Let me tell you a very short real-life story.

The year was 2008. A colleague told me about this thing called Eternity II puzzle. What was it? Some toy company was selling this 256 pieces puzzle (scrambled of course), and every piece was a rectangle, having different models on each side.

Side pieces only had 3 sides, the 4th indicating that it's a margin.
Corner pieces only had 2 sides, the other 2 indicating it's a corner.

There were no identical pieces, however there were only something like a dozen types of models. Very few actually. So, it was very easy to find and match 2 pieces together, and even 5 pieces together.

In fact, it was very easy to find and match hundreds of pieces together. The goal was to complete the puzzle using all 256 pieces, and claim a reward of 1 million $ if you were the first to do it.

The problem here is that this puzzle was developed in collaboration with a mathematician. The number of models for piece sides was calculated in advance to be at a minimum, but still for only ONE SOLUTION to exist. This drove people crazy, since it was seemingly a very easy task, even for a bedroom floor on a rainy day.

It wasn't hard to find the piece models (though it was illegal to make them public) and start throwing a brute force attempt at it.

However, that proved to only fill up something like a stack of 200 pieces, with 56 remaining pieces never finding a valid next spot to sit on. Of course, the first 200 pieces always stayed the same more or less, since the back track was back tracking, well, slow, due to the many matches being available.

So then came random picking: randomly pick some next piece and try to match it somewhere randomly.

This proved to be a much better strategy: since the pieces were put at random, many variants came up where I had like 230 pieces, and 26 pieces that remained, that had nowhere to sit. Sometimes less, sometimes more pieces matched in total.

Then came genetic algorithms, since it was my PhD thesis topic at the time. So, start off from some good random partial matches (the best ones), and start mutating some pieces here and there, removing randomly a few. Now, with this, I got somewhere at about 246 pieces matching in total. The last 10 pieces didn't find a spot anywhere. However, much better han both brte force or random search.

After a few months, full of experiments and Terminal colored grid display of solutions advancing in real-time, I decided to shift+delete the entire project.

This was the only time in mi life where I intendedly deleted a project I worked on, so to never touch it again or try to reconstruct it. I had in there even PNG files with the pieces, to display the solutions as if I owned the physical puzzle. It was becoming an addiction. Not just for me - I exchanged a lot of ideas with my colleagues, we all had different strategies and code to solve such an easy problem. And the 1 million $ prize didn't sound bad.

I guess we're now in 2025. The Eternity II puzzle was, AFAIK, never solved up to this day. We didn't even had CUDA at that time. But I'd say that it would not have helped anyway, and it would not help today as well. Why? Because the puzzle was developed in such a way to have a gazillion impressions that the puzzle is on its way of being solved, but you might as well end up with the last 2 pieces not matching.

But I bet that if someone would engage of rewarding a solver with, maybe 100 million $ in prize, everyone will get crazy on it (the deadline expired in 2011 btw).

What's the idea here: addiction can cause big problems. It can make you see things unnaturally. I'm sure a psychologist can explain it better.

Each private key acts as an independent random event, and the probability of finding a specific prefix in an address does not change regardless of previous results. This is what confuses most people since the probability of an individual event (such as finding prefix "X") remains the same on each attempt.

However, when we look for the match of multiple prefixes in a dataset example 1:256, we enter the realm of compound probability.

This is the part most intuitively ignore and therefore fail:

-Probability of finding "a": 1/16

-Probability of finding "ab": 1/256

-Probability of finding two "ab" in 256 attempts: approximately 0.18

As you can see, if you find "ab" in an early shot, the probability of finding another "ab" in the next 256 attempts is very low. This would allow you to skip those subsequent attempts without losing significant precision, since although each attempt is still an independent event, the chances of it being there are very low.

For this reason, in probabilistic searches you can skip unlikely private keys. It's not that the private key has a relationship with the hash of the address, but that each key is essentially an independent shot, and we would omit the less likely shots.

Unfortunately, my friend, I do not want to share this information.

Or rather, I want to share what I have with people who give me another prefix in return.

I can only give a little information about the 68th wallet range. It is located above C0.

Here is another good information for you, it remains under E2. 68th wallet

Once you find "ab", then the probability is no longer a probability, it's a certainty. It just proves, in long-term average, that the probability prediction was correct. So, once you find an "ab", that is great and all, but it doesn't affect at all the chances of the interval that follows. You're still at a 36% that no "ab" will be found in the next 256 samples. And still at the same probability of 1/256 that it will be found in the next sample.

Results are only useful to prove predictions, not the other way around. Maybe you found some way to use the conditional probability, as you call it, into the mix, and maybe that helps to find better prefixes, I'm not saying it doesn't. But that doesn't change at all the chances that you can always skip the key you're actually looking for - it's the same.

In the meantime i found out that machine learning can compute correct 3 hex digits of a privkey corresponding to the target pubkey... not much but interesting

It depends on what I'm looking for, assuming your strategy works.

If I'm looking for an exact total match, I'd scan the full range, first to last key. No exceptions. It's simply the fastest, most efficient way to do it. It's also the most parallel-friendly way to do it at massive (and I mean 68-bit massive) scale, since there is no need for complex logic, like stopping 65536 threads in the middle of their work just because some prefix matches somewhere, and then setting things up again, recomputing ranges, etc. Maybe you do that manually, which is a time waste, which can be used to simply scan more stuff, IDK.

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If I'm after a nice prefix but I don't care about a perfect match, just find it really fast - I'd go for 2. But in all honesty I would not even need to go for 2 - because a VanitySearch would run many times faster, for this purpose. For example, an RTX 4090 that searches for some target prefix, hard-coded, and using endomorphism, can do 9.6 billion hashes per second, and find a key having the desired prefix.

And here is why I wouldn't use 2 to find a complete match (I said this already on some of your first posts): even if you take that "1 in 1024" route, there is a chance you don't find what you wanted, but something else. But the overhead of repeating the process to exhaustion (starting over with the second "1 in 1024 chances", then the third ... then the millionth, etc), overall, results in a longer process than simply scanning the range start to finish. And the probability is identical in both cases, because you can't cheat your way out of searching linearly for something that is random. You may disagree here - it's OK.

Meanwhile, Bram already started hunting down 68 for several days now, since the crowd funding was completed, so I guess you should hurry up.

In my probability d and 8 , key not in these range

Ok master, everyone understands you now. lol

Everyone understood that it is more logical to start with the ranges you calculated and search for other ranges as you said. (except you)

It will start with the calculated ranges, how many people do you think there are here?

Remember;
1- You have many competitors, their hardware, software or money power is more than you.
2- Everyone has their own special thoughts and strategies.
3- After all these talks, I understood that the people who will agree with you are only those who make decisions because you give information about the kangaroo system and do not really understand what you wrote.

Do you have any work on this subject? Have you guessed any range? Or have others asked you for the prefix? Have you ever proven yourself on something? Have you won a bet?

The Swiss army knife showed the truth. But you lost. Now accept this.

If we were to vote here, you would not be able to get many votes for the idea of ​​scanning the entire range as you said.