I'll give you a hint: there are almost 4x more active players speedrunning Java.

@Karl_Maks You should always do probability math with numbers between 0 and 1 and never with percentages. Only multiply by 100 at the end to express it as a percentage. 4.73% should be 0.0473 when doing math. It's also easier to use exponents and fractions instead of many divisions. For example, 100/2/2/2/2/2/2 = 100*(1/2)^6.

Also, I used 2.18% (0.0218) because the ender pearl drop rate was recently changed. 4.73% (0.0473) should make a number more common than ~1 in 167 million.

If you use 4.73% then your equation should be 100/2/2/2/2/2/2/3/3/3*0.0473*0.0473*0.0473 = 6.12E-6%, but is much easier to write as [(1/2)^6 * (1/3 * 0.0473)^3] * 100%. As you can see, 1/2, 1/3, and 0.0473 are all numbers between 0 and 1.

@Karl_Maks Where do you get the number 45,87155963302752 from?

According to the wiki, ender pearl trade rates with piglins are now 10/459 or ~2.18%, roughly half of what they used to be (20/423 or ~4.73%).

"Perfect" drops are hard to define because end portals already spawn with a chance that some eyes of ender are already filled in, but let's assume you will craft all 12. Let's also assume you are lucky and get the maximum number of 4 ender pearls (from equally likely 2-4) for all your trades.

P(6 blaze rods) = (1/2)^6 = 1/64

P(12 pearls from 3 trades) = (10/459 * 1/3)^3 = 1000/2610969633

P(joint) = 1/64 * 1000/2610969633 = 125/20887757064 or ~5.99E-9

This is a ~1 in 167 million chance (given that we are looking to craft all 12 eyes of ender).

Let me know if I did anything wrong.

Hello, sorry if this has already been done before, but I made two graphs for the number of eyes of ender for end portals.

This shows the probability of an end portal being spawned with any number of eyes of ender already filled. As you can see 1 eye of ender already in an end portal is the most common (with 10% chance per slot). The graph stops after 6 because the chances become super close to 0. The chance of 6 eyes of ender spawning in an end portal is already ~1 in 2000.

These numbers have been known for a while, but I also made this second graph that visualizes how many eyes of ender speedrunners should aim for (once in the stronghold).

As you can see, you are 100% likely to fill an end portal with 12 eyes of ender on you, since the end portal always consists of 12 blocks around it. If you only have 10 eyes of ender on you, that will only be a 34.1% chance of being enough to fill the portal (of course, assuming you are gathering eyes of ender before actually finding the stronghold to see how many you need).

There is only a 2.6% chance that 8 eyes of ender will be enough, so if you were to shoot for that, expect to do an average of ~38 runs before eventually finding a seed where 8 will be enough to fill, ~250 runs for 7 eyes of ender, and ~1000 runs for 6 eyes of ender.

I hope these reference visualizations will find you helpful.