/*! * Chart.js * http://chartjs.org/ * * Copyright 2017 Nick Downie * Released under the MIT license * https://github.com/chartjs/Chart.js/blob/master/LICENSE.md */ !function(t){if("object"==typeof exports&&"undefined"!=typeof module)module.exports=t();else if("function"==typeof define&&define.amd)define([],t);else{("undefined"!=typeof window?window:"undefined"!=typeof global?global:"undefined"!=typeof self?self:this).Chart=t()}}(function(){return function t(e,n,i){function a(r,l){if(!n[r]){if(!e[r]){var s="function"==typeof require&&require;if(!l&&s)return s(r,!0);if(o)return o(r,!0);var u=new Error("Cannot find module '"+r+"'");throw u.code="MODULE_NOT_FOUND",u}var d=n[r]={exports:{}};e[r][0].call(d.exports,function(t){var n=e[r][1][t];return a(n||t)},d,d.exports,t,e,n,i)}return n[r].exports}for(var o="function"==typeof require&&require,r=0;rn?(e+.05)/(n+.05):(n+.05)/(e+.05)},level:function(t){var e=this.contrast(t);return e>=7.1?"AAA":e>=4.5?"AA":""},dark:function(){var 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e=Math.atan2(r,o),(n=360*e/2/Math.PI)<0&&(n+=360),i=Math.sqrt(o*o+r*r),[a,i,n]}function k(t){return v(x(t))}function w(t){var e,n,i,a=t[0],o=t[1];return i=t[2]/360*2*Math.PI,e=o*Math.cos(i),n=o*Math.sin(i),[a,e,n]}function M(t){return S[t]}e.exports={rgb2hsl:i,rgb2hsv:a,rgb2hwb:o,rgb2cmyk:l,rgb2keyword:s,rgb2xyz:u,rgb2lab:d,rgb2lch:function(t){return y(d(t))},hsl2rgb:c,hsl2hsv:function(t){var e,n,i=t[0],a=t[1]/100,o=t[2]/100;return 0===o?[0,0,0]:(o*=2,a*=o<=1?o:2-o,n=(o+a)/2,e=2*a/(o+a),[i,100*e,100*n])},hsl2hwb:function(t){return o(c(t))},hsl2cmyk:function(t){return l(c(t))},hsl2keyword:function(t){return s(c(t))},hsv2rgb:h,hsv2hsl:function(t){var e,n,i=t[0],a=t[1]/100,o=t[2]/100;return n=(2-a)*o,e=a*o,e/=n<=1?n:2-n,e=e||0,n/=2,[i,100*e,100*n]},hsv2hwb:function(t){return o(h(t))},hsv2cmyk:function(t){return l(h(t))},hsv2keyword:function(t){return s(h(t))},hwb2rgb:f,hwb2hsl:function(t){return i(f(t))},hwb2hsv:function(t){return a(f(t))},hwb2cmyk:function(t){return 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o.each(n.data,function(n,a){t=e.data[a],isNaN(t)||n.hidden||(i+=Math.abs(t))}),i},calculateCircumference:function(t){var e=this.getMeta().total;return e>0&&!isNaN(t)?2*Math.PI*(t/e):0},getMaxBorderWidth:function(t){for(var e,n,i=0,a=this.index,o=t.length,r=0;r(i=e>i?e:i)?n:i;return i}})}},{25:25,40:40,45:45}],18:[function(t,e,n){"use strict";var i=t(25),a=t(40),o=t(45);i._set("line",{showLines:!0,spanGaps:!1,hover:{mode:"label"},scales:{xAxes:[{type:"category",id:"x-axis-0"}],yAxes:[{type:"linear",id:"y-axis-0"}]}}),e.exports=function(t){function e(t,e){return o.valueOrDefault(t.showLine,e.showLines)}t.controllers.line=t.DatasetController.extend({datasetElementType:a.Line,dataElementType:a.Point,update:function(t){var n,i,a,r=this,l=r.getMeta(),s=l.dataset,u=l.data||[],d=r.chart.options,c=d.elements.line,h=r.getScaleForId(l.yAxisID),f=r.getDataset(),g=e(f,d);for(g&&(a=s.custom||{},void 0!==f.tension&&void 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0!==f.fill?f.fill:c.fill,steppedLine:a.steppedLine?a.steppedLine:o.valueOrDefault(f.steppedLine,c.stepped),cubicInterpolationMode:a.cubicInterpolationMode?a.cubicInterpolationMode:o.valueOrDefault(f.cubicInterpolationMode,c.cubicInterpolationMode)},s.pivot()),n=0,i=u.length;n');var n=t.data,i=n.datasets,a=n.labels;if(i.length)for(var o=0;o'),a[o]&&e.push(a[o]),e.push("");return e.push(""),e.join("")},legend:{labels:{generateLabels:function(t){var e=t.data;return e.labels.length&&e.datasets.length?e.labels.map(function(n,i){var a=t.getDatasetMeta(0),r=e.datasets[0],l=a.data[i].custom||{},s=o.valueAtIndexOrDefault,u=t.options.elements.arc;return{text:n,fillStyle:l.backgroundColor?l.backgroundColor:s(r.backgroundColor,i,u.backgroundColor),strokeStyle:l.borderColor?l.borderColor:s(r.borderColor,i,u.borderColor),lineWidth:l.borderWidth?l.borderWidth:s(r.borderWidth,i,u.borderWidth),hidden:isNaN(r.data[i])||a.data[i].hidden,index:i}}):[]}},onClick:function(t,e){var n,i,a,o=e.index,r=this.chart;for(n=0,i=(r.data.datasets||[]).length;n0&&!isNaN(t)?2*Math.PI/e:0}})}},{25:25,40:40,45:45}],20:[function(t,e,n){"use strict";var i=t(25),a=t(40),o=t(45);i._set("radar",{scale:{type:"radialLinear"},elements:{line:{tension:0}}}),e.exports=function(t){t.controllers.radar=t.DatasetController.extend({datasetElementType:a.Line,dataElementType:a.Point,linkScales:o.noop,update:function(t){var e=this,n=e.getMeta(),i=n.dataset,a=n.data,r=i.custom||{},l=e.getDataset(),s=e.chart.options.elements.line,u=e.chart.scale;void 0!==l.tension&&void 0===l.lineTension&&(l.lineTension=l.tension),o.extend(n.dataset,{_datasetIndex:e.index,_scale:u,_children:a,_loop:!0,_model:{tension:r.tension?r.tension:o.valueOrDefault(l.lineTension,s.tension),backgroundColor:r.backgroundColor?r.backgroundColor:l.backgroundColor||s.backgroundColor,borderWidth:r.borderWidth?r.borderWidth:l.borderWidth||s.borderWidth,borderColor:r.borderColor?r.borderColor:l.borderColor||s.borderColor,fill:r.fill?r.fill:void 0!==l.fill?l.fill:s.fill,borderCapStyle:r.borderCapStyle?r.borderCapStyle:l.borderCapStyle||s.borderCapStyle,borderDash:r.borderDash?r.borderDash:l.borderDash||s.borderDash,borderDashOffset:r.borderDashOffset?r.borderDashOffset:l.borderDashOffset||s.borderDashOffset,borderJoinStyle:r.borderJoinStyle?r.borderJoinStyle:l.borderJoinStyle||s.borderJoinStyle}}),n.dataset.pivot(),o.each(a,function(n,i){e.updateElement(n,i,t)},e),e.updateBezierControlPoints()},updateElement:function(t,e,n){var i=this,a=t.custom||{},r=i.getDataset(),l=i.chart.scale,s=i.chart.options.elements.point,u=l.getPointPositionForValue(e,r.data[e]);void 0!==r.radius&&void 0===r.pointRadius&&(r.pointRadius=r.radius),void 0!==r.hitRadius&&void 0===r.pointHitRadius&&(r.pointHitRadius=r.hitRadius),o.extend(t,{_datasetIndex:i.index,_index:e,_scale:l,_model:{x:n?l.xCenter:u.x,y:n?l.yCenter:u.y,tension:a.tension?a.tension:o.valueOrDefault(r.lineTension,i.chart.options.elements.line.tension),radius:a.radius?a.radius:o.valueAtIndexOrDefault(r.pointRadius,e,s.radius),backgroundColor:a.backgroundColor?a.backgroundColor:o.valueAtIndexOrDefault(r.pointBackgroundColor,e,s.backgroundColor),borderColor:a.borderColor?a.borderColor:o.valueAtIndexOrDefault(r.pointBorderColor,e,s.borderColor),borderWidth:a.borderWidth?a.borderWidth:o.valueAtIndexOrDefault(r.pointBorderWidth,e,s.borderWidth),pointStyle:a.pointStyle?a.pointStyle:o.valueAtIndexOrDefault(r.pointStyle,e,s.pointStyle),hitRadius:a.hitRadius?a.hitRadius:o.valueAtIndexOrDefault(r.pointHitRadius,e,s.hitRadius)}}),t._model.skip=a.skip?a.skip:isNaN(t._model.x)||isNaN(t._model.y)},updateBezierControlPoints:function(){var t=this.chart.chartArea,e=this.getMeta();o.each(e.data,function(n,i){var a=n._model,r=o.splineCurve(o.previousItem(e.data,i,!0)._model,a,o.nextItem(e.data,i,!0)._model,a.tension);a.controlPointPreviousX=Math.max(Math.min(r.previous.x,t.right),t.left),a.controlPointPreviousY=Math.max(Math.min(r.previous.y,t.bottom),t.top),a.controlPointNextX=Math.max(Math.min(r.next.x,t.right),t.left),a.controlPointNextY=Math.max(Math.min(r.next.y,t.bottom),t.top),n.pivot()})},setHoverStyle:function(t){var e=this.chart.data.datasets[t._datasetIndex],n=t.custom||{},i=t._index,a=t._model;a.radius=n.hoverRadius?n.hoverRadius:o.valueAtIndexOrDefault(e.pointHoverRadius,i,this.chart.options.elements.point.hoverRadius),a.backgroundColor=n.hoverBackgroundColor?n.hoverBackgroundColor:o.valueAtIndexOrDefault(e.pointHoverBackgroundColor,i,o.getHoverColor(a.backgroundColor)),a.borderColor=n.hoverBorderColor?n.hoverBorderColor:o.valueAtIndexOrDefault(e.pointHoverBorderColor,i,o.getHoverColor(a.borderColor)),a.borderWidth=n.hoverBorderWidth?n.hoverBorderWidth:o.valueAtIndexOrDefault(e.pointHoverBorderWidth,i,a.borderWidth)},removeHoverStyle:function(t){var e=this.chart.data.datasets[t._datasetIndex],n=t.custom||{},i=t._index,a=t._model,r=this.chart.options.elements.point;a.radius=n.radius?n.radius:o.valueAtIndexOrDefault(e.pointRadius,i,r.radius),a.backgroundColor=n.backgroundColor?n.backgroundColor:o.valueAtIndexOrDefault(e.pointBackgroundColor,i,r.backgroundColor),a.borderColor=n.borderColor?n.borderColor:o.valueAtIndexOrDefault(e.pointBorderColor,i,r.borderColor),a.borderWidth=n.borderWidth?n.borderWidth:o.valueAtIndexOrDefault(e.pointBorderWidth,i,r.borderWidth)}})}},{25:25,40:40,45:45}],21:[function(t,e,n){"use strict";t(25)._set("scatter",{hover:{mode:"single"},scales:{xAxes:[{id:"x-axis-1",type:"linear",position:"bottom"}],yAxes:[{id:"y-axis-1",type:"linear",position:"left"}]},showLines:!1,tooltips:{callbacks:{title:function(){return""},label:function(t){return"("+t.xLabel+", "+t.yLabel+")"}}}}),e.exports=function(t){t.controllers.scatter=t.controllers.line}},{25:25}],22:[function(t,e,n){"use strict";var i=t(25),a=t(26),o=t(45);i._set("global",{animation:{duration:1e3,easing:"easeOutQuart",onProgress:o.noop,onComplete:o.noop}}),e.exports=function(t){t.Animation=a.extend({chart:null,currentStep:0,numSteps:60,easing:"",render:null,onAnimationProgress:null,onAnimationComplete:null}),t.animationService={frameDuration:17,animations:[],dropFrames:0,request:null,addAnimation:function(t,e,n,i){var a,o,r=this.animations;for(e.chart=t,i||(t.animating=!0),a=0,o=r.length;a1&&(n=Math.floor(t.dropFrames),t.dropFrames=t.dropFrames%1),t.advance(1+n);var i=Date.now();t.dropFrames+=(i-e)/t.frameDuration,t.animations.length>0&&t.requestAnimationFrame()},advance:function(t){for(var e,n,i=this.animations,a=0;a=e.numSteps?(o.callback(e.onAnimationComplete,[e],n),n.animating=!1,i.splice(a,1)):++a}},Object.defineProperty(t.Animation.prototype,"animationObject",{get:function(){return this}}),Object.defineProperty(t.Animation.prototype,"chartInstance",{get:function(){return this.chart},set:function(t){this.chart=t}})}},{25:25,26:26,45:45}],23:[function(t,e,n){"use strict";var i=t(25),a=t(45),o=t(28),r=t(48);e.exports=function(t){function e(t){var e=(t=t||{}).data=t.data||{};return e.datasets=e.datasets||[],e.labels=e.labels||[],t.options=a.configMerge(i.global,i[t.type],t.options||{}),t}function n(t){var e=t.options;e.scale?t.scale.options=e.scale:e.scales&&e.scales.xAxes.concat(e.scales.yAxes).forEach(function(e){t.scales[e.id].options=e}),t.tooltip._options=e.tooltips}function l(t){return"top"===t||"bottom"===t}var s=t.plugins;t.types={},t.instances={},t.controllers={},a.extend(t.prototype,{construct:function(n,i){var o=this;i=e(i);var l=r.acquireContext(n,i),s=l&&l.canvas,u=s&&s.height,d=s&&s.width;o.id=a.uid(),o.ctx=l,o.canvas=s,o.config=i,o.width=d,o.height=u,o.aspectRatio=u?d/u:null,o.options=i.options,o._bufferedRender=!1,o.chart=o,o.controller=o,t.instances[o.id]=o,Object.defineProperty(o,"data",{get:function(){return o.config.data},set:function(t){o.config.data=t}}),l&&s?(o.initialize(),o.update()):console.error("Failed to create chart: can't acquire context from the given item")},initialize:function(){var t=this;return s.notify(t,"beforeInit"),a.retinaScale(t,t.options.devicePixelRatio),t.bindEvents(),t.options.responsive&&t.resize(!0),t.ensureScalesHaveIDs(),t.buildScales(),t.initToolTip(),s.notify(t,"afterInit"),t},clear:function(){return a.canvas.clear(this),this},stop:function(){return t.animationService.cancelAnimation(this),this},resize:function(t){var e=this,n=e.options,i=e.canvas,o=n.maintainAspectRatio&&e.aspectRatio||null,r=Math.max(0,Math.floor(a.getMaximumWidth(i))),l=Math.max(0,Math.floor(o?r/o:a.getMaximumHeight(i)));if((e.width!==r||e.height!==l)&&(i.width=e.width=r,i.height=e.height=l,i.style.width=r+"px",i.style.height=l+"px",a.retinaScale(e,n.devicePixelRatio),!t)){var u={width:r,height:l};s.notify(e,"resize",[u]),e.options.onResize&&e.options.onResize(e,u),e.stop(),e.update(e.options.responsiveAnimationDuration)}},ensureScalesHaveIDs:function(){var t=this.options,e=t.scales||{},n=t.scale;a.each(e.xAxes,function(t,e){t.id=t.id||"x-axis-"+e}),a.each(e.yAxes,function(t,e){t.id=t.id||"y-axis-"+e}),n&&(n.id=n.id||"scale")},buildScales:function(){var e=this,n=e.options,i=e.scales={},o=[];n.scales&&(o=o.concat((n.scales.xAxes||[]).map(function(t){return{options:t,dtype:"category",dposition:"bottom"}}),(n.scales.yAxes||[]).map(function(t){return{options:t,dtype:"linear",dposition:"left"}}))),n.scale&&o.push({options:n.scale,dtype:"radialLinear",isDefault:!0,dposition:"chartArea"}),a.each(o,function(n){var o=n.options,r=a.valueOrDefault(o.type,n.dtype),s=t.scaleService.getScaleConstructor(r);if(s){l(o.position)!==l(n.dposition)&&(o.position=n.dposition);var u=new s({id:o.id,options:o,ctx:e.ctx,chart:e});i[u.id]=u,u.mergeTicksOptions(),n.isDefault&&(e.scale=u)}}),t.scaleService.addScalesToLayout(this)},buildOrUpdateControllers:function(){var e=this,n=[],i=[];return a.each(e.data.datasets,function(a,o){var r=e.getDatasetMeta(o),l=a.type||e.config.type;if(r.type&&r.type!==l&&(e.destroyDatasetMeta(o),r=e.getDatasetMeta(o)),r.type=l,n.push(r.type),r.controller)r.controller.updateIndex(o);else{var s=t.controllers[r.type];if(void 0===s)throw new Error('"'+r.type+'" is not a chart type.');r.controller=new s(e,o),i.push(r.controller)}},e),i},resetElements:function(){var t=this;a.each(t.data.datasets,function(e,n){t.getDatasetMeta(n).controller.reset()},t)},reset:function(){this.resetElements(),this.tooltip.initialize()},update:function(t){var e=this;if(t&&"object"==typeof t||(t={duration:t,lazy:arguments[1]}),n(e),!1!==s.notify(e,"beforeUpdate")){e.tooltip._data=e.data;var i=e.buildOrUpdateControllers();a.each(e.data.datasets,function(t,n){e.getDatasetMeta(n).controller.buildOrUpdateElements()},e),e.updateLayout(),a.each(i,function(t){t.reset()}),e.updateDatasets(),e.tooltip.initialize(),e.lastActive=[],s.notify(e,"afterUpdate"),e._bufferedRender?e._bufferedRequest={duration:t.duration,easing:t.easing,lazy:t.lazy}:e.render(t)}},updateLayout:function(){var e=this;!1!==s.notify(e,"beforeLayout")&&(t.layoutService.update(this,this.width,this.height),s.notify(e,"afterScaleUpdate"),s.notify(e,"afterLayout"))},updateDatasets:function(){var t=this;if(!1!==s.notify(t,"beforeDatasetsUpdate")){for(var e=0,n=t.data.datasets.length;e=0;--n)e.isDatasetVisible(n)&&e.drawDataset(n,t);s.notify(e,"afterDatasetsDraw",[t])}},drawDataset:function(t,e){var n=this,i=n.getDatasetMeta(t),a={meta:i,index:t,easingValue:e};!1!==s.notify(n,"beforeDatasetDraw",[a])&&(i.controller.draw(e),s.notify(n,"afterDatasetDraw",[a]))},_drawTooltip:function(t){var e=this,n=e.tooltip,i={tooltip:n,easingValue:t};!1!==s.notify(e,"beforeTooltipDraw",[i])&&(n.draw(),s.notify(e,"afterTooltipDraw",[i]))},getElementAtEvent:function(t){return o.modes.single(this,t)},getElementsAtEvent:function(t){return o.modes.label(this,t,{intersect:!0})},getElementsAtXAxis:function(t){return o.modes["x-axis"](this,t,{intersect:!0})},getElementsAtEventForMode:function(t,e,n){var i=o.modes[e];return"function"==typeof i?i(this,t,n):[]},getDatasetAtEvent:function(t){return o.modes.dataset(this,t,{intersect:!0})},getDatasetMeta:function(t){var e=this,n=e.data.datasets[t];n._meta||(n._meta={});var i=n._meta[e.id];return i||(i=n._meta[e.id]={type:null,data:[],dataset:null,controller:null,hidden:null,xAxisID:null,yAxisID:null}),i},getVisibleDatasetCount:function(){for(var t=0,e=0,n=this.data.datasets.length;e0||(a.forEach(function(e){delete t[e]}),delete t._chartjs)}}var a=["push","pop","shift","splice","unshift"];t.DatasetController=function(t,e){this.initialize(t,e)},i.extend(t.DatasetController.prototype,{datasetElementType:null,dataElementType:null,initialize:function(t,e){var n=this;n.chart=t,n.index=e,n.linkScales(),n.addElements()},updateIndex:function(t){this.index=t},linkScales:function(){var t=this,e=t.getMeta(),n=t.getDataset();null===e.xAxisID&&(e.xAxisID=n.xAxisID||t.chart.options.scales.xAxes[0].id),null===e.yAxisID&&(e.yAxisID=n.yAxisID||t.chart.options.scales.yAxes[0].id)},getDataset:function(){return this.chart.data.datasets[this.index]},getMeta:function(){return this.chart.getDatasetMeta(this.index)},getScaleForId:function(t){return this.chart.scales[t]},reset:function(){this.update(!0)},destroy:function(){this._data&&n(this._data,this)},createMetaDataset:function(){var t=this,e=t.datasetElementType;return e&&new e({_chart:t.chart,_datasetIndex:t.index})},createMetaData:function(t){var e=this,n=e.dataElementType;return n&&new n({_chart:e.chart,_datasetIndex:e.index,_index:t})},addElements:function(){var t,e,n=this,i=n.getMeta(),a=n.getDataset().data||[],o=i.data;for(t=0,e=a.length;ti&&t.insertElements(i,a-i)},insertElements:function(t,e){for(var n=0;n=n[e].length&&n[e].push({}),!n[e][r].type||s.type&&s.type!==n[e][r].type?o.merge(n[e][r],[t.scaleService.getScaleDefaults(l),s]):o.merge(n[e][r],s)}else o._merger(e,n,i,a)}})},o.where=function(t,e){if(o.isArray(t)&&Array.prototype.filter)return t.filter(e);var n=[];return o.each(t,function(t){e(t)&&n.push(t)}),n},o.findIndex=Array.prototype.findIndex?function(t,e,n){return t.findIndex(e,n)}:function(t,e,n){n=void 0===n?t:n;for(var i=0,a=t.length;i=0;i--){var a=t[i];if(e(a))return a}},o.isNumber=function(t){return!isNaN(parseFloat(t))&&isFinite(t)},o.almostEquals=function(t,e,n){return Math.abs(t-e)t},o.max=function(t){return t.reduce(function(t,e){return isNaN(e)?t:Math.max(t,e)},Number.NEGATIVE_INFINITY)},o.min=function(t){return t.reduce(function(t,e){return isNaN(e)?t:Math.min(t,e)},Number.POSITIVE_INFINITY)},o.sign=Math.sign?function(t){return Math.sign(t)}:function(t){return 0==(t=+t)||isNaN(t)?t:t>0?1:-1},o.log10=Math.log10?function(t){return Math.log10(t)}:function(t){return Math.log(t)/Math.LN10},o.toRadians=function(t){return t*(Math.PI/180)},o.toDegrees=function(t){return t*(180/Math.PI)},o.getAngleFromPoint=function(t,e){var n=e.x-t.x,i=e.y-t.y,a=Math.sqrt(n*n+i*i),o=Math.atan2(i,n);return o<-.5*Math.PI&&(o+=2*Math.PI),{angle:o,distance:a}},o.distanceBetweenPoints=function(t,e){return Math.sqrt(Math.pow(e.x-t.x,2)+Math.pow(e.y-t.y,2))},o.aliasPixel=function(t){return t%2==0?0:.5},o.splineCurve=function(t,e,n,i){var a=t.skip?e:t,o=e,r=n.skip?e:n,l=Math.sqrt(Math.pow(o.x-a.x,2)+Math.pow(o.y-a.y,2)),s=Math.sqrt(Math.pow(r.x-o.x,2)+Math.pow(r.y-o.y,2)),u=l/(l+s),d=s/(l+s),c=i*(u=isNaN(u)?0:u),h=i*(d=isNaN(d)?0:d);return{previous:{x:o.x-c*(r.x-a.x),y:o.y-c*(r.y-a.y)},next:{x:o.x+h*(r.x-a.x),y:o.y+h*(r.y-a.y)}}},o.EPSILON=Number.EPSILON||1e-14,o.splineCurveMonotone=function(t){var e,n,i,a,r=(t||[]).map(function(t){return{model:t._model,deltaK:0,mK:0}}),l=r.length;for(e=0;e0?r[e-1]:null,(a=e0?r[e-1]:null,a=e=t.length-1?t[0]:t[e+1]:e>=t.length-1?t[t.length-1]:t[e+1]},o.previousItem=function(t,e,n){return n?e<=0?t[t.length-1]:t[e-1]:e<=0?t[0]:t[e-1]},o.niceNum=function(t,e){var n=Math.floor(o.log10(t)),i=t/Math.pow(10,n);return(e?i<1.5?1:i<3?2:i<7?5:10:i<=1?1:i<=2?2:i<=5?5:10)*Math.pow(10,n)},o.requestAnimFrame="undefined"==typeof 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i(this)?(t=n.x,e=(n.y+n.base)/2):(t=(n.x+n.base)/2,e=n.y),{x:t,y:e}},getArea:function(){var t=this._view;return t.width*Math.abs(t.y-t.base)},tooltipPosition:function(){var t=this._view;return{x:t.x,y:t.y}}})},{25:25,26:26}],40:[function(t,e,n){"use strict";e.exports={},e.exports.Arc=t(36),e.exports.Line=t(37),e.exports.Point=t(38),e.exports.Rectangle=t(39)},{36:36,37:37,38:38,39:39}],41:[function(t,e,n){"use strict";var i=t(42),n=e.exports={clear:function(t){t.ctx.clearRect(0,0,t.width,t.height)},roundedRect:function(t,e,n,i,a,o){if(o){var r=Math.min(o,i/2),l=Math.min(o,a/2);t.moveTo(e+r,n),t.lineTo(e+i-r,n),t.quadraticCurveTo(e+i,n,e+i,n+l),t.lineTo(e+i,n+a-l),t.quadraticCurveTo(e+i,n+a,e+i-r,n+a),t.lineTo(e+r,n+a),t.quadraticCurveTo(e,n+a,e,n+a-l),t.lineTo(e,n+l),t.quadraticCurveTo(e,n,e+r,n)}else t.rect(e,n,i,a)},drawPoint:function(t,e,n,i,a){var o,r,l,s,u,d;if(!e||"object"!=typeof e||"[object HTMLImageElement]"!==(o=e.toString())&&"[object 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Essential_physics_powers_winning_plays_in_the_plinko_game_and_maximizes_your_pri – Dr. Steven Kniffley Jr. Skip to main content
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Essential_physics_powers_winning_plays_in_the_plinko_game_and_maximizes_your_pri

By July 9, 2026No Comments

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Essential physics powers winning plays in the plinko game and maximizes your prize potential

The allure of the Plinko game lies in its deceptively simple mechanics. A disc is dropped from the top of a board filled with staggered pegs, and as it cascades downwards, it bounces randomly from side to side before eventually settling into a bin at the bottom, each bin having a different prize value. The seemingly chaotic nature of the descent presents a fascinating challenge – how can a player influence the outcome, or at least understand the principles that govern it, to maximize their chances of landing in the highest-value slot? The game's roots are firmly planted in physics, and understanding these principles is key to strategic play and increasing your potential reward.

At its core, the Plinko game is a demonstration of probability and momentum transfer. The initial drop sets the disc in motion, and from that point on, its path is determined by a series of collisions with the pegs. While each individual bounce appears random, the cumulative effect of these interactions follows predictable patterns. Factors such as the angle of the initial drop, the spacing and arrangement of the pegs, and the physical properties of the disc itself all contribute to the final outcome. Successfully navigating this random pathway to increase the chances of landing in the most lucrative slot requires some understanding of the underlying principles at play.

Understanding the Role of Initial Conditions

The initial conditions – specifically the angle and force with which the disc is released – play a surprisingly significant role in determining the final outcome. A disc dropped directly in the center has an equal probability of drifting towards either side with each bounce. However, introducing a slight bias, by releasing the disc a little to the left or right, can subtly influence the overall trajectory. This isn’t about precision aiming, as the bounces quickly introduce a degree of randomness. Instead, it's about nudging the probabilities in a favorable direction. More force imparts more energy to the disc, potentially causing it to travel further laterally before settling. Understanding how these initial conditions translate into a cascade of bounces is the first step toward more informed play.

The Impact of Release Height and Angle

The height from which the disc is released directly impacts its potential energy. A greater drop height translates to increased speed and momentum, leading to more dramatic bounces. The angle of release, even a small one, establishes an initial momentum component that will persist throughout the descent. This is because energy is conserved (minus energy dissipated in the collision), and the initial angle is converted into horizontal momentum. Experienced players often experiment with subtle adjustments to both height and angle to observe the resulting patterns and fine-tune their approach. Mastering this initial setup is paramount to maximizing the probability of a high-value result.

Release Angle
Expected Lateral Drift
Potential Outcome
0 Degrees (Center) Highly Variable Equal Probability Across All Bins
5 Degrees Right Slight Bias to the Right Increased Probability of Right-Side Bins
10 Degrees Left Strong Bias to the Left Increased Probability of Left-Side Bins
15 Degrees Right Significant Bias to the Right Higher Probability of High-Value Right Bins (If Present)

As shown above, even small adjustments to the release angle can lead to predictable changes in lateral drift. Note that these drifts are likely to be unpredictable after numerous bounces and may be rendered irrelevant by peg placement. However, if all other factors are equal, these principles can be useful in perfecting a Plinko strategy.

Analyzing Peg Placement and Distribution

The arrangement of pegs is arguably the most critical factor influencing the outcome of a Plinko game. The density of pegs, their spacing, and any intentional patterns in their placement all have a direct impact on the disc’s trajectory. A tightly packed arrangement of pegs will result in more frequent collisions and a more randomized path. Conversely, wider spacing allows for more extended lateral movement. Identifying potential ‘channels’ or pathways created by subtle gaps in the peg arrangement can reveal opportunities to influence the disc’s direction. A keen observation of the peg layout greatly enhances a player’s ability to predict the final destination.

Recognizing Patterns and Hotspots

While the Plinko board may appear random at first glance, closer inspection often reveals underlying patterns in peg distribution. Some boards might be deliberately designed with ‘hotspots’ – areas with fewer pegs that allow the disc to travel more freely in a particular direction. Identifying these hotspots can significantly improve a player’s chances of landing in higher-value bins. Recognizing the number of pegs in a given row and the arrangement of those pegs can also shed light on potential trajectories. Look for areas where pegs are intentionally skewed to direct the disc toward specific portions of the board.

  • Analyze the density of pegs in different sections of the board.
  • Identify potential channels or pathways created by gaps in peg placement.
  • Look for recurring patterns in peg arrangement.
  • Observe areas where pegs are deliberately skewed to direct the disc.
  • Pay attention to the spacing between pegs and its influence on lateral movement.

By carefully analyzing the peg placement, a player can gain a valuable understanding of the board’s inherent biases and develop a more informed approach to dropping the disc. This detailed observation can sometimes yield a significant advantage over relying on pure chance.

The Physics of Collision and Energy Transfer

Each time the disc strikes a peg, a portion of its kinetic energy is transferred to the peg, and the disc rebounds with altered momentum and direction. The angle of incidence – the angle at which the disc strikes the peg – significantly influences the angle of reflection, although it’s rarely a perfect reflection due to energy loss and friction. As the disc bounces, it gradually loses energy, causing its lateral movement to decrease. Understanding these physics principles helps to interpret the disc's behavior and make more informed predictions. The coefficient of restitution – a measure of how much energy is conserved during a collision – plays a crucial role in determining the bounce angle and height.

Friction and Energy Dissipation

Friction between the disc and the pegs, and between the disc and the board surface, causes a constant loss of energy throughout the descent. This energy loss reduces the disc’s speed, dampens its bounces, and ultimately influences the final bin it lands in. The material composition of both the disc and the pegs affects the coefficient of friction. A smoother disc surface and a polished peg surface will minimize friction and allow for more sustained momentum. Conversely, rougher surfaces will increase friction and lead to faster energy dissipation. This subtle but impactful element is often overlooked, yet it significantly shapes the trajectory of the disc.

  1. The disc loses energy with each collision due to energy transfer.
  2. The angle of incidence influences the angle of reflection.
  3. Friction between surfaces slows the disc down.
  4. Surface material impacts the friction coefficient.
  5. Energy loss determines the bounce height and lateral movement.

A strong understanding of the physics involved allows you to better assess the momentum, energy, and trajectory of the disc at each bounce, increasing your understanding of the game.

Leveraging Probability and Statistical Analysis

While each individual bounce in a Plinko game appears random, the collective effect of numerous bounces follows principles of probability. By tracking the outcomes of multiple drops, players can begin to identify patterns and calculate the probability of landing in each bin. This data-driven approach can reveal which bins are statistically more likely to receive the disc, even if the board appears symmetrical. A large sample size is crucial for accurate statistical analysis. The more data you collect, the more reliable your probability estimates will become. Harnessing the power of probability offers a systematic way to improve your chances over the long run.

Advanced Techniques: Spin and Initial Velocity Control

Beyond the basic principles of angle and force, some players attempt to introduce additional control by imparting spin to the disc during release. A slight spin can affect the way the disc interacts with the pegs, potentially influencing its trajectory. However, mastering this technique requires considerable skill and precision. Additionally, careful monitoring and control of the initial velocity imparted to the disc can fine-tune your predictions to a greater degree. Utilizing these advanced avenues offers chances to significantly impact a game, although their success is only moderate.

The Future of Plinko: Digital Simulations and Predictive Modeling

The growing interest in the Plinko game has spurred the development of digital simulations and predictive models. These tools allow players to analyze the game’s physics in a controlled environment and experiment with different strategies without the expense of actual play. By simulating thousands of drops, these models can generate accurate probability maps and identify optimal release parameters. As computing power continues to increase, these simulations will become even more sophisticated, providing players with powerful insights into the game’s mechanics. Digital modeling represents a significant advancement in the understanding and optimization of the Plinko experience.

These simulations don't merely calculate probabilities; they allow for the dynamic exploration of design variations. What if the peg density were altered in specific zones? How would changes to the board’s dimensions influence outcomes? Such questions are becoming readily answerable through advanced computational modeling, paving the way for optimized Plinko board designs and refined player strategies. The evolution of Plinko, from a simple game of chance to a playground for applied physics and statistical analysis, is a testament to its enduring appeal.

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