{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Some Variations of Banach's Matchbox Problem" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Banach's matchbox problem is a good entry point into stochastic stopping problems. A man buys two matchbooks and puts one in each of his two pockets. He then selects a matchbox at random from either pocket, uses a single match, and then returns the matchbox to the same pocket. This problem is slightly different from the classic matchbox problem in that when the last match is taken, the sequence ends. In the classic problem, discovery of the empty box happens only when the empty box is selected **after** being emptied.\n", "\n", "The question is: **What is the probability of $k$ matches in the remaining matchbox? **\n", "\n", "The problem is given two matchbooks containing $n$ matches each and with a matchbook placed in both the left and right pockets, if a person reaches into one or the other pocket at random with equal probability, what is the probability of there being $k$ matches in the other pocket when the matchbook in the selected pocket is found to be empty? That is, the person keeps reaching alternatively and at random to sample a match from either pocket until one of the pockets is exhausted of matches.\n", "\n", "This is easy to code up in Python using a generator:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from __future__ import division\n", "from collections import Counter, OrderedDict\n", "import pandas as pd\n", "import random\n", "import numpy as np\n", "from scipy.misc import comb\n", "random.seed(12345)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def step(n=4):\n", " 'keep track of remaining matches in each matchbook'\n", " a = b = n\n", " while a>0 and b>0:\n", " if random.randint(0,1):\n", " a-=1\n", " else:\n", " b-=1\n", " yield (a,b)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Thus, suppose there are $n=4$ matches in each matchbook, then a valid sequence of draws from the (left,right) pocket is the following:\n", "\n", "[(4, 3), (4, 2), (3, 2), (3, 1), (3, 0)]\n", "\n", "This means that the first draw is from the right pocket leaving 3 matches there and 4 matches in the left pocket. The next draw again\n", "samples a match from the right pocket leaving 2 matches there and 4 in the left pocket. For the following draw, the left pocket is chosen leaving 3 matches there and 2 matches in the right pocket. This continues until the right pocket is emptied (3,0). We can draw this sequence using the following code:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from __future__ import division\n", "%matplotlib inline\n", "from matplotlib.pylab import subplots,mgrid\n", "\n", "def draw_grid(n=4):\n", " 'draw square grid of n dimensions'\n", " fig,ax = subplots()\n", " i,j=mgrid[0:n+1,0:n+1]\n", " ax.scatter(i.flat,j.flat,alpha=.8,color='black')\n", " ax.set_aspect(1)\n", " ax.plot(0,0,'ow',mec='w'); # remove origin\n", " ax.plot([0,]*4,range(1,5),'or',mec='r',ms=10)\n", " ax.plot(range(1,5),[0,]*4,'or',mec='r',ms=10)\n", " return ax\n", "\n", "def draw_path(seq,ax,color='gray',alpha=0.5):\n", " x,y=zip(*seq)\n", " n = max(seq[0])\n", " ax.plot((n,)+x,(n,)+y,marker='o',markersize=20,\n", " alpha=alpha,color=color,lw=5)\n", " ax.set_title('Sequence Length=%d'%(len(x))) \n", " \n", "ax = draw_grid()\n", "draw_path([(4, 3), (4, 2), (3, 2), (3, 1), (3, 0)],ax)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the figure above, the red circles indicate the termination points where one of the pockets has been emptied. The (4,4) point is the starting point with incremental steps moving down and to the left until one of the red circles is encountered. The length of the sequence is indicated in the title. In this case it took five draws in total to exhaust one of the matchbooks and terminate the sequence.\n", "\n", "The classical matchbox problem is to find the probability of termination at a particular circle. For example, what is the probability that the sequence terminates with one match remaining in the other matchbook? In the figure above, this means terminating at (1,0) or (0,1).\n", "\n", "Specifically, termination at (1,0) means accumulating four steps down and three steps left in any sequence. This is the same as the $n$ *choose* $k$ binomial coefficient $\\texttt{Binom}(n,k)$. We can compute this using scipy as the following with $n=7,k=3$:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "35\n" ] } ], "source": [ "print comb(7,3,exact=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The problem with this approach is that we can accidentally count paths that would have terminated earlier. For example," ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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ZjgYGBoquaWwsycWLQyQSwpkzIWDKABIEgynKy5XGxioikaVlUy42lunIyJIr32AuMpkM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\nI5EIe/fuXXG5Bv3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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ax = draw_grid()\n", "draw_path([(3, 4), (3, 3), (2, 3), (2, 2), (1, 2), (1, 1), (1, 0)],ax)\n", "draw_path([(4,3), (4, 2), (4, 1), (4, 0), (3, 0), (2, 0), (1, 0)],ax,'blue',.2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The blue path would never have gotten so long because it would have encountered the termination point at (4,0). Thus, this straight-forward counting scheme would over-count by including these paths. The following figure shows these valid paths that terminate at (1,0):" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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2bLH2vf66VSZNFBcX2/Ij8Pl8thkBQG1trS2LhTweD7W1tTYoggMHDnD58uWU67l8+TIH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\nTsU+H5/Px5kzZ9i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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "paths=[[(3, 4),(2, 4),(1, 4),(1, 3),(1, 2),(1, 1),(1, 0)],\n", "[(3, 4),(2, 4),(2, 3),(1, 3),(1, 2),(1, 1),(1, 0)],\n", "[(3, 4),(2, 4),(2, 3),(2, 2),(1, 2),(1, 1),(1, 0)],\n", "[(3, 4),(2, 4),(2, 3),(2, 2),(2, 1),(1, 1),(1, 0)],\n", "[(3, 4),(3, 3),(2, 3),(1, 3),(1, 2),(1, 1),(1, 0)],\n", "[(3, 4),(3, 3),(2, 3),(2, 2),(1, 2),(1, 1),(1, 0)],\n", "[(3, 4),(3, 3),(2, 3),(2, 2),(2, 1),(1, 1),(1, 0)],\n", "[(3, 4),(3, 3),(3, 2),(2, 2),(1, 2),(1, 1),(1, 0)],\n", "[(3, 4),(3, 3),(3, 2),(2, 2),(2, 1),(1, 1),(1, 0)],\n", "[(3, 4),(3, 3),(3, 2),(3, 1),(2, 1),(1, 1),(1, 0)],\n", "[(4, 3),(3, 3),(2, 3),(1, 3),(1, 2),(1, 1),(1, 0)],\n", "[(4, 3),(3, 3),(2, 3),(2, 2),(1, 2),(1, 1),(1, 0)],\n", "[(4, 3),(3, 3),(2, 3),(2, 2),(2, 1),(1, 1),(1, 0)],\n", "[(4, 3),(3, 3),(3, 2),(2, 2),(1, 2),(1, 1),(1, 0)],\n", "[(4, 3),(3, 3),(3, 2),(2, 2),(2, 1),(1, 1),(1, 0)],\n", "[(4, 3),(3, 3),(3, 2),(3, 1),(2, 1),(1, 1),(1, 0)],\n", "[(4, 3),(4, 2),(3, 2),(2, 2),(1, 2),(1, 1),(1, 0)],\n", "[(4, 3),(4, 2),(3, 2),(2, 2),(2, 1),(1, 1),(1, 0)],\n", "[(4, 3),(4, 2),(3, 2),(3, 1),(2, 1),(1, 1),(1, 0)],\n", "[(4, 3),(4, 2),(4, 1),(3, 1),(2, 1),(1, 1),(1, 0)]]\n", "\n", "ax = draw_grid()\n", "for i in paths:\n", " draw_path(i,ax,alpha=.1)\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's change our perspective slightly. Instead let's examine the probability of a sequence of a certain length and see if we can use that to answer the classic question. To start with, the following figure shows valid four-long sequences. The diagonal elements are indicated in green and these are the termination points for all four-long sequences. There are $2^4=16$ such sequences." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ax = draw_grid()\n", "for i in zip(range(5)[::-1],range(5)):\n", " ax.plot(i[0],i[1],'sg',ms=15,alpha=.3)\n", "draw_path([(3,4),(2,4),(1,4),(0,4)],ax)\n", "draw_path([(4,3),(4,2),(4,1),(4,0)],ax)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Because only two of the sixteen valid sequences result in termination, the probability of termination with a four-long sequence is $P_4 = \\frac{2}{16}= \\frac{1}{8}$. Now let's examine the diagonal elements with the following labels." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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q5lVQ80YNr7e+PirvIS7OzTJIpyGVykztA949XsaIrfu3cu0nru35+YoZVzBz8kwATvpJ\nCqyAd9Lv0H584P/PhRMKuf3zt1N+eTmFEwoHHDO9cDpXX3I12/ZvC/8NxMiEqAPkVWsrrF4NO3f2\nvdfiVVfBQw/pXotj0K5Du/j6Z77e57kXWl5g2ZPLaOtswzDWf2E90ybldgu9+R+fz65Du3JaRtyF\nUgZm9gNgGfCeu38mjGWGbrC7MB88mJmamnQX5jGotaOVosKiPs8tvnQxrXe10tbZxmO7H2NW0ayc\n11NUWDTudxPC2jJ4FLgf2BzS8sK3evXgt2OHzLw1a6C6On+ZekmlUlRVVQGwcuVKFi1aFEmO/uKY\nq3emiZ+aSFtn24DjigqLWFu2lpnfncncC+Yy5/w5Z73Ots62nt2P4TLF5XMaqVDKwN2fN7PLwljW\nqEinM7sGw2loyBxDyPNdmVOpFCtWrODUjWlramrYvHlz5L9QcczVP9MH7R9QM72GtWVrBxzf7d0c\n7z7OwdaDOZVB4/uN3DT7pqwyxeFzOhvnxgHExsbTxwiG0tKSGZtnVVVVuDvFxcUUFxfj7j1/ZaIU\nx1z9M01tmUrNmzU987//z9/n7ba3ATj80WHW/nwtkydM7jlT0PxhMwX3FlDXXNfzmuPdx+no6uCk\nn6TrZBedXZ10nezqmd9+vJ2GtxtYPmd5Vpni8DmdjbweQNywYUPP42QySTKZzOfqZRyacmgKHd5B\nXXMdSy5bws53drKxbiNtnW1MnzSdskvKeHbFs3xsyscAaD7WzIzJM1hw4YKeZcx5YA4txzJ/LJ5v\neZ57f3Uvty24jR/e/EMAqvdUc80V15CYmcj/GzwLtbW11NbWjvyF7h7KBFwG/MsQ8z0y6bR7IuEO\nQ0+JRGZsntXX13tJSYknEglPJBJeUlLi9fX1ec8xFnINlGnTtk1e/mh5Vq+/u+Zuv++F+7JeX2dX\np8++f7bvP7x/RJmi/px6C757w36HzYP9nFyZ2eXAz9x9/iDzPax1nZWKCtiyZegxlZU6gNhPHHMp\n08iYGe5uw44L4wtqZtVAEvgY8B5wj7s/2m9MtGUw2KnFU0pLdWpRxqW8lkE2Ii8DyBTCmjWZswa9\nLzoqK4MHH1QRyLikMhhKOg1792Yez5uX91OJIvmkMhARIPsyODeuMxCRYakMRARQGYhIQGUgIoDK\nQEQCKgMRAVQGIhJQGYgIoDIQkYDKQEQAlYGIBFQGIgKoDEQkoDIQEUBlICIBlYGIACoDEQmoDEQE\nUBmISEBlICKAykBEAioDEQFUBiISUBmICKAyEJHAhKgDSCCdhsbGzOP58+Nzy7c45lKm0ZHNfduH\nm4DrgFeBJuCuQcaEeMf5ceToUfeKCvdEwn3ixMyUSLjfemtmnnIpU46C797w3+NsBg25gMyuxgHg\nMmAisBv45ADj8vG+x5ajR91LSzP/GwaaSkuj+YWKYy5lOmv5LIPPA//U6+dvDrR1EKcySKfT3tHR\n4R0dHZ5Op6MLUlEx+C/SqamyUrmUKSfZlkEYBxAvAd7q9fNvg+diqb29nWnTplFYWEhhYSHTpk2j\nvb09/0HSadi5c/hxDQ2Qz3xxzKVMeXHOnU2YOHFiVs+NusZGaGkZflxLy+kDU/kQx1zKlBdhnE14\nG7i018+zgufOsGHDhp7HyWSSZDIZwupFpLfa2lpqa2tH/sJs9iWGmoDzOH0AcRKZA4ifGmBcPnaP\nhjXQMYJIjhuk05mjzsPtcyYSmbHnci5lygn5Ombg7t3AWmAHsBf4kbu/kutyR8upYwSdnZ10dnb2\nHEOIIAhcddXw48rK8nvOOo65lCk/smmMMCZismUQK3E9NRXHXMp01sjXqcVsJ5XBII4ezZx+6n/R\nSmVl9BcdxS2XMp2VbMvAMmNHn5l5vtY1JqXTsHdv5vG8efHZtIxjLmUaETPD3W3YcSoDkfEt2zI4\n564zEJGBqQxEBFAZiEhAZSAigMpARAIqAxEBVAYiElAZiAigMhCRgMpARACVgYgEVAYiAqgMRCSg\nMhARQGUgIgGVgYgAKgMRCagMRARQGYhIQGUgIoDKQEQCKgMRAVQGIhJQGYgIoDIQkUBOZWBmXzGz\nRjPrNrN/H1YoEcm/XLcM9gC3AL8KIUve1dbWRh3hDHHMBPHMpUzhyqkM3H2/u78GDHsftziK4/+4\nOGaCeOZSpnDpmIGIADBhuAFm9gxwYe+nAAf+q7v/bLSCiUh+hXJLdjN7DviGu+8aYozuxy4SkWxu\nyT7slsEIDLmybMKISHRyPbX4ZTN7C/g88H/N7J/CiSUi+RbKboKIjH15PZsQp4uUzOw6M3vVzJrM\n7K4oswR5fmBm75nZv0Sd5RQzm2VmNWa218z2mNmfxyBToZm9aGYvB5nuiTrTKWZWYGa7zGxb1FlO\nMbM3zew3wefVMNTYfJ9ajMVFSmZWADwA/AHwaaDSzD4ZZSbg0SBPnHQB69z908AiYE3Un5O7dwJL\n3b0UWAhcb2ZlUWbq5XZgX9Qh+jkJJN291N2H/JzyWgYxukipDHjN3Zvd/QTwI+DmKAO5+/NAa5QZ\n+nP3d919d/C4HXgFuCTaVODuHwUPC8kcBI98X9fMZgE3AI9EnaUfI8vv+bl60dElwFu9fv4tMfgl\njzMzu5zMX+IXo03Sszn+MvAu8Iy774w6E/A/gTuJQTH148AzZrbTzP50qIFhnloEdJHSeGRm04Cn\ngNuDLYRIuftJoNTMioCnzWyuu0e2eW5mNwLvuftuM0sS/ZZvb4vd/ZCZXUCmFF4JtkLPEHoZuPuX\nwl7mKHgbuLTXz7OC56QfM5tApgged/etUefpzd3bggveriPaffXFwHIzuwGYDEw3s83uviLCTAC4\n+6Hgvx+Y2U/J7CIPWAZR7iZE2Z47gRIzu8zMJgEVQByOABvx+qsC8ENgn7v/r6iDAJjZ+Wb2b4PH\nk4EvAa9Gmcndv+Xul7r7J8j8LtXEoQjMbEqwVYeZTQV+H2gcbHy+Ty3G4iIld+8G1gI7gL3Aj9z9\nlSiynGJm1UA9MNvMWszsj6PME2RaDPxn4Jrg1NQuM7su4lgXA8+Z2W4yxy+2u/vPI84UVxcCzwfH\nV/4f8DN33zHYYF10JCLAuXs2QUT6URmICKAyEJGAykBEAJWBiARUBiICqAxEJKAyEBEA/j/z66GC\nb+KQrQAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ax = draw_grid()\n", "for i in zip(range(1,4)[::-1],range(1,4)):\n", " ax.text(i[0],i[1],'(%d,%d)'%i,fontsize=13,color='g')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can use the labels to compute the number of paths that terminate at each of the diagonal elements.\n", "\n", "| Label | Number of Paths|\n", "|-------|----------------|\n", "| (1,3) | $\\texttt{binom}(4,1)=4$|\n", "| (2,2) | $\\texttt{binom}(4,2)=6$|\n", "| (3,1) | $\\texttt{binom}(4,1)=4$|\n", "\n", "This means that there are 16-2=4+6+4=14 paths out of the initial group of 16 that have yet to terminate. Now, let's consider sequences of length five. The following figure shows the migration of paths to the next lower diagonal corresponding to the five-long sequences." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# construct matrix of indices for convenience\n", "i,j=np.meshgrid(range(5),range(4,-1,-1))\n", "m= i+1j*j\n", "\n", "ax = draw_grid()\n", "for i in np.diagonal(m,-1):\n", " ax.plot(i.real,i.imag,'sg',ms=15,alpha=.3)\n", "\n", "for i in np.diagonal(m,0):\n", " if i.real==0 or i.imag==0: continue\n", " ax.text(i.real,i.imag,'(%d,%d)'%(i.real,i.imag),fontsize=13,color='g')\n", "\n", "# add arrow markers\n", "heads=map(lambda i:(i.real,i.imag),np.diagonal(m,0))[1:-1]\n", "\n", "for i,j in heads:\n", " t=(i-1,j)\n", " ax.annotate(\"\",xy=(i-1,j),xytext=(i,j),\n", " arrowprops=dict(width=.5,color='green'),\n", " )\n", " ax.annotate(\"\",xy=(i,j-1),xytext=(i,j),\n", " arrowprops=dict(width=.5,color='green'),\n", " )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that two arrows end up at red termini. There are 28=2*14 paths in total (because each diagonal element can go either down or right). Of these 28, eight terminate on a red circle. Thus, under these conditions, the probability of a terminating five-long sequence is therefore $p_5 = \\frac{8}{28}=\\frac{2}{7}$. Next, we can draw the next layer corresponding to six-long sequences." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ax = draw_grid()\n", "for i in np.diagonal(m,-2):\n", "# if i.real==0 or i.imag==0: continue\n", " ax.plot(i.real,i.imag,'sg',ms=15,alpha=.3)\n", " \n", "for i in np.diagonal(m,-1):\n", " if i.real==0 or i.imag==0: continue\n", " ax.text(i.real,i.imag,'(%d,%d)'%(i.real,i.imag),fontsize=13,color='g')\n", "\n", "for i in np.diagonal(m,-2):\n", "# if i.real==0 or i.imag==0: continue\n", " ax.text(i.real-0.5,i.imag-0.5,'(%d,%d)'%(i.real,i.imag),fontsize=13,color='blue')\n", "\n", " \n", "# add arrow markers\n", "heads=map(lambda i:(i.real,i.imag),np.diagonal(m,-1))[1:-1]\n", "\n", "for i,j in heads:\n", " t=(i-1,j)\n", " ax.annotate(\"\",xy=(i-1,j),xytext=(i,j),\n", " arrowprops=dict(width=.5,color='green'),\n", " )\n", " ax.annotate(\"\",xy=(i,j-1),xytext=(i,j),\n", " arrowprops=dict(width=.5,color='green'),\n", " )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the last stage, there were 8 out of 28 paths that terminated. That leaves 20 paths still in play and therefore 40 paths on the indicated diagonal. In terms of our earlier accounting, we have\n", "\n", "| Label | Number of Paths|\n", "|-------|----------------|\n", "| (1,2) | 10|\n", "| (2,1) | 10|\n", "\n", "\n", "For the next layer, we have the following:\n", "\n", "| Label | Number of Paths|\n", "|-------|----------------|\n", "| (0,2) | 10|\n", "| (2,0) | 10|\n", "| (1,1) | 20|\n", "\n", "With this accounting, the probability of termination with a six-long\n", "sequence is $p_6=\\frac{20}{40}=\\frac{1}{2}$. Finally, because all paths going through (1,1) terminate at either (1,0) or (0,1), we have $p_7=1$.\n", "\n", "To assemble all these results, recall we have\n", "$$P_4=\\frac{1}{8}$$\n", "\n", "and also, because $p_4 = P(T_5| \\hat{T}_4)$ where $T_5$ is the probability of termination in five steps and $\\hat{T}_4$ is the probability of not terminating in four steps, we have\n", "\n", "$$P_5 = p_5 (1-P_4) = \\frac{2}{7} \\frac{7}{8}=\\frac{1}{4}$$\n", "\n", "Likewise for $P_6$,\n", "\n", "$$P_6 = p_6 (1-P_4)(1-p_5) = \\frac{1}{2}\\frac{7}{8}\\frac{5}{7} =\\frac{5}{16}$$\n", "\n", "Finally, for $P_7$, we have the following:\n", "\n", "$$P_7 = p_7 (1-P_4)(1-p_5)(1-p_6) = 1\\frac{7}{8}\\frac{5}{7}\\frac{1}{2} =\\frac{5}{16}$$\n", "\n", "Note that\n", "\n", "$$P_4+P_5+P_6+P_7 = 1$$\n", "\n", "A quick simulation can bear this out. " ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "Counter({4: 125, 5: 232, 6: 330, 7: 313})" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Counter([len(tuple(step())) for i in range(1000)])" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "We can automate this process in the following code" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from scipy.misc import comb\n", "import numpy as np" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1 4 6 4 1]\n" ] }, { "data": { "text/plain": [ "(4, 4)" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from __future__ import division\n", "n=4\n", "t = np.array([comb(n,i,exact=True) for i in range(n+1)],dtype=int)\n", "print t\n", "t[[0,-1]].sum()/t.sum()\n", "# split\n", "(t[1],t[-2])" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 4, 10, 10, 4])" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from numpy.lib.stride_tricks import as_strided\n", "np.hstack([t[1],as_strided(t[1:-1],(2,3-2+1),(t.itemsize,)*2).sum(axis=1),t[-2]])" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from scipy.misc import comb" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1, 4, 6, 4, 1]\n", "0.125\n" ] } ], "source": [ "x=[comb(4,i,exact=True) for i in range(5)]\n", "print x\n", "print x[0]*2/sum(x)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [], "source": [ "a = x.pop(0)\n", "b = x.pop()\n", "x=[ x[0] ]+[ sum(x[slice(i,i+2)]) for i in range(len(x)-1) ]+[ x[-1] ]" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.285714285714\n" ] } ], "source": [ "print 2*x[0]/sum(x)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def probstop(n=4):\n", " o=OrderedDict()\n", " k=n\n", " x=[comb(n,i,exact=True) for i in range(n+1)]\n", " o[k]=2*x[0]/sum(x)\n", " while len(x)>2:\n", " a = x.pop(0)\n", " b = x.pop()\n", " x=[x[0]]+[sum(x[slice(i,i+2)]) for i in range(len(x)-1)]+[x[-1]]\n", " k+=1\n", " o[k]=2*x[0]/sum(x)\n", " assert o[k]>0\n", " p = OrderedDict()\n", " factor=1\n", " for k,v in o.iteritems():\n", " p[k]=factor*o[k]\n", " factor = factor*(1-v) \n", " return o,p" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [], "source": [ "o,p=probstop(30)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "OrderedDict([(30, 1.862645149230957e-09),\n", " (31, 2.7939677238464355e-08),\n", " (32, 2.1653249859809875e-07),\n", " (33, 1.1548399925231934e-06),\n", " (34, 4.763714969158173e-06),\n", " (35, 1.6196630895137787e-05),\n", " (36, 4.724017344415188e-05),\n", " (37, 0.0001214747317135334),\n", " (38, 0.000280910317087546),\n", " (39, 0.0005930328916292638),\n", " (40, 0.0011564141386770643),\n", " (41, 0.002102571161231026),\n", " (42, 0.003591892400436336),\n", " (43, 0.005802287723781774),\n", " (44, 0.008910656147236296),\n", " (45, 0.0130689623492799),\n", " (46, 0.01837822830367486),\n", " (47, 0.024864661822618928),\n", " (48, 0.032462197379530267),\n", " (49, 0.041004880900459284),\n", " (50, 0.05023097910306262),\n", " (51, 0.059798784646503116),\n", " (52, 0.0693122276584468),\n", " (53, 0.07835295300520073),\n", " (54, 0.08651471894324247),\n", " (55, 0.09343589645870187),\n", " (56, 0.0988264289467039),\n", " (57, 0.10248666705584109),\n", " (58, 0.10431678611040969),\n", " (59, 0.10431678611040969)])" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "p" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "1.0" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sum(p.values())" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig,ax=subplots()\n", "ax.plot(p.keys(),p.values(),'-o')" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "w=pd.Series(Counter([len(tuple(step(30))) for i in range(5000)]))\n", "(w/5000.).plot(ax=ax,marker='s')" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fig" ] }, { "cell_type": "code", "execution_count": 56, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig,ax=subplots()\n", "ax.plot(p.keys(),np.cumsum(p.values()),'-o')\n", "ax.grid()" ] }, { "cell_type": "code", "execution_count": 103, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(-1, 100.0, -1, 100.0)" ] }, "execution_count": 103, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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pPjKwkoxcXs/PA3YpbcPGR4TQZMS8AB6Vv1LmyTBDuHpCf5E+oZTSEuhkfYCQ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\ndHRT6t6P3st9H7mPVDlFeihNZjSD2+uyurZKkIpEGaprVUIvpFavRRmlG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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig,ax=subplots()\n", "fig.set_size_inches((10,5))\n", "for i in range(150):\n", " x,y=zip(*tuple(step(100)))\n", " ax.plot(x,y,'o-',color='gray',alpha=.1/5.)\n", " ax.plot(x[-1],y[-1],'sg',alpha=.3)\n", "ax.set_aspect(1)\n", "ax.axis(xmin=-1,ymin=-1)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.11" } }, "nbformat": 4, "nbformat_minor": 0 }