Viking rings.ipynb

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      "┌ Info: Recompiling stale cache file /Users/john/.julia/compiled/v1.2/Plots/ld3vC.ji for Plots [91a5bcdd-55d7-5caf-9e0b-520d859cae80]\n",
      "└ @ Base loading.jl:1240\n"
     ]
    }
   ],
   "source": [
    "using Plots\n",
    "gr()\n",
    "default(leg=false)\n",
    "\n",
    "using Distributions"
   ]
  },
  {
   "cell_type": "code",
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    "V = 1113 # Number of vikings\n",
    "R = 1123 # Number of rings\n",
    "\n",
    "# Winner's f\n",
    "w = Float64[]\n",
    "\n",
    "# Deaths per run\n",
    "d = Int[]\n",
    "\n",
    "default(show=:inline)\n",
    "for j in 1:5000\n",
    "    \n",
    "# Assign rings evenly to each viking\n",
    "r = zeros(Int, V)\n",
    "for i in 1:R\n",
    "    r[i%V+1] += 1\n",
    "end\n",
    "\n",
    "# Assign each viking a fighting skill between 0 and 1\n",
    "f = 1.0.-rand(Beta(), V)\n",
    "\n",
    "deaths = 0\n",
    "for i in 1:12000\n",
    "    k = rand(1:V)\n",
    "    l = rand(1:V)\n",
    "\n",
    "    # Viking k challenges viking l according to collective encoding (number of rings)\n",
    "    if k!=l && (r[k]!=0 || r[l]!=0) && rand() < r[k] / r[k] + r[l]\n",
    "    #if f[k] > 0.5\n",
    "        deaths += 1\n",
    "        # Win/lose according to actual individual skill, f\n",
    "        if rand() < f[k] / (f[k] + f[l])\n",
    "            r[k] = r[k] + r[l]\n",
    "            r[l] = 0\n",
    "            #f[l] = rand()\n",
    "        else\n",
    "            r[l] = r[k] + r[l]\n",
    "            r[k] = 0\n",
    "            #f[k] = rand()\n",
    "        end\n",
    "    end\n",
    "        \n",
    "    m,_ = findmax(r)\n",
    "    if m == R\n",
    "        break\n",
    "    end\n",
    "    # Viking with most rings dies and spreads his rings to others\n",
    "    #for n in 1:m\n",
    "    #    r[rand(1:V)] += 1\n",
    "    #end\n",
    "    #r[m] = 0\n",
    "    #f[m] = rand()\n",
    "\n",
    "end\n",
    "\n",
    "_,m = findmax(r)\n",
    "push!(w, f[m])\n",
    "push!(d, deaths)\n",
    "histogram(w, bins=0:0.1:1)\n",
    "print(j, \" \", f[m], \" \", deaths)\n",
    "\n",
    "end\n"
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     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "default(show=:nothing)\n",
    "plot(histogram(w, normed=true))\n",
    "plot!(p1, 0:0.1:1, 0:0.2:2, lw=4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Normal{Float64}(μ=2746.5226, σ=50.829580848556915)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dist = fit(Normal, d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
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      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(histogram(d, normed=true))\n",
    "plot!(2600:2:2900, pdf.(dist, 2600:2:2900), lw=4)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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