Quote from: nullius on Today at 09:05:34 AM

Mr. Brendon, you asked a smart question.

The saying that a Bitcoin block happens “every 10 minutes” or “about every 10 minutes” is misinformation. It is a form of classic Gambler’s Fallacy. It is endlessly repeated by people who should know better—even after they have been corrected. I know of only two or three other people who have actively tried to correct this fallacy in the Bitcoin community—and all of them have sometimes been accused of being my alts (including Lauda, lolz). Thus, I must thank you for inquiring based on your own empirical observations, instead of mindlessly believing and repeating what everyone else says. (Cf. the Asch conformity experiment.)

Quote from: Jason Brendon on Today at 06:17:41 AM

So from my personal BTC explorer, i realized that sometimes a blockchain isn't really 10 minutes or anything close.

Indeed not! To understand this will require some maths. For an initial explanation, I will not try to delve deeply into that.

The Bitcoin mining process, already described above by mocacinno, is modelled as a Poisson process. This statistical process is memoryless: The expected time to the next block does not start from the last block, but from any particular moment in time. The expected arrival time of the next block follows the exponential distribution, with λ = 0.1 if you are working in units of minutes.

Accordingly, the average time to the next block is 10 minutes; and about 63.2% of blocks actually arrive within 10 minutes. However, the exponential distribution has a curve which defies human intuition: It is frontloaded with a high density of fast arrival times, followed by a long tail of slow arrival times. That long tail includes those slow-seeming blocks which you observed; those drag the average up to 10 minutes.

More useful to practical everyday life are median and the quartiles.

The median expected time to the next block is about 6 minutes and 56 seconds. An equivalent statement: At any particular moment—at the moment when you read these words—you can expect a block within 6:56 with 50% probability. Of course, that means a 50% chance that the next block will take longer than 6:56 to arrive.

The next block has a 25% chance of arriving within 2:53, and a 25% chance of taking longer than 13:52 (the long tail).

Incidentally, many games of chance, including classic Bitcoin dice games, can be usefully modelled according to the same process and the same probability distribution for the arrival of wins. (Pedants may argue that that’s a discrete process, whereas the exponential distribution is continuous; but for the purpose of this discussion, that is not relevant.) Studying the mathematics of Bitcoin block arrival times can help give an understanding of why you can’t beat the house—and on the flipside, studying the mathematics of gambling will give a firm theoretical grasp of why Bitcoin block arrivals have the behaviour that you observe empirically.

Gambler’s Fallacy is ever popular—as is social conformity in the repetition of obviously wrong statements. Thus, I am pessimistic about my prospect for fighting off the misinformation that “Bitcoin blocks take about 10 minutes”.

Thank you sir for the details. That's very well explained in-depth. Yes, we must go into details so that we are not blindly following the stream. So, anothrr point crossed off my list.