{"id":2064,"date":"2026-08-01T18:03:52","date_gmt":"2026-08-01T11:03:52","guid":{"rendered":"https:\/\/people.usd.ac.id\/~ydkristanto\/?page_id=2064"},"modified":"2026-08-03T19:20:12","modified_gmt":"2026-08-03T12:20:12","slug":"lucky-duck-hunt","status":"publish","type":"page","link":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/lucky-duck-hunt\/","title":{"rendered":"Lucky Duck Hunt"},"content":{"rendered":"\n<div class=\"wp-block-buttons is-content-justification-right\">\n<div class=\"wp-block-button is-style-outline\"><a class=\"wp-block-button__link\" href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/media-pengajaran\/berburu-bebek-keberuntungan\/\">ID<\/a><\/div>\n<\/div>\n\n\n\n<p class=\"has-drop-cap\">Let&#8217;s play a game! Here&#8217;s how it works. You pay $1.00 to choose three out of ten rubber ducks that continuously float along a waterway. Three of the ducks have a red mark on the bottom. For each red-marked duck you choose, you win $1.00.<\/p>\n\n\n\n<div class=\"wp-block-group alignfull has-gray-background-color has-background\"><div class=\"wp-block-group__inner-container\">\n<h3 class=\"has-text-align-center\">Lucky Duck Game<\/h3>\n\n\n\n<p>Click three rubber ducks and see how much you win. Play the game several times to observe the pattern in your outcomes.<\/p>\n\n\n\n<div class=\"wp-block-columns alignwide\">\n<div class=\"wp-block-column\">\n<figure>\n<div id=\"calculator1\" class=\"aligncenter size-full\" style=\"width: 480px; height: 480px;\"><\/div>\n<figcaption>Game Area<\/figcaption>\n<\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column\">\n<figure>\n<div id=\"calculator2\" class=\"aligncenter size-full\" style=\"width: 480px; height: 480px;\"><\/div>\n<figcaption>Simulation Results<\/figcaption>\n<\/figure>\n\n<script>\n  var successSound = new Audio( 'https:\/\/people.usd.ac.id\/~ydkristanto\/wp-content\/uploads\/2026\/06\/freesound_community-tada-fanfare-a-6313.mp3'\n  );\n  successSound.preload = 'auto';\n  \n  var calculator1 = Desmos.GraphingCalculator(document.getElementById('calculator1'), {\n    expressions: false,\n    settingsMenu: false,\n    trace: false\n  });\n  var calculator2 = Desmos.GraphingCalculator(document.getElementById('calculator2'), {\n    expressions: false,\n    settingsMenu: false,\n    trace: false\n  });\n\n  var state1 = {\n    \"version\": 11,\n    \"graph\": {\n        \"viewport\": {\n            \"xmin\": -10,\n            \"ymin\": -14.981482611762154,\n            \"xmax\": 10,\n            \"ymax\": 14.981482611762154\n        },\n        \"showGrid\": false,\n        \"showXAxis\": false,\n        \"showYAxis\": false,\n        \"userLockedViewport\": true,\n        \"__v12ViewportLatexStash\": {\n            \"xmin\": \"-10\",\n            \"xmax\": \"10\",\n            \"ymin\": \"-14.981482611762154\",\n            \"ymax\": \"14.981482611762154\"\n        }\n    },\n    \"expressions\": {\n        \"list\": [\n            {\n                \"type\": \"folder\",\n                \"id\": \"46\",\n                \"title\": \"Variabel\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"55\",\n                \"folderId\": \"46\",\n                \"color\": \"#000000\",\n                \"latex\": \"P=0\",\n                \"hidden\": true,\n                \"slider\": {\n                    \"hardMin\": true,\n                    \"hardMax\": true,\n                    \"min\": \"0\",\n                    \"max\": \"1\",\n                    \"step\": \"1\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"47\",\n                \"folderId\": \"46\",\n                \"color\": \"#388c46\",\n                \"latex\": \"t_{0}=\\\\frac{t_{ms}}{1000}\",\n                \"slider\": {\n                    \"hardMin\": true,\n                    \"animationPeriod\": 80000,\n                    \"loopMode\": \"PLAY_ONCE\",\n                    \"min\": \"0\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"54\",\n                \"folderId\": \"46\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"t_{ms}=0\",\n                \"hidden\": true,\n                \"slider\": {\n                    \"hardMin\": true,\n                    \"min\": \"0\",\n                    \"max\": \"52013\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"53\",\n                \"folderId\": \"46\",\n                \"color\": \"#388c46\",\n                \"latex\": \"j_{alan}\\\\left(x\\\\right)=t_{ms}\\\\to t_{ms}+x\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"202\",\n                \"folderId\": \"46\",\n                \"text\": \"Banyak permainan:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"204\",\n                \"folderId\": \"46\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"m_{ain}=n_{main}\\\\to n_{main}+1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"203\",\n                \"folderId\": \"46\",\n                \"color\": \"#388c46\",\n                \"latex\": \"n_{main}=1\"\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"2\",\n                \"title\": \"Latar bawah\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"22\",\n                \"folderId\": \"2\",\n                \"text\": \"Tanah:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"4\",\n                \"folderId\": \"2\",\n                \"color\": \"#388c46\",\n                \"latex\": \"y\\\\ge5\",\n                \"lines\": false,\n                \"colorLatex\": \"w_{tanah}\",\n                \"fillOpacity\": \"1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"8\",\n                \"folderId\": \"2\",\n                \"color\": \"#388c46\",\n                \"latex\": \"y\\\\le-5\",\n                \"lines\": false,\n                \"colorLatex\": \"w_{tanah}\",\n                \"fillOpacity\": \"1\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"24\",\n                \"folderId\": \"2\",\n                \"text\": \"Saluran air:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"25\",\n                \"folderId\": \"2\",\n                \"color\": \"#000000\",\n                \"latex\": \"y\\\\le4\\\\left\\\\{y\\\\ge-4\\\\right\\\\}\\\\left\\\\{-10\\\\le x\\\\le10\\\\right\\\\}\",\n                \"lines\": false,\n                \"colorLatex\": \"w_{air}\",\n                \"fillOpacity\": \"1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"36\",\n                \"folderId\": \"2\",\n                \"color\": \"#000000\",\n                \"latex\": \"x=\\\\left[-10,10\\\\right]\\\\left\\\\{-4\\\\le y\\\\le4\\\\right\\\\}\",\n                \"lineOpacity\": \".3\",\n                \"lineWidth\": \"5\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"20\",\n                \"folderId\": \"2\",\n                \"text\": \"Tepian saluran air:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"3\",\n                \"folderId\": \"2\",\n                \"color\": \"#000000\",\n                \"latex\": \"y=\\\\left[-5,-4,4,5\\\\right]\",\n                \"lineOpacity\": \".8\",\n                \"lineWidth\": \"3\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"11\",\n                \"folderId\": \"2\",\n                \"color\": \"#388c46\",\n                \"latex\": \"p_{merah}=\\\\left[-15,-11...17\\\\right]\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"12\",\n                \"folderId\": \"2\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"p_{putih}=\\\\left[-13,-9...15\\\\right]\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"14\",\n                \"folderId\": \"2\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(\\\\left(p_{merah}-1,4\\\\right),\\\\left(p_{merah}+1,4\\\\right),\\\\left(p_{merah}+1,5\\\\right),\\\\left(p_{merah}-1,5\\\\right)\\\\right)\",\n                \"colorLatex\": \"w_{merah}\",\n                \"fillOpacity\": \"1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"16\",\n                \"folderId\": \"2\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(\\\\left(p_{putih}-1,4\\\\right),\\\\left(p_{putih}+1,4\\\\right),\\\\left(p_{putih}+1,5\\\\right),\\\\left(p_{putih}-1,5\\\\right)\\\\right)\",\n                \"colorLatex\": \"w_{putih}\",\n                \"fillOpacity\": \"1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"13\",\n                \"folderId\": \"2\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(\\\\left(p_{merah}-1,-4\\\\right),\\\\left(p_{merah}+1,-4\\\\right),\\\\left(p_{merah}+1,-5\\\\right),\\\\left(p_{merah}-1,-5\\\\right)\\\\right)\",\n                \"colorLatex\": \"w_{merah}\",\n                \"fillOpacity\": \"1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"17\",\n                \"folderId\": \"2\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(\\\\left(p_{putih}-1,-4\\\\right),\\\\left(p_{putih}+1,-4\\\\right),\\\\left(p_{putih}+1,-5\\\\right),\\\\left(p_{putih}-1,-5\\\\right)\\\\right)\",\n                \"colorLatex\": \"w_{putih}\",\n                \"fillOpacity\": \"1\"\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"32\",\n                \"title\": \"Bebek karet\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"37\",\n                \"folderId\": \"32\",\n                \"text\": \"Posisi awal:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"218\",\n                \"folderId\": \"32\",\n                \"color\": \"#388c46\",\n                \"latex\": \"x_{1}=\\\\left[-11,-13...-29\\\\right]\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"219\",\n                \"folderId\": \"32\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"y_{1}=\\\\left[0,0,2,-2,0,-2,2,-2,2,2\\\\right]\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"220\",\n                \"folderId\": \"32\",\n                \"color\": \"#000000\",\n                \"latex\": \"a_{cakY}=y_{1}\\\\to\\\\operatorname{shuffle}\\\\left(y_{1}\\\\right)\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"52\",\n                \"folderId\": \"32\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"L=12-\\\\left(-30\\\\right)\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"44\",\n                \"folderId\": \"32\",\n                \"color\": \"#c74440\",\n                \"latex\": \"x_{2}=\\\\operatorname{mod}\\\\left(2t_{0}+x_{1}+30,L\\\\right)-30\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"48\",\n                \"folderId\": \"32\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"\\\\left(x_{2},y_{1}\\\\right)\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"image\",\n                \"id\": \"136\",\n                \"folderId\": \"32\",\n                \"image_url\": \"https:\/\/uploads.desmos.com\/calculator-images\/5886c3955e75830748b6c907fdfc19b9\",\n                \"name\": \"rubber-duck-top.svg\",\n                \"foreground\": true,\n                \"center\": \"\\\\left(x_{2},y_{1}\\\\left\\\\{-12\\\\le x_{2}\\\\le12\\\\right\\\\}\\\\right)\",\n                \"width\": \"1.5\",\n                \"height\": \"1.5\",\n                \"opacity\": \"o_{L}\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"86\",\n                \"folderId\": \"32\",\n                \"text\": \"Transparansi:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"130\",\n                \"folderId\": \"32\",\n                \"color\": \"#388c46\",\n                \"latex\": \"r_{eseto}=o_{1}\\\\to1,o_{2}\\\\to1,o_{3}\\\\to1,o_{4}\\\\to1,o_{5}\\\\to1,o_{6}\\\\to1,o_{7}\\\\to1,o_{8}\\\\to1,o_{9}\\\\to1,o_{10}\\\\to1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"87\",\n                \"folderId\": \"32\",\n                \"color\": \"#c74440\",\n                \"latex\": \"o_{1}=1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"88\",\n                \"folderId\": \"32\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"o_{2}=1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"89\",\n                \"folderId\": \"32\",\n                \"color\": \"#388c46\",\n                \"latex\": \"o_{3}=1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"90\",\n                \"folderId\": \"32\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"o_{4}=1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"91\",\n                \"folderId\": \"32\",\n                \"color\": \"#000000\",\n                \"latex\": \"o_{5}=1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"92\",\n                \"folderId\": \"32\",\n                \"color\": \"#c74440\",\n                \"latex\": \"o_{6}=1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"93\",\n                \"folderId\": \"32\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"o_{7}=1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"94\",\n                \"folderId\": \"32\",\n                \"color\": \"#388c46\",\n                \"latex\": \"o_{8}=1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"95\",\n                \"folderId\": \"32\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"o_{9}=1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"96\",\n                \"folderId\": \"32\",\n                \"color\": \"#000000\",\n                \"latex\": \"o_{10}=1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"107\",\n                \"folderId\": \"32\",\n                \"color\": \"#c74440\",\n                \"latex\": \"o_{L}=\\\\left[o_{1},o_{2},o_{3},o_{4},o_{5},o_{6},o_{7},o_{8},o_{9},o_{10}\\\\right]\"\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"27\",\n                \"title\": \"Latar atas\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"28\",\n                \"folderId\": \"27\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"x\\\\le-10\\\\left\\\\{-4.5\\\\le y\\\\le4.5\\\\right\\\\}\",\n                \"lines\": false,\n                \"colorLatex\": \"w_{jembatan}\",\n                \"fillOpacity\": \"1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"30\",\n                \"folderId\": \"27\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"x\\\\ge10\\\\left\\\\{-4.5\\\\le y\\\\le4.5\\\\right\\\\}\",\n                \"lines\": false,\n                \"colorLatex\": \"w_{jembatan}\",\n                \"fillOpacity\": \"1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"35\",\n                \"folderId\": \"27\",\n                \"color\": \"#c74440\",\n                \"latex\": \"x=\\\\left[-10,10\\\\right]\\\\left\\\\{-4.5\\\\le y\\\\le4.5\\\\right\\\\}\",\n                \"colorLatex\": \"w_{jembatan2}\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"139\",\n                \"folderId\": \"27\",\n                \"text\": \"Kotak penyimpan:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"140\",\n                \"folderId\": \"27\",\n                \"color\": \"#388c46\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(\\\\left(-3.25,6.25\\\\right),\\\\left(3.25,6.25\\\\right),\\\\left(3.25,8.75\\\\right),\\\\left(-3.25,8.75\\\\right)\\\\right)\",\n                \"lines\": false,\n                \"colorLatex\": \"w_{jembatan}\",\n                \"fillOpacity\": \"1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"141\",\n                \"folderId\": \"27\",\n                \"color\": \"#388c46\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(\\\\left(-3,6.5\\\\right),\\\\left(3,6.5\\\\right),\\\\left(3,8.5\\\\right),\\\\left(-3,8.5\\\\right)\\\\right)\",\n                \"lines\": false,\n                \"colorLatex\": \"w_{jembatan2}\",\n                \"fillOpacity\": \"1\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"144\",\n                \"folderId\": \"27\",\n                \"text\": \"Bebek:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"148\",\n                \"folderId\": \"27\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"L_{Bebek}=\\\\left[-2,0,2\\\\right]\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"149\",\n                \"folderId\": \"27\",\n                \"color\": \"#388c46\",\n                \"latex\": \"L_{xBebek}=L_{Bebek}\\\\left[0...n_{klikB}\\\\right]\"\n            },\n            {\n                \"type\": \"image\",\n                \"id\": \"146\",\n                \"folderId\": \"27\",\n                \"image_url\": \"https:\/\/uploads.desmos.com\/calculator-images\/7f7b592480e8d960f7f936277ad24d7c\",\n                \"name\": \"rubber-duck-right.svg\",\n                \"foreground\": true,\n                \"center\": \"\\\\left(L_{xBebek},7.5\\\\left\\\\{n_{klikB}\\\\le3\\\\right\\\\}\\\\right)\",\n                \"width\": \"1.5\",\n                \"height\": \"1.5\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"179\",\n                \"folderId\": \"27\",\n                \"color\": \"#388c46\",\n                \"latex\": \"L_{xSukses}=\\\\left(\\\\frac{0}{L_{ambil}}+1\\\\right)\\\\cdot L_{Bebek}\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"181\",\n                \"folderId\": \"27\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"L_{xGagal}=\\\\left(\\\\frac{0}{1-L_{ambil}}+1\\\\right)\\\\cdot L_{Bebek}\"\n            },\n            {\n                \"type\": \"image\",\n                \"id\": \"178\",\n                \"folderId\": \"27\",\n                \"image_url\": \"https:\/\/uploads.desmos.com\/calculator-images\/50cf7e4250b78ee733d50a64fc8607d5\",\n                \"name\": \"rubber-duck-bottom-success.svg\",\n                \"foreground\": true,\n                \"center\": \"\\\\left(L_{xSukses},7.5\\\\left\\\\{n_{klikB}=4\\\\right\\\\}\\\\right)\",\n                \"width\": \"1.5\",\n                \"height\": \"1.5\"\n            },\n            {\n                \"type\": \"image\",\n                \"id\": \"183\",\n                \"folderId\": \"27\",\n                \"image_url\": \"https:\/\/uploads.desmos.com\/calculator-images\/84991ed352f0c1f88ae4ea6acee72b6c\",\n                \"name\": \"rubber-duck-bottom.svg\",\n                \"foreground\": true,\n                \"center\": \"\\\\left(L_{xGagal},7.5\\\\left\\\\{n_{klikB}=4\\\\right\\\\}\\\\right)\",\n                \"width\": \"1.5\",\n                \"height\": \"1.5\"\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"57\",\n                \"title\": \"Tombol\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"61\",\n                \"folderId\": \"57\",\n                \"text\": \"Tiap-tiap bebek:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"132\",\n                \"folderId\": \"57\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"k_{likB}=n_{klikB}\\\\to n_{klikB}+1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"133\",\n                \"folderId\": \"57\",\n                \"color\": \"#388c46\",\n                \"latex\": \"n_{klikB}=0\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"129\",\n                \"folderId\": \"57\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"r_{esetTb}=T_{b1}\\\\to1,T_{b2}\\\\to1,T_{b3}\\\\to1,T_{b4}\\\\to1,T_{b5}\\\\to1,T_{b6}\\\\to1,T_{b7}\\\\to1,T_{b8}\\\\to1,T_{b9}\\\\to1,T_{b10}\\\\to1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"62\",\n                \"folderId\": \"57\",\n                \"color\": \"#388c46\",\n                \"latex\": \"\\\\left(x-x_{2}\\\\left[1\\\\right]\\\\right)^{2}+\\\\left(y-y_{1}\\\\left[1\\\\right]\\\\right)^{2}\\\\le0.75^{2}\\\\left\\\\{T_{b1}=1\\\\right\\\\}\\\\left\\\\{-12\\\\le x_{2}\\\\left[1\\\\right]\\\\le12\\\\right\\\\}\\\\left\\\\{n_{klikB}<3\\\\right\\\\}\",\n                \"lines\": false,\n                \"colorLatex\": \"w_{putih}\",\n                \"fillOpacity\": \"0\",\n                \"clickableInfo\": {\n                    \"enabled\": true,\n                    \"latex\": \"o_{1}\\\\to0,T_{b1}\\\\to0,k_{likB},a_{cakPos}\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"108\",\n                \"folderId\": \"57\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"T_{b1}=1\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"65\",\n                \"folderId\": \"57\",\n                \"color\": \"#388c46\",\n                \"latex\": \"\\\\left(x-x_{2}\\\\left[2\\\\right]\\\\right)^{2}+\\\\left(y-y_{1}\\\\left[2\\\\right]\\\\right)^{2}\\\\le0.75^{2}\\\\left\\\\{T_{b2}=1\\\\right\\\\}\\\\left\\\\{-12\\\\le x_{2}\\\\left[2\\\\right]\\\\le12\\\\right\\\\}\\\\left\\\\{n_{klikB}<3\\\\right\\\\}\",\n                \"lines\": false,\n                \"colorLatex\": \"w_{putih}\",\n                \"fillOpacity\": \"0\",\n                \"clickableInfo\": {\n                    \"enabled\": true,\n                    \"latex\": \"o_{2}\\\\to0,T_{b2}\\\\to0,k_{likB},a_{cakPos}\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"109\",\n                \"folderId\": \"57\",\n                \"color\": \"#388c46\",\n                \"latex\": \"T_{b2}=1\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"74\",\n                \"folderId\": \"57\",\n                \"color\": \"#388c46\",\n                \"latex\": \"\\\\left(x-x_{2}\\\\left[3\\\\right]\\\\right)^{2}+\\\\left(y-y_{1}\\\\left[3\\\\right]\\\\right)^{2}\\\\le0.75^{2}\\\\left\\\\{T_{b3}=1\\\\right\\\\}\\\\left\\\\{-12\\\\le x_{2}\\\\left[3\\\\right]\\\\le12\\\\right\\\\}\\\\left\\\\{n_{klikB}<3\\\\right\\\\}\",\n                \"lines\": false,\n                \"colorLatex\": \"w_{putih}\",\n                \"fillOpacity\": \"0\",\n                \"clickableInfo\": {\n                    \"enabled\": true,\n                    \"latex\": \"o_{3}\\\\to0,T_{b3}\\\\to0,k_{likB},a_{cakPos}\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"110\",\n                \"folderId\": \"57\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"T_{b3}=1\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"72\",\n                \"folderId\": \"57\",\n                \"color\": \"#388c46\",\n                \"latex\": \"\\\\left(x-x_{2}\\\\left[4\\\\right]\\\\right)^{2}+\\\\left(y-y_{1}\\\\left[4\\\\right]\\\\right)^{2}\\\\le0.75^{2}\\\\left\\\\{T_{b4}=1\\\\right\\\\}\\\\left\\\\{-12\\\\le x_{2}\\\\left[4\\\\right]\\\\le12\\\\right\\\\}\\\\left\\\\{n_{klikB}<3\\\\right\\\\}\",\n                \"lines\": false,\n                \"colorLatex\": \"w_{putih}\",\n                \"fillOpacity\": \"0\",\n                \"clickableInfo\": {\n                    \"enabled\": true,\n                    \"latex\": \"o_{4}\\\\to0,T_{b4}\\\\to0,k_{likB},a_{cakPos}\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"111\",\n                \"folderId\": \"57\",\n                \"color\": \"#000000\",\n                \"latex\": \"T_{b4}=1\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"71\",\n                \"folderId\": \"57\",\n                \"color\": \"#388c46\",\n                \"latex\": \"\\\\left(x-x_{2}\\\\left[5\\\\right]\\\\right)^{2}+\\\\left(y-y_{1}\\\\left[5\\\\right]\\\\right)^{2}\\\\le0.75^{2}\\\\left\\\\{T_{b5}=1\\\\right\\\\}\\\\left\\\\{-12\\\\le x_{2}\\\\left[5\\\\right]\\\\le12\\\\right\\\\}\\\\left\\\\{n_{klikB}<3\\\\right\\\\}\",\n                \"lines\": false,\n                \"colorLatex\": \"w_{putih}\",\n                \"fillOpacity\": \"0\",\n                \"clickableInfo\": {\n                    \"enabled\": true,\n                    \"latex\": \"o_{5}\\\\to0,T_{b5}\\\\to0,k_{likB},a_{cakPos}\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"112\",\n                \"folderId\": \"57\",\n                \"color\": \"#c74440\",\n                \"latex\": \"T_{b5}=1\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"70\",\n                \"folderId\": \"57\",\n                \"color\": \"#388c46\",\n                \"latex\": \"\\\\left(x-x_{2}\\\\left[6\\\\right]\\\\right)^{2}+\\\\left(y-y_{1}\\\\left[6\\\\right]\\\\right)^{2}\\\\le0.75^{2}\\\\left\\\\{T_{b6}=1\\\\right\\\\}\\\\left\\\\{-12\\\\le x_{2}\\\\left[6\\\\right]\\\\le12\\\\right\\\\}\\\\left\\\\{n_{klikB}<3\\\\right\\\\}\",\n                \"lines\": false,\n                \"colorLatex\": \"w_{putih}\",\n                \"fillOpacity\": \"0\",\n                \"clickableInfo\": {\n                    \"enabled\": true,\n                    \"latex\": \"o_{6}\\\\to0,T_{b6}\\\\to0,k_{likB},a_{cakPos}\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"113\",\n                \"folderId\": \"57\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"T_{b6}=1\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"69\",\n                \"folderId\": \"57\",\n                \"color\": \"#388c46\",\n                \"latex\": \"\\\\left(x-x_{2}\\\\left[7\\\\right]\\\\right)^{2}+\\\\left(y-y_{1}\\\\left[7\\\\right]\\\\right)^{2}\\\\le0.75^{2}\\\\left\\\\{T_{b7}=1\\\\right\\\\}\\\\left\\\\{-12\\\\le x_{2}\\\\left[7\\\\right]\\\\le12\\\\right\\\\}\\\\left\\\\{n_{klikB}<3\\\\right\\\\}\",\n                \"lines\": false,\n                \"colorLatex\": \"w_{putih}\",\n                \"fillOpacity\": \"0\",\n                \"clickableInfo\": {\n                    \"enabled\": true,\n                    \"latex\": \"o_{7}\\\\to0,T_{b7}\\\\to0,k_{likB},a_{cakPos}\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"114\",\n                \"folderId\": \"57\",\n                \"color\": \"#388c46\",\n                \"latex\": \"T_{b7}=1\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"68\",\n                \"folderId\": \"57\",\n                \"color\": \"#388c46\",\n                \"latex\": \"\\\\left(x-x_{2}\\\\left[8\\\\right]\\\\right)^{2}+\\\\left(y-y_{1}\\\\left[8\\\\right]\\\\right)^{2}\\\\le0.75^{2}\\\\left\\\\{T_{b8}=1\\\\right\\\\}\\\\left\\\\{-12\\\\le x_{2}\\\\left[8\\\\right]\\\\le12\\\\right\\\\}\\\\left\\\\{n_{klikB}<3\\\\right\\\\}\",\n                \"lines\": false,\n                \"colorLatex\": \"w_{putih}\",\n                \"fillOpacity\": \"0\",\n                \"clickableInfo\": {\n                    \"enabled\": true,\n                    \"latex\": \"o_{8}\\\\to0,T_{b8}\\\\to0,k_{likB},a_{cakPos}\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"115\",\n                \"folderId\": \"57\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"T_{b8}=1\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"67\",\n                \"folderId\": \"57\",\n                \"color\": \"#388c46\",\n                \"latex\": \"\\\\left(x-x_{2}\\\\left[9\\\\right]\\\\right)^{2}+\\\\left(y-y_{1}\\\\left[9\\\\right]\\\\right)^{2}\\\\le0.75^{2}\\\\left\\\\{T_{b9}=1\\\\right\\\\}\\\\left\\\\{-12\\\\le x_{2}\\\\left[9\\\\right]\\\\le12\\\\right\\\\}\\\\left\\\\{n_{klikB}<3\\\\right\\\\}\",\n                \"lines\": false,\n                \"colorLatex\": \"w_{putih}\",\n                \"fillOpacity\": \"0\",\n                \"clickableInfo\": {\n                    \"enabled\": true,\n                    \"latex\": \"o_{9}\\\\to0,T_{b9}\\\\to0,k_{likB},a_{cakPos}\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"116\",\n                \"folderId\": \"57\",\n                \"color\": \"#000000\",\n                \"latex\": \"T_{b9}=1\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"66\",\n                \"folderId\": \"57\",\n                \"color\": \"#388c46\",\n                \"latex\": \"\\\\left(x-x_{2}\\\\left[10\\\\right]\\\\right)^{2}+\\\\left(y-y_{1}\\\\left[10\\\\right]\\\\right)^{2}\\\\le0.75^{2}\\\\left\\\\{T_{b10}=1\\\\right\\\\}\\\\left\\\\{-12\\\\le x_{2}\\\\left[10\\\\right]\\\\le12\\\\right\\\\}\\\\left\\\\{n_{klikB}<3\\\\right\\\\}\",\n                \"lines\": false,\n                \"colorLatex\": \"w_{putih}\",\n                \"fillOpacity\": \"0\",\n                \"clickableInfo\": {\n                    \"enabled\": true,\n                    \"latex\": \"o_{10}\\\\to0,T_{b10}\\\\to0,k_{likB},a_{cakPos}\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"117\",\n                \"folderId\": \"57\",\n                \"color\": \"#c74440\",\n                \"latex\": \"T_{b10}=1\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"171\",\n                \"folderId\": \"57\",\n                \"text\": \"Periksa:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"172\",\n                \"folderId\": \"57\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(\\\\left(9.5,9.5\\\\right),\\\\left(5.5,9.5\\\\right),\\\\left(5.5,8\\\\right),\\\\left(9.5,8\\\\right)\\\\right)\\\\left\\\\{n_{klikB}=3\\\\right\\\\}\",\n                \"lines\": false,\n                \"colorLatex\": \"w_{putih}\",\n                \"fillOpacity\": \".6\",\n                \"lineWidth\": \"1.5\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"174\",\n                \"folderId\": \"57\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(\\\\left(9.5,9.5\\\\right),\\\\left(5.5,9.5\\\\right),\\\\left(5.5,8\\\\right),\\\\left(9.5,8\\\\right)\\\\right)\\\\left\\\\{n_{klikB}=3\\\\right\\\\}\",\n                \"fillOpacity\": \"0\",\n                \"lineWidth\": \"1.5\",\n                \"clickableInfo\": {\n                    \"enabled\": true,\n                    \"latex\": \"k_{likB},g_{abungUang},g_{abungHarapan}\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"175\",\n                \"folderId\": \"57\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(\\\\frac{9.5+5.5}{2},\\\\frac{9.5+8}{2}\\\\left\\\\{n_{klikB}=3\\\\right\\\\}\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"Check\",\n                \"hidden\": true,\n                \"labelSize\": \".9\",\n                \"suppressTextOutline\": true,\n                \"pointOpacity\": \".8\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"193\",\n                \"folderId\": \"57\",\n                \"text\": \"Main lagi:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"194\",\n                \"folderId\": \"57\",\n                \"color\": \"#388c46\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(\\\\left(9.5,9.5\\\\right),\\\\left(5,9.5\\\\right),\\\\left(5,8\\\\right),\\\\left(9.5,8\\\\right)\\\\right)\\\\left\\\\{n_{klikB}=4\\\\right\\\\}\",\n                \"lines\": false,\n                \"colorLatex\": \"w_{putih}\",\n                \"fillOpacity\": \".6\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"195\",\n                \"folderId\": \"57\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(\\\\left(9.5,9.5\\\\right),\\\\left(5,9.5\\\\right),\\\\left(5,8\\\\right),\\\\left(9.5,8\\\\right)\\\\right)\\\\left\\\\{n_{klikB}=4\\\\right\\\\}\",\n                \"fillOpacity\": \"0\",\n                \"lineWidth\": \"1.5\",\n                \"clickableInfo\": {\n                    \"enabled\": true,\n                    \"latex\": \"n_{klikB}\\\\to0,r_{esetTb},r_{eseto},m_{ain},a_{cakY}\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"196\",\n                \"folderId\": \"57\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(\\\\frac{9.5+5}{2},\\\\frac{9.5+8}{2}\\\\left\\\\{n_{klikB}=4\\\\right\\\\}\\\\left\\\\{n_{main}\\\\le100\\\\right\\\\}\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"Play again\",\n                \"hidden\": true,\n                \"labelSize\": \".9\",\n                \"suppressTextOutline\": true,\n                \"pointOpacity\": \".8\"\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"152\",\n                \"title\": \"Indikator\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"163\",\n                \"folderId\": \"152\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"L_{pos}=\\\\left[0,0,0,0,1,1,0,0,0,1\\\\right]\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"165\",\n                \"folderId\": \"152\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"a_{cakPos}=L_{pos}\\\\to\\\\operatorname{shuffle}\\\\left(L_{pos}\\\\right)\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"164\",\n                \"folderId\": \"152\",\n                \"color\": \"#388c46\",\n                \"latex\": \"L_{ambil}=L_{pos}\\\\left[1...3\\\\right]\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"199\",\n                \"folderId\": \"152\",\n                \"text\": \"Distribusi uang yang diterima atau hilang:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"185\",\n                \"folderId\": \"152\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"n_{sukses}=\\\\operatorname{total}\\\\left(L_{ambil}\\\\right)\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"186\",\n                \"folderId\": \"152\",\n                \"color\": \"#388c46\",\n                \"latex\": \"u_{ang}=n_{sukses}\\\\cdot10000-10000\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"187\",\n                \"folderId\": \"152\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"L_{uang}=\\\\left[\\\\right]\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"188\",\n                \"folderId\": \"152\",\n                \"color\": \"#000000\",\n                \"latex\": \"g_{abungUang}=L_{uang}\\\\to\\\\operatorname{join}\\\\left(L_{uang},u_{ang}\\\\right)\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"221\",\n                \"folderId\": \"152\",\n                \"color\": \"#c74440\",\n                \"latex\": \"h_{arapan}=\\\\operatorname{mean}\\\\left(L_{uang}\\\\right)\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"222\",\n                \"folderId\": \"152\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"L_{harapan}=\\\\left[\\\\right]\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"223\",\n                \"folderId\": \"152\",\n                \"color\": \"#388c46\",\n                \"latex\": \"g_{abungHarapan}=L_{harapan}\\\\to\\\\operatorname{join}\\\\left(L_{harapan},h_{arapan}\\\\right)\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"207\",\n                \"folderId\": \"152\",\n                \"text\": \"Teks indikator:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"213\",\n                \"folderId\": \"152\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"I_{1}=\\\\left\\\\{n_{klikB}=4:1,0\\\\right\\\\}\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"214\",\n                \"folderId\": \"152\",\n                \"color\": \"#388c46\",\n                \"latex\": \"I_{2}=\\\\left\\\\{n_{sukses}\\\\ge2:1,0\\\\right\\\\}\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"215\",\n                \"folderId\": \"152\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"I=\\\\left\\\\{I_{1}+I_{2}=2:1,0\\\\right\\\\}\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"208\",\n                \"folderId\": \"152\",\n                \"color\": \"#388c46\",\n                \"latex\": \"\\\\left(0,-7.5\\\\right)\\\\left\\\\{n_{klikB}=4\\\\right\\\\}\\\\left\\\\{n_{sukses}=3\\\\right\\\\}\",\n                \"showLabel\": true,\n                \"label\": \"Jackpot!\",\n                \"hidden\": true,\n                \"labelSize\": \"1.5\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"211\",\n                \"folderId\": \"152\",\n                \"color\": \"#388c46\",\n                \"latex\": \"\\\\left(0,-7.5\\\\right)\\\\left\\\\{n_{klikB}=4\\\\right\\\\}\\\\left\\\\{n_{sukses}=2\\\\right\\\\}\",\n                \"showLabel\": true,\n                \"label\": \"You won $1.00!\",\n                \"hidden\": true,\n                \"labelSize\": \"1.5\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"210\",\n                \"folderId\": \"152\",\n                \"color\": \"#fa7e19\",\n                \"latex\": \"\\\\left(0,-7.5\\\\right)\\\\left\\\\{n_{klikB}=4\\\\right\\\\}\\\\left\\\\{n_{sukses}=1\\\\right\\\\}\",\n                \"showLabel\": true,\n                \"label\": \"Break even\",\n                \"hidden\": true,\n                \"labelSize\": \"1.5\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"209\",\n                \"folderId\": \"152\",\n                \"color\": \"#c74440\",\n                \"latex\": \"\\\\left(0,-7.5\\\\right)\\\\left\\\\{n_{klikB}=4\\\\right\\\\}\\\\left\\\\{n_{sukses}=0\\\\right\\\\}\",\n                \"showLabel\": true,\n                \"label\": \"You lost $1.00\",\n                \"hidden\": true,\n                \"labelSize\": \"1.5\"\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"6\",\n                \"title\": \"Warna\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"7\",\n                \"folderId\": \"6\",\n                \"color\": \"#000000\",\n                \"latex\": \"w_{tanah}=\\\\operatorname{rgb}\\\\left(179,144,97\\\\right)\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"18\",\n                \"folderId\": \"6\",\n                \"color\": \"#c74440\",\n                \"latex\": \"w_{air}=\\\\operatorname{rgb}\\\\left(56,172,235\\\\right)\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"29\",\n                \"folderId\": \"6\",\n                \"color\": \"#388c46\",\n                \"latex\": \"w_{jembatan}=\\\\operatorname{rgb}\\\\left(177,117,57\\\\right)\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"34\",\n                \"folderId\": \"6\",\n                \"color\": \"#388c46\",\n                \"latex\": \"w_{jembatan2}=\\\\operatorname{rgb}\\\\left(119,78,38\\\\right)\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"9\",\n                \"folderId\": \"6\",\n                \"color\": \"#c74440\",\n                \"latex\": \"w_{putih}=\\\\operatorname{rgb}\\\\left(255,255,255\\\\right)\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"10\",\n                \"folderId\": \"6\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"w_{merah}=\\\\operatorname{rgb}\\\\left(216,49,40\\\\right)\"\n            }\n        ],\n        \"ticker\": {\n            \"handlerLatex\": \"j_{alan}\\\\left(\\\\operatorname{dt}\\\\right)\",\n            \"playing\": true,\n            \"open\": true\n        }\n    },\n    \"includeFunctionParametersInRandomSeed\": true,\n    \"doNotMigrateMovablePointStyle\": true\n};\n  var state2 = {\n    \"version\": 11,\n    \"graph\": {\n        \"viewport\": {\n            \"xmin\": -25000,\n            \"ymin\": -0.3,\n            \"xmax\": 30000,\n            \"ymax\": 1.3\n        },\n        \"showGrid\": false,\n        \"showXAxis\": false,\n        \"showYAxis\": false,\n        \"userLockedViewport\": true,\n        \"squareAxes\": false,\n        \"__v12ViewportLatexStash\": {\n            \"xmin\": \"-25000\",\n            \"xmax\": \"30000\",\n            \"ymin\": \"-0.3\",\n            \"ymax\": \"1.3\"\n        }\n    },\n    \"expressions\": {\n        \"list\": [\n            {\n                \"type\": \"folder\",\n                \"id\": \"42\",\n                \"title\": \"Variabel dan parameter\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"3\",\n                \"folderId\": \"42\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"L_{uang}=\\\\left[\\\\right]\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"73\",\n                \"folderId\": \"42\",\n                \"color\": \"#c74440\",\n                \"latex\": \"L_{harapan}=\\\\left[\\\\right]\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"36\",\n                \"folderId\": \"42\",\n                \"color\": \"#c74440\",\n                \"latex\": \"n_{main}=1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"63\",\n                \"folderId\": \"42\",\n                \"color\": \"#388c46\",\n                \"latex\": \"V=0\"\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"44\",\n                \"title\": \"Latar belakang plot\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"12\",\n                \"folderId\": \"44\",\n                \"text\": \"Latar belakang solid:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"11\",\n                \"folderId\": \"44\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(\\\\left(27500,-0.05\\\\right),\\\\left(27500,1.05\\\\right),\\\\left(-17500,1.05\\\\right),\\\\left(-17500,-0.05\\\\right)\\\\right)\",\n                \"lines\": false,\n                \"colorLatex\": \"w_{putih}\",\n                \"fillOpacity\": \"1\"\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"5\",\n                \"title\": \"Histogram\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"17\",\n                \"folderId\": \"5\",\n                \"text\": \"Kisi-kisi:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"18\",\n                \"folderId\": \"5\",\n                \"color\": \"#388c46\",\n                \"latex\": \"x=\\\\left[-10000,0...20000\\\\right]\\\\left\\\\{-0.05\\\\le y\\\\le1.05\\\\right\\\\}\\\\left\\\\{V=0\\\\right\\\\}\",\n                \"colorLatex\": \"w_{lightgray}\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"19\",\n                \"folderId\": \"5\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"x=\\\\left[-15000,-5000...25000\\\\right]\\\\left\\\\{-0.05\\\\le y\\\\le1.05\\\\right\\\\}\\\\left\\\\{V=0\\\\right\\\\}\",\n                \"colorLatex\": \"w_{lightgray}\",\n                \"lineWidth\": \"1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"20\",\n                \"folderId\": \"5\",\n                \"color\": \"#000000\",\n                \"latex\": \"y=\\\\left[0.1,0.3...0.9\\\\right]\\\\left\\\\{-17500\\\\le x\\\\le27500\\\\right\\\\}\\\\left\\\\{V=0\\\\right\\\\}\",\n                \"colorLatex\": \"w_{lightgray}\",\n                \"lineWidth\": \"1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"21\",\n                \"folderId\": \"5\",\n                \"color\": \"#000000\",\n                \"latex\": \"y=\\\\left[0.2,0.4...1\\\\right]\\\\left\\\\{-17500\\\\le x\\\\le27500\\\\right\\\\}\\\\left\\\\{V=0\\\\right\\\\}\",\n                \"colorLatex\": \"w_{lightgray}\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"6\",\n                \"folderId\": \"5\",\n                \"color\": \"#c74440\",\n                \"latex\": \"\\\\operatorname{histogram}\\\\left(L_{uang}\\\\left\\\\{V=0\\\\right\\\\},10000\\\\right)\",\n                \"vizProps\": {\n                    \"histogramMode\": \"relative\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"22\",\n                \"folderId\": \"5\",\n                \"color\": \"#c74440\",\n                \"latex\": \"y=0\\\\left\\\\{-17500\\\\le x\\\\le27500\\\\right\\\\}\\\\left\\\\{V=0\\\\right\\\\}\",\n                \"colorLatex\": \"w_{lightgray}\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"38\",\n                \"folderId\": \"5\",\n                \"text\": \"Nilai harapan:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"39\",\n                \"folderId\": \"5\",\n                \"color\": \"#000000\",\n                \"latex\": \"x=\\\\operatorname{mean}\\\\left(L_{uang}\\\\right)\\\\left\\\\{-0.05\\\\le y\\\\le1.05\\\\right\\\\}\\\\left\\\\{n_{main}\\\\ge3\\\\right\\\\}\\\\left\\\\{V=0\\\\right\\\\}\",\n                \"lineStyle\": \"DASHED\",\n                \"lineWidth\": \"1.5\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"41\",\n                \"folderId\": \"5\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"n_{harapan}=\\\\operatorname{mean}\\\\left(L_{uang}\\\\right)\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"144\",\n                \"folderId\": \"5\",\n                \"color\": \"#c74440\",\n                \"latex\": \"n_{harapDollar}=\\\\frac{n_{harapan}}{10000}\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"148\",\n                \"folderId\": \"5\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"n_{harapDollarR}=\\\\operatorname{round}\\\\left(n_{harapDollar},2\\\\right)\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"40\",\n                \"folderId\": \"5\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(\\\\operatorname{mean}\\\\left(L_{uang}\\\\right),0.8\\\\left\\\\{n_{main}\\\\ge3\\\\right\\\\}\\\\left\\\\{V=0\\\\right\\\\}\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"`\\\\bar{x}=${n_{harapDollarR}}`\",\n                \"hidden\": true,\n                \"labelSize\": \".8\",\n                \"pointOpacity\": \".9\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"24\",\n                \"folderId\": \"5\",\n                \"text\": \"Tik:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"25\",\n                \"folderId\": \"5\",\n                \"color\": \"#000000\",\n                \"latex\": \"x=\\\\left[-10000,0...20000\\\\right]\\\\left\\\\{-0.07\\\\le y\\\\le-0.05\\\\right\\\\}\\\\left\\\\{V=0\\\\right\\\\}\",\n                \"lineWidth\": \"1.5\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"26\",\n                \"folderId\": \"5\",\n                \"color\": \"#000000\",\n                \"latex\": \"y=\\\\left[0,0.2...1\\\\right]\\\\left\\\\{-18000\\\\le x\\\\le-17500\\\\right\\\\}\\\\left\\\\{V=0\\\\right\\\\}\",\n                \"lineWidth\": \"1.5\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"28\",\n                \"folderId\": \"5\",\n                \"text\": \"Teks:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"30\",\n                \"folderId\": \"5\",\n                \"color\": \"#388c46\",\n                \"latex\": \"t_{eksX}=\\\\left[-10000,0...20000\\\\right]\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"145\",\n                \"folderId\": \"5\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"t_{eksXDollar}=\\\\frac{t_{eksX}}{10000}\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"29\",\n                \"folderId\": \"5\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(t_{eksX},-0.07\\\\left\\\\{V=0\\\\right\\\\}\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"${t_{eksXDollar}}.00\",\n                \"hidden\": true,\n                \"labelOrientation\": \"below\",\n                \"labelSize\": \".8\",\n                \"pointOpacity\": \".8\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"31\",\n                \"folderId\": \"5\",\n                \"color\": \"#c74440\",\n                \"latex\": \"t_{eksY}=\\\\left[0,20...100\\\\right]\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"32\",\n                \"folderId\": \"5\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(-18000,\\\\frac{t_{eksY}}{100}\\\\left\\\\{V=0\\\\right\\\\}\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"${t_{eksY}}%\",\n                \"hidden\": true,\n                \"labelOrientation\": \"left\",\n                \"labelSize\": \".8\",\n                \"pointOpacity\": \".8\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"34\",\n                \"folderId\": \"5\",\n                \"text\": \"Judul sumbu:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"35\",\n                \"folderId\": \"5\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(\\\\frac{-10000+20000}{2},-0.175\\\\left\\\\{V=0\\\\right\\\\}\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"Net Outcome (Dollar)\",\n                \"hidden\": true,\n                \"labelSize\": \".9\",\n                \"pointOpacity\": \".8\"\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"49\",\n                \"title\": \"Diagram garis\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"50\",\n                \"folderId\": \"49\",\n                \"color\": \"#000000\",\n                \"latex\": \"p=27500-\\\\left(-17500\\\\right)\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"72\",\n                \"folderId\": \"49\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"p_{L}=\\\\operatorname{length}\\\\left(L_{uang}\\\\right)\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"74\",\n                \"folderId\": \"49\",\n                \"color\": \"#c74440\",\n                \"latex\": \"x_{1}=\\\\left[1...100\\\\right]\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"98\",\n                \"folderId\": \"49\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"x_{2}=\\\\left\\\\{p_{L}\\\\le10:x_{1}\\\\cdot\\\\frac{p}{10}-17500,10<p_{L}\\\\le20:x_{1}\\\\cdot\\\\frac{p}{20}-17500,20<p_{L}\\\\le50:x_{1}\\\\cdot\\\\frac{p}{50}-17500,50<p_{L}\\\\le100:x_{1}\\\\cdot\\\\frac{p}{100}-17500\\\\right\\\\}\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"76\",\n                \"folderId\": \"49\",\n                \"text\": \"Kisi-kisi (N <= 10):\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"77\",\n                \"folderId\": \"49\",\n                \"color\": \"#388c46\",\n                \"latex\": \"x=\\\\left[-13000,-4000...23000\\\\right]\\\\left\\\\{-0.05\\\\le y\\\\le1.05\\\\right\\\\}\\\\left\\\\{p_{L}\\\\le10\\\\right\\\\}\\\\left\\\\{V=1\\\\right\\\\}\",\n                \"colorLatex\": \"w_{lightgray}\",\n                \"lineWidth\": \"1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"85\",\n                \"folderId\": \"49\",\n                \"color\": \"#388c46\",\n                \"latex\": \"x=\\\\left[-8500,500...18500\\\\right]\\\\left\\\\{-0.05\\\\le y\\\\le1.05\\\\right\\\\}\\\\left\\\\{p_{L}\\\\le10\\\\right\\\\}\\\\left\\\\{V=1\\\\right\\\\}\",\n                \"colorLatex\": \"w_{lightgray}\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"79\",\n                \"folderId\": \"49\",\n                \"text\": \"Kisi-kisi (10 < N <= 20):\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"89\",\n                \"folderId\": \"49\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"x=\\\\left[-15250,-13000...27500\\\\right]\\\\left\\\\{-0.05\\\\le y\\\\le1.05\\\\right\\\\}\\\\left\\\\{10<p_{L}\\\\le20\\\\right\\\\}\\\\left\\\\{V=1\\\\right\\\\}\",\n                \"colorLatex\": \"w_{lightgray}\",\n                \"lineWidth\": \"1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"91\",\n                \"folderId\": \"49\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"x=\\\\left[-6250,5000,16250\\\\right]\\\\left\\\\{-0.05\\\\le y\\\\le1.05\\\\right\\\\}\\\\left\\\\{10<p_{L}\\\\le20\\\\right\\\\}\\\\left\\\\{V=1\\\\right\\\\}\",\n                \"colorLatex\": \"w_{lightgray}\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"81\",\n                \"folderId\": \"49\",\n                \"text\": \"Kisi-kisi (20 < N <= 50):\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"92\",\n                \"folderId\": \"49\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"x=\\\\left[-13000,-4000...23000\\\\right]\\\\left\\\\{-0.05\\\\le y\\\\le1.05\\\\right\\\\}\\\\left\\\\{20<p_{L}\\\\le50\\\\right\\\\}\\\\left\\\\{V=1\\\\right\\\\}\",\n                \"colorLatex\": \"w_{lightgray}\",\n                \"lineWidth\": \"1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"94\",\n                \"folderId\": \"49\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"x=\\\\left[-8500,500...18500\\\\right]\\\\left\\\\{-0.05\\\\le y\\\\le1.05\\\\right\\\\}\\\\left\\\\{20<p_{L}\\\\le50\\\\right\\\\}\\\\left\\\\{V=1\\\\right\\\\}\",\n                \"colorLatex\": \"w_{lightgray}\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"83\",\n                \"folderId\": \"49\",\n                \"text\": \"Kisi-kisi (50 < N <= 100):\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"95\",\n                \"folderId\": \"49\",\n                \"color\": \"#c74440\",\n                \"latex\": \"x=\\\\left[-13000,-4000...23000\\\\right]\\\\left\\\\{-0.05\\\\le y\\\\le1.05\\\\right\\\\}\\\\left\\\\{50<p_{L}\\\\le100\\\\right\\\\}\\\\left\\\\{V=1\\\\right\\\\}\",\n                \"colorLatex\": \"w_{lightgray}\",\n                \"lineWidth\": \"1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"97\",\n                \"folderId\": \"49\",\n                \"color\": \"#388c46\",\n                \"latex\": \"x=\\\\left[-8500,500...18500\\\\right]\\\\left\\\\{-0.05\\\\le y\\\\le1.05\\\\right\\\\}\\\\left\\\\{50<p_{L}\\\\le100\\\\right\\\\}\\\\left\\\\{V=1\\\\right\\\\}\",\n                \"colorLatex\": \"w_{lightgray}\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"87\",\n                \"folderId\": \"49\",\n                \"color\": \"#000000\",\n                \"latex\": \"y=\\\\left[0,\\\\frac{1}{3}...1\\\\right]\\\\left\\\\{-17500\\\\le x\\\\le27500\\\\right\\\\}\\\\left\\\\{V=1\\\\right\\\\}\",\n                \"colorLatex\": \"w_{lightgray}\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"88\",\n                \"folderId\": \"49\",\n                \"color\": \"#c74440\",\n                \"latex\": \"y=\\\\left[\\\\frac{1}{6},\\\\frac{1}{6}+\\\\frac{1}{3},\\\\frac{1}{6}+\\\\frac{2}{3}\\\\right]\\\\left\\\\{-17500\\\\le x\\\\le27500\\\\right\\\\}\\\\left\\\\{V=1\\\\right\\\\}\",\n                \"colorLatex\": \"w_{lightgray}\",\n                \"lineWidth\": \"1\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"100\",\n                \"folderId\": \"49\",\n                \"text\": \"Data:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"149\",\n                \"folderId\": \"49\",\n                \"color\": \"#388c46\",\n                \"latex\": \"L_{harapanG}=\\\\operatorname{join}\\\\left(L_{harapan},n_{harapan}\\\\right)\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"109\",\n                \"folderId\": \"49\",\n                \"color\": \"#388c46\",\n                \"latex\": \"L_{harapanTrans}=\\\\frac{1}{30000}\\\\cdot\\\\left(L_{harapanG}+10000\\\\right)\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"101\",\n                \"folderId\": \"49\",\n                \"color\": \"#c74440\",\n                \"latex\": \"\\\\left(x_{2},L_{harapanTrans}\\\\left\\\\{V=1\\\\right\\\\}\\\\right)\",\n                \"lines\": true\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"111\",\n                \"folderId\": \"49\",\n                \"text\": \"Tik (N <= 10):\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"112\",\n                \"folderId\": \"49\",\n                \"color\": \"#000000\",\n                \"latex\": \"x=\\\\left[-17500,-8500,...27500\\\\right]\\\\left\\\\{-0.07\\\\le y\\\\le-0.05\\\\right\\\\}\\\\left\\\\{p_{L}\\\\le10\\\\right\\\\}\\\\left\\\\{V=1\\\\right\\\\}\",\n                \"lineWidth\": \"1.5\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"115\",\n                \"folderId\": \"49\",\n                \"text\": \"Tik (10 < N <= 20):\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"116\",\n                \"folderId\": \"49\",\n                \"color\": \"#000000\",\n                \"latex\": \"x=\\\\left[-17500,-6250,5000,16250,27500\\\\right]\\\\left\\\\{-0.07\\\\le y\\\\le-0.05\\\\right\\\\}\\\\left\\\\{10<p_{L}\\\\le20\\\\right\\\\}\\\\left\\\\{V=1\\\\right\\\\}\",\n                \"lineWidth\": \"1.5\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"118\",\n                \"folderId\": \"49\",\n                \"text\": \"Tik (20 < N <= 100):\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"119\",\n                \"folderId\": \"49\",\n                \"color\": \"#000000\",\n                \"latex\": \"x=\\\\left[-17500,-8500...27500\\\\right]\\\\left\\\\{-0.07\\\\le y\\\\le-0.05\\\\right\\\\}\\\\left\\\\{20<p_{L}\\\\le100\\\\right\\\\}\\\\left\\\\{V=1\\\\right\\\\}\",\n                \"lineWidth\": \"1.5\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"123\",\n                \"folderId\": \"49\",\n                \"color\": \"#000000\",\n                \"latex\": \"y=\\\\left[0,\\\\frac{1}{3},\\\\frac{2}{3},1\\\\right]\\\\left\\\\{-18000\\\\le x\\\\le-17500\\\\right\\\\}\\\\left\\\\{V=1\\\\right\\\\}\",\n                \"lineWidth\": \"1.5\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"125\",\n                \"folderId\": \"49\",\n                \"text\": \"Teks sumbu y:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"126\",\n                \"folderId\": \"49\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"t_{Y}=\\\\left[-10000,0,10000,20000\\\\right]\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"146\",\n                \"folderId\": \"49\",\n                \"color\": \"#388c46\",\n                \"latex\": \"t_{YDollar}=\\\\frac{t_{Y}}{10000}\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"127\",\n                \"folderId\": \"49\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(-18000,\\\\frac{1}{30000}\\\\left(t_{Y}+10000\\\\right)\\\\right)\\\\left\\\\{V=1\\\\right\\\\}\",\n                \"showLabel\": true,\n                \"label\": \"${t_{YDollar}}.00\",\n                \"hidden\": true,\n                \"points\": false,\n                \"labelOrientation\": \"left\",\n                \"labelSize\": \".8\",\n                \"pointOpacity\": \".8\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"129\",\n                \"folderId\": \"49\",\n                \"text\": \"Teks sumbu-x (N <= 10):\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"130\",\n                \"folderId\": \"49\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"t_{X10}=\\\\left[0,2...10\\\\right]\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"131\",\n                \"folderId\": \"49\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(t_{X10}\\\\cdot\\\\frac{p}{10}-17500,-0.07\\\\right)\\\\left\\\\{p_{L}\\\\le10\\\\right\\\\}\\\\left\\\\{V=1\\\\right\\\\}\",\n                \"showLabel\": true,\n                \"label\": \"${t_{X10}}\",\n                \"hidden\": true,\n                \"points\": false,\n                \"labelOrientation\": \"below\",\n                \"labelSize\": \".8\",\n                \"pointOpacity\": \".8\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"133\",\n                \"folderId\": \"49\",\n                \"text\": \"Teks sumbu-x (10 < N <= 20):\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"134\",\n                \"folderId\": \"49\",\n                \"color\": \"#000000\",\n                \"latex\": \"t_{X20}=\\\\left[0,5,10,15,20\\\\right]\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"135\",\n                \"folderId\": \"49\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(t_{X20}\\\\cdot\\\\frac{p}{20}-17500,-0.07\\\\right)\\\\left\\\\{10<p_{L}\\\\le20\\\\right\\\\}\\\\left\\\\{V=1\\\\right\\\\}\",\n                \"showLabel\": true,\n                \"label\": \"${t_{X20}}\",\n                \"hidden\": true,\n                \"points\": false,\n                \"labelOrientation\": \"below\",\n                \"labelSize\": \".8\",\n                \"pointOpacity\": \".8\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"138\",\n                \"folderId\": \"49\",\n                \"text\": \"Teks sumbu-x (20 < N <= 50):\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"139\",\n                \"folderId\": \"49\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"t_{X50}=\\\\left[0,10...50\\\\right]\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"140\",\n                \"folderId\": \"49\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(t_{X50}\\\\cdot\\\\frac{p}{50}-17500,-0.07\\\\right)\\\\left\\\\{20<p_{L}\\\\le50\\\\right\\\\}\\\\left\\\\{V=1\\\\right\\\\}\",\n                \"showLabel\": true,\n                \"label\": \"${t_{X50}}\",\n                \"hidden\": true,\n                \"points\": false,\n                \"labelOrientation\": \"below\",\n                \"labelSize\": \".8\",\n                \"pointOpacity\": \".8\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"141\",\n                \"folderId\": \"49\",\n                \"text\": \"Teks sumbu-x (50 < N <= 100):\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"142\",\n                \"folderId\": \"49\",\n                \"color\": \"#c74440\",\n                \"latex\": \"t_{X100}=\\\\left[0,20...100\\\\right]\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"143\",\n                \"folderId\": \"49\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(t_{X100}\\\\cdot\\\\frac{p}{100}-17500,-0.07\\\\right)\\\\left\\\\{50<p_{L}\\\\le100\\\\right\\\\}\\\\left\\\\{V=1\\\\right\\\\}\",\n                \"showLabel\": true,\n                \"label\": \"${t_{X100}}\",\n                \"hidden\": true,\n                \"points\": false,\n                \"labelOrientation\": \"below\",\n                \"labelSize\": \".8\",\n                \"pointOpacity\": \".8\"\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"47\",\n                \"title\": \"Latar depan plot\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"14\",\n                \"folderId\": \"47\",\n                \"text\": \"Bingkai:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"15\",\n                \"folderId\": \"47\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(\\\\left(27500,-0.05\\\\right),\\\\left(27500,1.05\\\\right),\\\\left(-17500,1.05\\\\right),\\\\left(-17500,-0.05\\\\right)\\\\right)\",\n                \"fill\": false,\n                \"lineWidth\": \"1.5\"\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"53\",\n                \"title\": \"Tombol\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"59\",\n                \"folderId\": \"53\",\n                \"text\": \"Tombol distribusi:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"56\",\n                \"folderId\": \"53\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(\\\\left(15000,1.26\\\\right),\\\\left(1000,1.26\\\\right),\\\\left(1000,1.14\\\\right),\\\\left(15000,1.14\\\\right)\\\\right)\",\n                \"lines\": false,\n                \"colorLatex\": \"w_{putih}\",\n                \"fillOpacity\": \"1\",\n                \"lineWidth\": \"1.5\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"65\",\n                \"folderId\": \"53\",\n                \"color\": \"#c74440\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(\\\\left(15000,1.26\\\\right),\\\\left(1000,1.26\\\\right),\\\\left(1000,1.14\\\\right),\\\\left(15000,1.14\\\\right)\\\\right)\\\\left\\\\{V=0\\\\right\\\\}\",\n                \"lines\": false,\n                \"fillOpacity\": \".9\",\n                \"lineWidth\": \"1.5\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"61\",\n                \"folderId\": \"53\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(\\\\left(15000,1.26\\\\right),\\\\left(1000,1.26\\\\right),\\\\left(1000,1.14\\\\right),\\\\left(15000,1.14\\\\right)\\\\right)\",\n                \"fillOpacity\": \"0\",\n                \"lineWidth\": \"1.5\",\n                \"clickableInfo\": {\n                    \"enabled\": true,\n                    \"latex\": \"V\\\\to0\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"67\",\n                \"folderId\": \"53\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(8000,\\\\frac{1.26+1.14}{2}\\\\left\\\\{V=1\\\\right\\\\}\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"Distribution\",\n                \"hidden\": true,\n                \"labelSize\": \".9\",\n                \"suppressTextOutline\": true,\n                \"pointOpacity\": \".8\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"68\",\n                \"folderId\": \"53\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(8000,\\\\frac{1.26+1.14}{2}\\\\left\\\\{V=0\\\\right\\\\}\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"Distribution\",\n                \"hidden\": true,\n                \"labelSize\": \".9\",\n                \"suppressTextOutline\": true,\n                \"colorLatex\": \"w_{putih}\",\n                \"pointOpacity\": \".9\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"55\",\n                \"folderId\": \"53\",\n                \"text\": \"Tombol tren:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"60\",\n                \"folderId\": \"53\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(\\\\left(15000,1.26\\\\right),\\\\left(29000,1.26\\\\right),\\\\left(29000,1.14\\\\right),\\\\left(15000,1.14\\\\right)\\\\right)\",\n                \"lines\": false,\n                \"colorLatex\": \"w_{putih}\",\n                \"fillOpacity\": \"1\",\n                \"lineWidth\": \"1.5\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"66\",\n                \"folderId\": \"53\",\n                \"color\": \"#c74440\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(\\\\left(15000,1.26\\\\right),\\\\left(29000,1.26\\\\right),\\\\left(29000,1.14\\\\right),\\\\left(15000,1.14\\\\right)\\\\right)\\\\left\\\\{V=1\\\\right\\\\}\",\n                \"lines\": false,\n                \"fillOpacity\": \".9\",\n                \"lineWidth\": \"1.5\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"62\",\n                \"folderId\": \"53\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(\\\\left(15000,1.26\\\\right),\\\\left(29000,1.26\\\\right),\\\\left(29000,1.14\\\\right),\\\\left(15000,1.14\\\\right)\\\\right)\",\n                \"fillOpacity\": \"0\",\n                \"lineWidth\": \"1.5\",\n                \"clickableInfo\": {\n                    \"enabled\": true,\n                    \"latex\": \"V\\\\to1\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"69\",\n                \"folderId\": \"53\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(\\\\frac{15000+29000}{2},\\\\frac{1.26+1.14}{2}\\\\left\\\\{V=0\\\\right\\\\}\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"Mean Trend\",\n                \"hidden\": true,\n                \"labelSize\": \".9\",\n                \"suppressTextOutline\": true,\n                \"pointOpacity\": \".8\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"70\",\n                \"folderId\": \"53\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(\\\\frac{15000+29000}{2},\\\\frac{1.26+1.14}{2}\\\\left\\\\{V=1\\\\right\\\\}\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"Mean Trend\",\n                \"hidden\": true,\n                \"labelSize\": \".9\",\n                \"suppressTextOutline\": true,\n                \"colorLatex\": \"w_{putih}\",\n                \"pointOpacity\": \".9\"\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"8\",\n                \"title\": \"Warna\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"9\",\n                \"folderId\": \"8\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"w_{lightgray}=\\\\operatorname{rgb}\\\\left(211,211,211\\\\right)\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"10\",\n                \"folderId\": \"8\",\n                \"color\": \"#388c46\",\n                \"latex\": \"w_{putih}=\\\\operatorname{rgb}\\\\left(255,255,255\\\\right)\"\n            }\n        ]\n    },\n    \"includeFunctionParametersInRandomSeed\": true,\n    \"doNotMigrateMovablePointStyle\": true\n};\n\n  calculator1.setState(state1);\n  calculator2.setState(state2);\n  \n  \/\/ Source\n  var Luang = calculator1.HelperExpression({ latex: 'L_{uang}' });\n  var Lharapan = calculator1.HelperExpression({ latex: 'L_{harapan}' });\n  var nmain = calculator1.HelperExpression({ latex: 'n_{main}' });\n  var Iconf = calculator1.HelperExpression({ latex: 'I' });\n  \n  \/\/ Sink\n  Luang.observe('listValue', function() {\n    var value = Luang.listValue;\n\tcalculator2.setExpression({ id: '3', latex: `L_{uang}=[${value.join(',')}]` });\n  });\n  Lharapan.observe('listValue', function() {\n    var value = Lharapan.listValue;\n\tcalculator2.setExpression({ id: '73', latex: `L_{harapan}=[${value.join(',')}]` });\n  });\n  nmain.observe('numericValue', function() {\n    var value = nmain.numericValue;\n    if (!isNaN(value)) {\n      calculator2.setExpression({ id: '36', latex: `n_{main}=${value}` });\n    }\n  });\n  Iconf.observe('numericValue', function () {\n\tvar nilai = Iconf.numericValue;\n\tif (nilai === 1) {\n\t\tif (!confettiSudahMuncul) {\n\t\t\tsuccessSound.volume = 0.4;\n\t\t\tsuccessSound.currentTime = 0;\n\t\t\tsuccessSound.play();\n\t\t\tconfetti({\n\t\t\t\tparticleCount: 500,\n\t\t\t\tstartVelocity: 70,\n\t\t\t\tangle: 60,\n\t\t\t\tspread: 70,\n\t\t\t\torigin: { x: 0, y: 1 }\n\t\t\t});\n\t\t\tconfetti({\n\t\t\t\tparticleCount: 500,\n\t\t\t\tstartVelocity: 70,\n\t\t\t\tangle: 120,\n\t\t\t\tspread: 70,\n\t\t\t\torigin: { x: 1, y: 1 }\n\t\t\t});\n\t\t\tconfettiSudahMuncul = true;\n\t\t}\n\t}\n\tif (nilai !== 1) {\n\t\tconfettiSudahMuncul = false;\n\t}\n  });\n  \n<\/script>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group is-style-twentytwentyone-border\"><div class=\"wp-block-group__inner-container\">\n<p class=\"has-small-font-size\"><strong><em>Note:<\/em><\/strong> The <a href=\"#calculator2\">Simulation Results<\/a> panel contains two charts that you can switch between. The Distribution chart shows the proportion of games that result in each net outcome. Your net outcome is the prize you win minus the cost of playing the game. The Mean Trend chart shows how the average net outcome changes as more games are played.<\/p>\n<\/div><\/div>\n\n\n\n<h3>Ready for More?<\/h3>\n\n\n\n<p>This game was inspired by a set of problems in the Indonesian textbook <a href=\"https:\/\/buku.kemendikdasmen.go.id\/katalog\/matematika-untuk-smpmts-kelas-ix\" target=\"_blank\" rel=\"noreferrer noopener\"><em>Matematika untuk SMP\/MTs Kelas IX<\/em> [Mathematics for Grade 9]<\/a> (p. 279). Below is an adapted English version of the original problems. Give them a try and use what you discovered while playing the game to support your reasoning.<\/p>\n\n\n\n<div class=\"wp-block-group is-style-twentytwentyone-border\"><div class=\"wp-block-group__inner-container\">\n<p class=\"has-small-font-size\">Karuna runs a game booth at a funfair. The booth has a tub of water containing 10 rubber ducks. Three of the ducks have a red mark on the bottom. The rules of the game are as follows.<\/p>\n\n\n\n<ul class=\"has-small-font-size\"><li>Anyone who wants to play must pay $1.00.<\/li><li>Karuna shuffles the positions of the rubber ducks in the tub and then invites the player to choose three ducks at the same time.<\/li><li>For each red-marked duck selected, the player wins $1.00. For example, if a player selects two red-marked ducks, they receive a prize of $2.00.<\/li><\/ul>\n\n\n\n<p class=\"has-small-font-size\">With a game like this, can Karuna make a profit? Why? To answer this question, complete the following tasks.<\/p>\n\n\n\n<ol class=\"has-small-font-size\"><li>Determine the sample space for the game. Based on the sample space, decide whether Karuna makes a profit.<\/li><li>Simulate the game for 50 players. Based on the simulation, does Karuna make a profit?<\/li><li>Based on your findings, what advice would you give Karuna?<\/li><\/ol>\n<\/div><\/div>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<div style=\"height:100px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-group is-style-twentytwentyone-border\"><div class=\"wp-block-group__inner-container\">\n<div class=\"related-topics\">\n  <h3>Explore related topics<\/h3>\n  <p>Discover more contents with related topics in this website.<\/p>\n  <ul class=\"topics-list\">\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Mathematics\">Mathematics<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Statistics\">Statistics<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Probability\">Probability<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Expected+Value\">Expected Value<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Mean\">Mean<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Randomization\">Randomization<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Data+Visualization\">Data Visualization<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Game+Based+Learning\">Game-Based Learning<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Interactive+Learning+Resource\">Interactive Learning Resource<\/a><\/li>\n  <\/ul>\n<\/div>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Let&#8217;s play a game! Here&#8217;s how it works. You pay $1.00 to choose three out of ten rubber ducks that continuously float along a waterway. Three of the ducks have a red mark on the bottom. For each red-marked duck you choose, you win $1.00. Lucky Duck Game Click three rubber ducks and see how&hellip; <a class=\"more-link\" href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/lucky-duck-hunt\/\">Continue reading <span class=\"screen-reader-text\">Lucky Duck Hunt<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":2060,"parent":1140,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Lucky Duck Hunt<\/title>\n<meta name=\"description\" content=\"Play Lucky Duck Hunt to explore probability and expected value through an interactive simulation. Observe the distribution of your outcomes.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/lucky-duck-hunt\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Lucky Duck Hunt\" \/>\n<meta property=\"og:description\" content=\"Play Lucky Duck Hunt to explore probability and expected value through an interactive simulation. Observe the distribution of your outcomes.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/lucky-duck-hunt\/\" \/>\n<meta property=\"og:site_name\" content=\"Yosep Dwi Kristanto \u2014 Universitas Sanata Dharma\" \/>\n<meta property=\"article:modified_time\" content=\"2026-08-03T12:20:12+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/people.usd.ac.id\/~ydkristanto\/wp-content\/uploads\/2026\/08\/header-lucky-duck-hunt.png\" \/>\n\t<meta property=\"og:image:width\" content=\"1200\" \/>\n\t<meta property=\"og:image:height\" content=\"600\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"7 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebSite\",\"@id\":\"https:\/\/people.usd.ac.id\/~ydkristanto\/#website\",\"url\":\"https:\/\/people.usd.ac.id\/~ydkristanto\/\",\"name\":\"Yosep Dwi Kristanto \\u2014 Universitas Sanata Dharma\",\"description\":\"\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/lucky-duck-hunt\/#primaryimage\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/people.usd.ac.id\/~ydkristanto\/wp-content\/uploads\/2026\/08\/header-lucky-duck-hunt.png\",\"contentUrl\":\"https:\/\/people.usd.ac.id\/~ydkristanto\/wp-content\/uploads\/2026\/08\/header-lucky-duck-hunt.png\",\"width\":1200,\"height\":600},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/lucky-duck-hunt\/#webpage\",\"url\":\"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/lucky-duck-hunt\/\",\"name\":\"Lucky Duck Hunt\",\"isPartOf\":{\"@id\":\"https:\/\/people.usd.ac.id\/~ydkristanto\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/lucky-duck-hunt\/#primaryimage\"},\"datePublished\":\"2026-08-01T11:03:52+00:00\",\"dateModified\":\"2026-08-03T12:20:12+00:00\",\"description\":\"Play Lucky Duck Hunt to explore probability and expected value through an interactive simulation. Observe the distribution of your outcomes.\",\"breadcrumb\":{\"@id\":\"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/lucky-duck-hunt\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/lucky-duck-hunt\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/lucky-duck-hunt\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/people.usd.ac.id\/~ydkristanto\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Interactive Mathematics Learning Resources\",\"item\":\"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Lucky Duck Hunt\"}]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Lucky Duck Hunt","description":"Play Lucky Duck Hunt to explore probability and expected value through an interactive simulation. Observe the distribution of your outcomes.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/lucky-duck-hunt\/","og_locale":"en_US","og_type":"article","og_title":"Lucky Duck Hunt","og_description":"Play Lucky Duck Hunt to explore probability and expected value through an interactive simulation. Observe the distribution of your outcomes.","og_url":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/lucky-duck-hunt\/","og_site_name":"Yosep Dwi Kristanto \u2014 Universitas Sanata Dharma","article_modified_time":"2026-08-03T12:20:12+00:00","og_image":[{"width":1200,"height":600,"url":"https:\/\/people.usd.ac.id\/~ydkristanto\/wp-content\/uploads\/2026\/08\/header-lucky-duck-hunt.png","type":"image\/png"}],"twitter_card":"summary_large_image","twitter_misc":{"Est. reading time":"7 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebSite","@id":"https:\/\/people.usd.ac.id\/~ydkristanto\/#website","url":"https:\/\/people.usd.ac.id\/~ydkristanto\/","name":"Yosep Dwi Kristanto \u2014 Universitas Sanata Dharma","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/people.usd.ac.id\/~ydkristanto\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"ImageObject","@id":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/lucky-duck-hunt\/#primaryimage","inLanguage":"en-US","url":"https:\/\/people.usd.ac.id\/~ydkristanto\/wp-content\/uploads\/2026\/08\/header-lucky-duck-hunt.png","contentUrl":"https:\/\/people.usd.ac.id\/~ydkristanto\/wp-content\/uploads\/2026\/08\/header-lucky-duck-hunt.png","width":1200,"height":600},{"@type":"WebPage","@id":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/lucky-duck-hunt\/#webpage","url":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/lucky-duck-hunt\/","name":"Lucky Duck Hunt","isPartOf":{"@id":"https:\/\/people.usd.ac.id\/~ydkristanto\/#website"},"primaryImageOfPage":{"@id":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/lucky-duck-hunt\/#primaryimage"},"datePublished":"2026-08-01T11:03:52+00:00","dateModified":"2026-08-03T12:20:12+00:00","description":"Play Lucky Duck Hunt to explore probability and expected value through an interactive simulation. Observe the distribution of your outcomes.","breadcrumb":{"@id":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/lucky-duck-hunt\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/lucky-duck-hunt\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/lucky-duck-hunt\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/people.usd.ac.id\/~ydkristanto\/"},{"@type":"ListItem","position":2,"name":"Interactive Mathematics Learning Resources","item":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/"},{"@type":"ListItem","position":3,"name":"Lucky Duck Hunt"}]}]}},"_links":{"self":[{"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/pages\/2064"}],"collection":[{"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/comments?post=2064"}],"version-history":[{"count":8,"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/pages\/2064\/revisions"}],"predecessor-version":[{"id":2096,"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/pages\/2064\/revisions\/2096"}],"up":[{"embeddable":true,"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/pages\/1140"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/media\/2060"}],"wp:attachment":[{"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/media?parent=2064"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}