6 blocks in 4 minutes | Bitcointalksearch.org

Jace

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Quote from: jonald_fyookball on July 27, 2015, 07:54:34 PM

I see your point. Because the inputs keep changing (different timestamp header, etc), there
is a near infinite set of values we could hash, so it more resembles a random function, even
though the hash function is deterministic.

Exactly, I believe there are two 32-bit nonces in the block header, and several other variables you can change (timestamp, and which transactions to include or exclude, amongst other things) so that gives a huge set of possibilities. Any number of possibilities we can feasibly process through brute force (which is what Bitcoin mining does) is still insignificant, so indeed it resembles a random process.

jonald_fyookball

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Quote from: Jace on July 27, 2015, 07:36:22 PM

Quote from: jonald_fyookball on July 27, 2015, 03:20:12 PM

I think the longer time that passes, the more likely it is a block will be found sooner.
All the nonces that have to be tried and failed, will be tried (and fail) as time goes on, bringing us
closer to the solution.

Nope. I haven't actually measured the following statistic myself, but if you were to take all blocks that took more than 37 minutes to mine (since their preceding block), I'm sure you will find that they still took 10 minutes *on average* after that 37 minute mark.
(obviously the 37 minutes is just an arbitrary period, any other will yield the same result).

Quote

Think of an isolated intersection on the outskirts of town where only one car drives through
every ten minutes. The longer that passes, the closer you get to the next car.

Intuitionally this may seem the case, but it's not true. Exponentially distributed variables (or poisson distributed events) are independent of the past.

In a fair casino roulette, one can expect that red and black will roughly come up equally as much.
If you wait patiently until a sequence of straight 23 reds comes up, is the probability of the next roll being black now larger than 50%?

I see your point. Because the inputs keep changing (different timestamp header, etc), there
is a near infinite set of values we could hash, so it more resembles a random function, even
though the hash function is deterministic.

Jace

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Quote from: jonald_fyookball on July 27, 2015, 03:20:12 PM

I think the longer time that passes, the more likely it is a block will be found sooner.
All the nonces that have to be tried and failed, will be tried (and fail) as time goes on, bringing us
closer to the solution.

Nope. I haven't actually measured the following statistic myself, but if you were to take all blocks that took more than 37 minutes to mine (since their preceding block), I'm sure you will find that they still took 10 minutes *on average* after that 37 minute mark.
(obviously the 37 minutes is just an arbitrary period, any other will yield the same result).

Quote

Think of an isolated intersection on the outskirts of town where only one car drives through
every ten minutes. The longer that passes, the closer you get to the next car.

Intuitionally this may seem the case, but it's not true. Exponentially distributed variables (or poisson distributed events) are independent of the past.

In a fair casino roulette, one can expect that red and black will roughly come up equally as much.
If you wait patiently until a sequence of straight 23 reds comes up, is the probability of the next roll being black now larger than 50%?

Jace

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Quote from: jonald_fyookball on July 27, 2015, 03:50:21 PM

Uh no...guys its a Poisson distribution. Different math entirely.

The poisson and exponential distributions are closely related, but be careful not to mistake one for the other:

Block time (a continuous variable, can by anything ≥0) is distributed exponentially, in this case with mean λ=10 minutes.
The number of blocks per time interval (a discrete variable, can be any integer ≥0) is a poisson distribution, in this case with mean λ=one block per 10 minutes.

Quote

This is what you use when there is "X number of something every Y minutes."

When calculating the probability of 6 blocks being found within 4 minutes, using Poisson distribution is most likely the wrong approach.

However "the probability of 6 blocks being found within 4 minutes" is somewhat ambiguous. Do we mean:
1. the probability that the number of blocks in any random 4 minute interval is 6 (could ask the same question for e.g. 5 or 13 or 0 blocks)
or
2. the probability that you succeed in mining 6 blocks within 4 minutes (could ask the same question for e.g. 2 or 19.54 or 180 minutes)

If you're observing the total time time it takes to mine 6 blocks, then it's an Erlang distributed variable, because each individual block's mining time is exponentially distributed, and we're observing the sum of 6 of those.

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Quote from: spazzdla on July 27, 2015, 03:40:02 PM

Quote from: biodieselchris on July 27, 2015, 01:24:10 PM

Quote from: Jace on July 22, 2015, 07:13:02 AM

Quote from: biodieselchris on July 21, 2015, 11:27:49 PM

For more clarity, I was wondering what the probability of such of an event was.

The time it takes to mine one block is exponentially distributed with λ (mean) = 10 minutes.

This means the total time to mine four blocks is Erlang-distributed with k=4 and λ=10 minutes, and the probability to find 4 blocks within 6 minutes is about 0.336%.

So, roughly speaking (and strongly simplified, probability-wise), once every 100/0.33581 ≈ 298 chunks of 4 blocks, or once every (100/0.33581)*4*10 minutes ≈ 8.3 days, you can expect 4 subsequent blocks to appear within 6 minutes.

thank you Jace, good quant analysis. Also worth noting that you are assuming the difficulty, which could've been set as long as two weeks ago, still accurately matches the hash rate, producing blocks with a mean target of 600s.

Also note that the probability (W) being calculated is (p) mining 6 blocks within 6 minutes (so it would be the probability of 5 subsequent blocks being mined after any particular block, not 4) and also, given p, (q) the probability of no block being mined for an hour, so the probability I was looking for was:

W = p * q

I was guessing originally around 10,000 to 1

what about the 7th block being an hour? 1 / Huh

Uh no...guys its a Poisson distribution. Different math entirely.
This is what you use when there is "X number of something every Y minutes."

https://en.wikipedia.org/wiki/Poisson_distribution

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Quote from: NorrisK on July 27, 2015, 03:43:59 PM

Quote from: spazzdla on July 27, 2015, 01:38:02 PM

I wonder what the chances of that are. I just like seeing rare things lol.

I think it was calculated in the post above you Wink

It's small, but big enough to happen. And it gets bigger as the hash power increases before diff adjustment.

That was just the 6 blocks in a row though!!

Unless it's 1 / 1 000 000 000 000 000 000 000

I'm not too worried. The situation doesn't sound that rare but rare.

NorrisK

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Quote from: spazzdla on July 27, 2015, 01:38:02 PM

I wonder what the chances of that are. I just like seeing rare things lol.

I think it was calculated in the post above you Wink

It's small, but big enough to happen. And it gets bigger as the hash power increases before diff adjustment.

spazzdla

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Quote from: biodieselchris on July 27, 2015, 01:24:10 PM

Quote from: Jace on July 22, 2015, 07:13:02 AM

Quote from: biodieselchris on July 21, 2015, 11:27:49 PM

For more clarity, I was wondering what the probability of such of an event was.

The time it takes to mine one block is exponentially distributed with λ (mean) = 10 minutes.

This means the total time to mine four blocks is Erlang-distributed with k=4 and λ=10 minutes, and the probability to find 4 blocks within 6 minutes is about 0.336%.

So, roughly speaking (and strongly simplified, probability-wise), once every 100/0.33581 ≈ 298 chunks of 4 blocks, or once every (100/0.33581)*4*10 minutes ≈ 8.3 days, you can expect 4 subsequent blocks to appear within 6 minutes.

thank you Jace, good quant analysis. Also worth noting that you are assuming the difficulty, which could've been set as long as two weeks ago, still accurately matches the hash rate, producing blocks with a mean target of 600s.

Also note that the probability (W) being calculated is (p) mining 6 blocks within 6 minutes (so it would be the probability of 5 subsequent blocks being mined after any particular block, not 4) and also, given p, (q) the probability of no block being mined for an hour, so the probability I was looking for was:

W = p * q

I was guessing originally around 10,000 to 1

what about the 7th block being an hour? 1 / Huh

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Quote from: Kazimir on July 22, 2015, 06:57:34 AM

Quote from: odolvlobo on July 22, 2015, 02:00:34 AM

Here is something to think about:

Regardless of how long ago the last block was added, the average time to the next block is 10 minutes from now.

Yep, and if starting now you wait 2 hours and no block gets mined, then the expected time for the next block to appear is still 10 minutes after that (rather than 'any moment now!')

Exponential probability distribution vs people's intuition

Not sure if this is 100% correct. I think the longer time that passes, the more likely it is a block will be found sooner.
All the nonces that have to be tried and failed, will be tried (and fail) as time goes on, bringing us
closer to the solution.

Think of an isolated intersection on the outskirts of town where only one car drives through
every ten minutes. The longer that passes, the closer you get to the next car.

spazzdla

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I wonder what the chances of that are. I just like seeing rare things lol.

biodieselchris

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CoinQuacker

Quote from: Jace on July 22, 2015, 07:13:02 AM

Quote from: biodieselchris on July 21, 2015, 11:27:49 PM

For more clarity, I was wondering what the probability of such of an event was.

The time it takes to mine one block is exponentially distributed with λ (mean) = 10 minutes.

This means the total time to mine four blocks is Erlang-distributed with k=4 and λ=10 minutes, and the probability to find 4 blocks within 6 minutes is about 0.336%.

So, roughly speaking (and strongly simplified, probability-wise), once every 100/0.33581 ≈ 298 chunks of 4 blocks, or once every (100/0.33581)*4*10 minutes ≈ 8.3 days, you can expect 4 subsequent blocks to appear within 6 minutes.

thank you Jace, good quant analysis. Also worth noting that you are assuming the difficulty, which could've been set as long as two weeks ago, still accurately matches the hash rate, producing blocks with a mean target of 600s.

Also note that the probability (W) being calculated is (p) mining 6 blocks within 6 minutes (so it would be the probability of 5 subsequent blocks being mined after any particular block, not 4) and also, given p, (q) the probability of no block being mined for an hour, so the probability I was looking for was:

W = p * q

I was guessing originally around 10,000 to 1

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Jace

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Quote from: biodieselchris on July 21, 2015, 11:27:49 PM

For more clarity, I was wondering what the probability of such of an event was.

The time it takes to mine one block is exponentially distributed with λ (mean) = 10 minutes.

This means the total time to mine four blocks is Erlang-distributed with k=4 and λ=10 minutes, and the probability to find 4 blocks within 6 minutes is about 0.336%.

So, roughly speaking (and strongly simplified, probability-wise), once every 100/0.33581 ≈ 298 chunks of 4 blocks, or once every (100/0.33581)*4*10 minutes ≈ 8.3 days, you can expect 4 subsequent blocks to appear within 6 minutes.

Kazimir

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Quote from: odolvlobo on July 22, 2015, 02:00:34 AM

Here is something to think about:

Regardless of how long ago the last block was added, the average time to the next block is 10 minutes from now.

Yep, and if starting now you wait 2 hours and no block gets mined, then the expected time for the next block to appear is still 10 minutes after that (rather than 'any moment now!')

Exponential probability distribution vs people's intuition

On topic: TS doesn't understand the maths behind Bitcoin's block time statistics. You should raise an alarmed topic if something like 6 blocks in 4 minutes (or zero blocks in an hour) would not occur once in a while.

Derrike

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It is not fishy that 6 blocks in 4 minutes.
It sometimes take more time and sometimes take less to mine the bitcoin blocks.

odolvlobo

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Here is something to think about:

Regardless of how long ago the last block was added, the average time to the next block is 10 minutes from now.

biodieselchris

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CoinQuacker

Quote from: odolvlobo on July 20, 2015, 04:03:18 PM

random
[ran-duh m]
adjective
1.
proceeding, made, or occurring without definite aim, reason, or pattern:
the random selection of numbers.

Probability:
A number between 0 and 1.

btccashacc

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Quote from: notbatman on July 20, 2015, 08:09:14 PM

Quote from: btccashacc on July 20, 2015, 07:41:09 PM

Quote from: notbatman on July 20, 2015, 04:04:12 PM

Quote from: biodieselchris on July 20, 2015, 03:47:11 PM

and then none for almost an hour: Shocked

Height   Age   Transactions   Total Sent   Relayed By   Size (kB)
366198   55 minutes   180   $ 326,607.88   8baochi   98.73
366197   56 minutes   2   $ 7,065.06   BTCChina Pool   0.46
366196   57 minutes   512   $ 198,246.97   F2Pool   243.99
366195   58 minutes   252   $ 499,984.66   EclipseMC   236.32
366194   59 minutes   1   $ 6,950.00   BW.COM   0.23
366193   1 hour 0 minutes   913   $ 1,945,522.50   BW.COM   555.81

I see Josh is still mining away happily on his customers rigs...

josh garza from GAW miner Huh

No, Zerlan from BFL.

Get your scammers named Josh straight!

ohh Thank's

biodieselchris

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CoinQuacker

For more clarity, I was wondering what the probability of such of an event was.

subSTRATA

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:^)

its not that surprising, maybe uncommon for it to occur, but that's the extent of it. miners pretty much guess the hashes that will solve the blocks, and it seems the miners just got lucky in guessing during this hour, nothing more, nothing less. ive seen blocks get confirmed within a minute of each other too, its not something to get that excited over.

Topic: 6 blocks in 4 minutes (Read 1438 times)