up again, since the OB is now getting closer and closer to the pocket.\n",
    "\n",
    "Since this data is generated from a small number of trials, there is some variance in the plot, but if you increase `num_trials` the curve smooths."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ed7c0e05",
   "metadata": {},
   "source": [
    "## What about skill level?\n",
    "\n",
    "Since $d\\phi$ is a measure of how precise the shot is, it is a reasonable proxy for skill level. With that in mind, how should we expect the shot success trajectory to vary as a function of skill level? Let's repeat the experiment for 3 different skill levels."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "5d781ff9",
   "metadata": {
    "editable": true,
    "execution": {
     "iopub.execute_input": "2026-03-15T06:52:24.631628Z",
     "iopub.status.busy": "2026-03-15T06:52:24.631167Z",
     "iopub.status.idle": "2026-03-15T06:53:18.562490Z",
     "shell.execute_reply": "2026-03-15T06:53:18.561009Z"
    },
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "nbsphinx-gallery"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished dphi=0.15\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished dphi=0.25\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished dphi=0.5\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Define the range of 'd' values you want to test\n",
    "d_values = np.linspace(2.001 * cue_ball.params.R, D - 0.001, 12)\n",
    "\n",
    "# Define the range of 'dphi' values (in degrees)\n",
    "dphi_values = [0.15, 0.25, 0.5]\n",
    "\n",
    "num_trials = 400\n",
    "results = {}\n",
    "\n",
    "for dphi in dphi_values:\n",
    "    pot_fractions = []\n",
    "    for d in d_values:\n",
    "        successes = []\n",
    "        for _ in range(num_trials):\n",
    "            system = create_system(d, D)\n",
    "            strike(system, V0, a, phi, theta, dphi=dphi)\n",
    "            pt.simulate(system, inplace=True)\n",
    "            success = successful_pot(system)\n",
    "            successes.append(success)\n",
    "\n",
    "        pot_fraction = sum(successes) / len(successes)\n",
    "        pot_fractions.append(pot_fraction)\n",
    "        \n",
    "    print(f\"Finished {dphi=}\")\n",
    "    results[dphi] = pot_fractions\n",
    "\n",
    "plt.figure(figsize=(8, 6))\n",
    "for dphi in dphi_values:\n",
    "    plt.plot(d_values, results[dphi], marker='o', label=f'dphi = {dphi}°')\n",
    "\n",
    "plt.xlabel('Distance d (m)')\n",
    "plt.ylabel('Success Rate')\n",
    "plt.title('Success Rate vs. Distance d for Different Skill (dphi) Values')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d3a6acf6",
   "metadata": {},
   "source": [
    "Regardless of skill level, when $\\lim_{d \\rightarrow 2R^{+}}$ and $\\lim_{d \\rightarrow D^{-}}$, the success rate converges to $100\\%$. That's expected—when the object ball OB is practically touching the CB or hanging over the pocket, potting becomes nearly automatic for all skill levels. \n",
    "\n",
    "But what’s more interesting is observing the extent and sharpness with which success rate drops when the OB is at an intermediate distance $d$. The least skilled players experience the earliest, sharpest, and lowest plummet in success rate, whereas high skilled players maintain higher success rate for longer. Yet no matter the skill, the minimum seems to be right at around $d=D/2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "19c96b60",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "jupytext": {
   "notebook_metadata_filter": "all"
  },
  "kernelspec": {
   "display_name": "pooltool-dev",
   "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": "3.13.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}