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Main question

The following animation runs smoothly in my Wolfram Desktop. However, it's extremely choppy in the cloud notebook I published it to. I tested it in Firefox and Safari, and it's choppy in both.

Here's a link to the notebook... scroll down to the very bottom of the page to see the relevant animation:

https://www.wolframcloud.com/obj/jonahx/Published/Riddler10-22-21.nb

Is this a bug in the cloud notebook, or are there configuration options I should be using to make it work more smoothly?

Related Question

What is the most efficient way to create a video of this animation?

One method that I tried, which worked but was slow, was to convert the list of Graphic objects to a list of Image objects, and pass that list to AnimatedImage. Is there a better approach?

Code

So that this question will be self contained for posterity, here's the code for animation:

randpt[x_, y_] := (
   r = RandomReal[];
   r x + (1 - r) y
   );

a = {0, 0};
b = {1, Sqrt[3]};
c = {2, 0};

randtri[] := {
   randpt[{0, 0}, {1, Sqrt[3]}],
   randpt[{0, 0}, {2, 0}],
   randpt[{2, 0}, {1, Sqrt[3]}]
   };

center = {1, 1/Sqrt[3]};
cnt = 0;
n = 500;
gs = {};
For[i = 0, i < n, i++, (
  hull = ConvexHullMesh[randtri[]];
  cnt += If[RegionMember[hull, center], 1, 0];
  AppendTo[
   gs,
   Graphics[{
     {If[RegionMember[hull, center], Red, Green], hull},
     {EdgeForm[Thick], Transparent, Triangle[{a, b, c}]},
     {Red, PointSize[.02], Point[center]},
     {Text[
       Style[
        "Step: " <> ToString[i] <> ". Estimate: " <> 
         ToString[N[cnt/(i + 1), 2]], Large], {2, 2}]},
     }]
   ];
  )
 ]
Animate[
 gs[[i]],
 {i, Range[Length[gs]]},
  AnimationRate -> 2,
 SaveDefinitions -> True
 ]
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