/*! * 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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Probability_and_skill_combine_with_plinko_for_potential_jackpot_rewards_today

By June 30, 2026No Comments

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Probability and skill combine with plinko for potential jackpot rewards today

The concept of a ball dropping through a series of obstacles to reach a prize is a classic example of probability in action. When players engage with plinko, they experience a blend of anticipation and physics where every ricochet determines the final destination of the sphere. The visual appeal of the falling object combined with the sense of randomness creates a compelling atmosphere for those seeking a quick thrill. This specific mechanic relies on the interaction between gravity and the physical layout of the board to distribute potential rewards across various slots.

Understanding the physics behind this experience requires an appreciation of how small deviations in the starting position can lead to vastly different outcomes. Each peg serves as a pivot point, pushing the ball toward the left or right side of the grid. Over several rows of obstacles, these choices accumulate, creating a bell curve distribution of results. The excitement stems from the following the trajectory as it dances across the pins, hoping for a landing in the most lucrative outer edge slots which are statistically less likely to be hit.

Mechanics of the Gravity Based Board

The core engine of the game involves a vertical board populated by rows of pins. As a ball is released from the top, it must navigate through these barriers of steel or plastic, bouncing unpredictably. The goal is to reach the bottom where a series of multipliers or prize bins are located, as these determine the value of the return. Because each impact with a pin causes a shift in direction, the path is never truly linear, and the probability of hitting the center is always higher than the hitting the edges.

The physical interaction between the sphere and the pins is governed by the laws of motion. Factors such as the surface friction, the elasticity of the ball, and the precise angle of the drop point all play a role in the final outcome. While the player provides the initial push, the subsequent movements are largely autonomous, making the experience a test of luck and timing. The complexity arises from how a single bounce can send the ball spiraling away from the center, potentially leading toward the high-value targets on the periphery.

The Role of Distribution Curves

The distribution of outcomes in this type of game is closely related to the binomial distribution. Since each pin represents a binary choice—left or right—the number of paths leading to the center slots is far greater than the paths leading to the outer edges. This means that the middle bins typically offer lower rewards or even return a portion of the stake, while the outer bins provide the maximum possible win. The mathematical reality ensures that the house maintains an edge, but the allure of the rare outer landing remains the primary driver for participants.

Impact of Peg Placement

The geometry of the board determines how the ball behaves during its descent. If the pins are spaced wider, the ball has more room to move laterally, increasing the chance of reaching the edge bins. Conversely, tighter spacing forces the ball to stay closer to the center. Modern versions of these games often allow players to customize the level of risk by choosing the number of rows of pins, which directly affects the volatility of the resulting prize distribution.

Risk Level
Pin Rows
Potential Outcome
Low 8 Rows More frequent small wins
Medium 12 Rows Balanced reward distribution
High 16 Rows Rare but massive payouts

As shown in the table, the risk profile changes based on the number of obstacles the ball must cross. A higher number of pins increases the dilution of the probability, making it harder to hit the absolute edge but increasing the reward for doing so. Players often experiment with these settings to find a balance between their available budget and the desire for a substantial windfall. This strategic layer adds a level of depth to a simple physics-based premise.

Strategies for Navigating the Peg Grid

Navigating the descent of a sphere through a peg board is primarily a game of chance, but observing patterns can be an interesting mental exercise. Some players believe that the timing of the release can influence the trajectory, though the randomness of the ricochets often overrides these efforts. The primary strategy involves bankroll management and understanding how the multipliers are laid out across the bottom. By knowing which slots are the most valuable, a player can better understand the risks they are taking with each drop.

The psychological aspect of the game is also important, as the desire to chase a big win can lead to a loss of control. It is essential to set limits on the amount of money spent and to avoid the temptation to increase bets after a series of losses. A disciplined approach allows the player to enjoy the experience without the stress of financial ruin. Many experienced participants focus on a consistent betting pattern rather than trying to actually control the physical path of the ball.

Optimizing the Starting Position

The precise point of release is the only variable the player can truly control. While the board is perfectly centered, any slight tilt or offset in the release can shift the probability toward one side. Some argue that dropping the ball slightly off-center increases the chance of hitting a side bin, but the physics of the randomness ensure that the most common path is still toward the middle. Experimenting with different release points is a common habit among those trying to find an edge in the game.

Understanding Volatility and Variance

Volatility refers to how often a player wins and how infrequently they are large. In a high-volatility setup, the prizes are very far apart in value, meaning you might go through many drops without a significant win. In a low-volatility setup, the wins are are more frequent but smaller. Understanding these differences allows a player to tailor their experience to their specific risk tolerance and desired outcome, ensuring an enjoyable session.

  • Consistent betting patterns to avoid rapid depletion of funds.
  • Selection of risk levels based on current bankroll availability.
  • Observation of previous outcomes to identify potential cold or hot streaks.
  • Careful monitoring of the number of pins to maximize reward potential.

The list above highlights the basic tenets of a sustainable approach to the game. While no single method can guarantee a win, focusing on these principles helps maintain a level of play that is sustainable. The goal is to enjoy the visual journey of the ball as it bounces, regardless of whether the result is a high or low multiplier. This mindful approach prevents the game from becoming a source of frustration and allows the focus to remain on the same excitement.

Analyzing the Probability of Outer Bins

The mathematical foundation of the game is based on the Galton Board, which is a device used to demonstrate the central limit theorem. In this system, the ball is dropped and must move either left or right at each pin. This creates a series of binary events, and the sum of these events determines the final bin. The probability of landing in the center bin is the highest because there are more unique paths a ball can take to reach that specific location than there are to reach the edges.

The outer bins are the most sought after because they hold the highest multipliers. However, the probability of a ball consistently moving in the same direction across multiple rows of pins is mathematically very low. For example, if there is a ten-row board, the chance of the ball moving right every single time is one in two to the power of ten, which is a very small number. This fact is what makes the outer bins so alluring yet so difficult to achieve in a real-game scenario.

The Concept of the Binomial Coefficient

The binomial coefficient is used to calculate the number of ways a ball can land in a specific bin. For a given number of rows, the coefficient tells us how many paths lead to the center versus the edges. This explains why the rewards are structured as a pyramid, with the lowest values in the center and the highest values on the edges. The game design mirrors the natural distribution of probability, ensuring that the most likely outcomes are the least rewarding.

Variance in Physical versus Digital Versions

In a physical board, the balls may have slight imperfections or the pins may be slightly bent, which can introduce a degree of unpredictability that differs from a digital simulation. Digital versions use a Random Number Generator, or RNG, to determine the path of the ball. While the RNG is designed to be fair and transparent, it lacks the minute physical variables of a real-world board. This difference means that digital versions are more consistent in their probability distribution but may feel less visceral than a physical game.

  1. Identify the total number of rows of pins on the board.
  2. Calculate the probability of landing in the center bin using binomial distribution.
  3. Compare the probability of the center bin to the probability of the edges.
  4. Assess the risk relative to the multiplier value offered in the outer slots.

Following these steps allows a player to actually understand the odds they are facing. By breaking down the process into mathematical components, the mystery of the game is removed, and the game becomes a series of calculated risks. This analytical approach is the best way to avoid emotional betting and to treat the game as a a form of intellectual entertainment. The realization that the center is the most probable outcome helps manage expectations during a session.

Comparing Different Variants of the Experience

There are many different versions of this game available, ranging from traditional arcade machines to modern digital applications. Each version introduces its own set of rules, additional features, and risk levels. Some versions offer bonus games or special multipliers that can trigger during a descent. Others might change the number of pins or the layout of the board mid-game. The diversity in these variants allows players to find a version that suits their personal preference for risk and reward.

The transition from physical boards to digital platforms has changed the way people interact with these games. Digital interfaces allow for instant changes in settings, such as the number of rows or the bet amount, which would be impossible in a physical machine. This accessibility has made the game more popular globally, as anyone with a device can now experience the thrill of the falling ball. Furthermore, the social aspect of gaming has been enhanced by the ability to share results and compete with others in real-time.

The Influence of Visuals and Sound

The sensory experience of these games is heavily influenced by the visuals and audio. The sound of a ball hitting a pin is a key part of the excitement, and digital versions replicate this with high-fidelity audio. The visual of the ball bouncing unpredictably creates a tension that is released only when the ball finally settles in a bin. This combination of sight and sound is designed to keep the player engaged and create a positive psychological response to the win.

Customization and Player Agency

Modern digital versions offer a high degree of player agency. Players can choose their risk level, as mentioned previously, and can even set the motion of the ball to be automated. This allows for a faster pace of play, which can be a huge advantage for those who want to see more results quickly. The ability to customize the experience ensures that the game remains fresh and interesting, as players can constantly tweak their settings to try and find a new way to win.

Exploring the Psychology of the Near Miss

The psychology of the near miss is a powerful driver in gaming. In the context of this particular experience, a near miss occurs when the ball bounces toward the edge but then ricochets back toward the center. The feeling that the ball was almost in the high-value bin creates a strong urge to play again, as the player believes they are getting closer to the big win. This phenomenon is a a key part of why people find the game so addictive and engaging, as it keeps the hope of a jackpot alive.

This feeling of almost winning is often what keeps a player in the game longer than they might have intended. The brain processes a near miss as a partial win rather than a complete loss, which triggers a release of dopamine. This biological response encourages the player to believe that their strategy is working or that they are just a few pins away from a massive payout. It is a cycle of anticipation and reward that makes the experience a compelling psychological journey.

The Illusion of Control

Many players believe they can influence the ball's path by how they release it or by using certain patterns. This is known as the illusion of control, where the player feels they have a a degree of influence over a random event. In reality, the RNG or the physical physics of the board ensure that the randomness is maintained. However, the belief that one can control the outcome adds a layer of excitement and a sense of achievement when a win occurs, making the game more rewarding on a psychological level.

Developing a Healthy Gaming Mindset

Developing a healthy mindset is crucial for anyone engaging in games of chance. This involves recognizing the patterns of near misses and understanding that each drop is an independent event. By acknowledging that the probability is fixed and that the outcome of one ball is not influenced by the other, a player can avoid the frustration of chasing losses. A disciplined approach focuses on the game as entertainment, treating the amount spent as the cost of a ticket to a show, rather than an investment.

Future Perspectives on Interactive Probability

The evolution of these games will likely involve more integration with augmented reality and virtual reality. Imagine a world where a player can physically interact with a 3D holographic board, adjusting the pins and releasing the ball in a real-time virtual environment. This would bring the a level of immersion that is currently unavailable in 2D screens. The ability to feel the haptic feedback of the ball hitting the pins would make the digital experience almost indistinguishable from the physical one, adding a new dimension of sensory engagement.

Moreover, the integration of social competition and blockchain technology could transform the way rewards are handled. Smart contracts could ensure transparency in the payout and a verifiable way to prove that every drop was fair. This would eliminate any suspicion regarding the fairness of the game and allow for a global, decentralized tournament system. The future of these probability-based games is one of increasing transparency and the possibility of a more an immersive, personalized experience for every user.

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