Mining and what is the probability of success?

Question

bitcoin

I've been reading bitcoin's specification for a long time. More than once I came across materials on the net (including on Habré), where it was said that the power of the bitcoin network is now very large and the probability of mining on your old Pentium is 0.000000%d. These words have always made me sick, and now I will explain why. Years later, I decided to look into the details. After re-reading the specification, I realized that I had been hurt for a reason.
The miner does proof-of-work based on the hash of the previous block. Having mined a new block, the network accepts it and everyone mines the trail. block. From here, it becomes clear that all your mining results with the hash of an obsolete block can be discarded as unnecessary, because. the network has accepted another block and needs to be re-mined.
What is the probability in this case? About none. (Unless the search (search for proof-of-work) is not sequential, but random (due to unpredictability, I don’t consider this option).
And look what happens. There are two miners A & B. P (x) - computing power miner x.
Let's say that P(A) != P(B) (which is actually the case) Let's say P(A) > P(B) This means that miner A will always be the first to find the necessary nonce for satisfaction of the network, given that they started mining at the same time.
This means that even if we have at our disposal even a huge data center, but in terms of total capacity it is still inferior to a Chinese farm, the probability of successful mining is equal not to some shares, but to zero, because. ceteris paribus, we will never be the first to find the desired nonce (if it is sorted sequentially).
Isn't it all right?
Maybe miners do randomly change the nonce of a block in search of a satisfying hash?

Answer 1

Unless the search (search for proof-of-work) is not sequential, but random

The enumeration can be sequential, but the index from which this sequence begins must be chosen randomly. If the desired number X can be in any position in the range N with equal probability , then the probability that X will be included in the sequence A is directly proportional to the length of this sequence and does not depend on any other factors. If all sequences had zero length at the initial time T ₀ , then the length of sequence A at time T is directly proportional to the average rate at which this sequence grows. And the speed is directly proportional to the processing power of the mining equipment.
Total: Probability of finding X first among othersdirectly proportional to processing power.