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It's all a matter of perspective.
From the perspective of time T, the probability that the next block is found between T+60min and T+70min (~0.1%) is much smaller than the probability that the next block is found between T+0min and T+10min (~63%).
But from the perspective of time T+60min, the probability that the next block is found between T+60min and T+70min is equivalent to the probability of (T+0min, T+10min) from the perspective of time T (~63%)
Why is there a difference?
Because from the perspective of time T, you are comparing the possibility of (T+60,T+70) to many other possibilities: (T,T+10), (T+10,T+20), etc.
From the perspective of time T+60, you have already ruled out (T,T+10), (T+10,T+20), etc.
from the perspective of time T+60min, the probability that the next block is found between T+60min and T+70min is equivalent to the probability of (T+0min, T+10min) from the perspective of time T (~63%)
Reading this over and over and not making progress. How can an improbable, outlier event (60-min block time) have the same probability as a standard, middle-of-the-diastribution one (10-min).
Surely I'm missing something
Reading this over and over and not making progress. How can an improbable, outlier event (60-min block time) have the same probability as a standard, middle-of-the-diastribution one (10-min).
It doesn't. I think you misunderstood the claim.
Imagine you roll 1 dice every minute, no matter what.
It's now 12:00. What's the probability that you roll a 1 between 12:00 and 12:10? What's the probability that your next 1 occurs between 1:00 and 1:10?
It's now 1:00. Forget about what happened in the past. What's the probability that you'll roll a 1 between 1:00 and 1:10?
Something else that might help.
It's important to distinguish these two questions:
(i) What is the probability that a block is found within any particular 10 minute interval?
(ii) What is the probability that the next is found within any particular 10 minute interval?
These are two different questions.
Example:
It's now 12:00. What is the probability that the next block is found between 1:00 and 1:10? Answer: very small. What is the probability that a block is found between 1:00 and 1:10? Answer: same as always, about 63%.
yeah, i realized that this is probably where much of the confusion lay
Ah yes, this is kind of helpful. I understand the memory point now, I think
The memoryless aspect is really cool to me.
Right now, I can say: "The next bitcoin block should be mined within ten minutes."
Yet, if no block is mined in the next twenty minutes, I cannot say: "It is more likely that the next bitcoin block will be mined in the next 5 minutes than the five minutes after that."
This feels so counterintuitive to me. The common sense answer feels like it should be anything after 10 minutes is decreasingly likely and this is true...as long as you are asking from the vantage point of this moment right now.
But now I think I've confused myself. Let me try a toy example:
Thinking about the blockchain as a it is displayed on mempool.space:
If we ask for all blocks, any time there was a 60 minute delay after a block was found, was the next block found in 60+1 minute, 60+2 minutes, 60+3 minutes or so on.
Wouldn't we expect the number of blocks found 69 minutes after their predecessor to be fewer than the number of blocks that were found 61 minutes after their predecessor?
And if this is the case, how do we understand the statement that if no block has been found for the last hour, the next block is equally likely to be found at any point in the next ten minutes?