Gold collapsing. Bitcoin UP.

[Peter R]

@Mengerian: Yes the answer is still 20 min. It is quite mind boggling how this can be true while it is also true that the average block interval is 10 minutes.

To answer your other questions: you expect that block N-1 came 10 minutes earlier and you expect that block N will come 10 minutes later.

 

[freetrader]

Or would it help the network to run BUCash, ABC and XT on the same server? In terms of disk space, RAM and bandwidth it should be no problem for the server I have running.

This is actually a really neat idea.

Those of us who have powerful PCs can run several Cash clients with their own datadir and ports for redundancy during the fork.

 

[albin]

Maybe a good explanation is that if you've already waited 10 minutes and no block, the sample space of outcomes you're now in is a subset of the sample space of possible outcomes 10 min ago, and all the outcomes where a block had been found within the last 10 min have been pruned from the set.

 

[Mengerian]

@Mengerian: Yes the answer is still 20 min. It is quite mind boggling how this can be true while it is also true that the average block interval is 10 minutes.

To answer your other questions: you expect that block N-1 came 10 minutes earlier and you expect that block N will come 10 minutes later.

It's hard to see how that can be correct.

I think the thing that is "expected" is that "the average block interval is 10 minutes".

I don't think it is expected that "the next block will be found in 10 minutes".

Seems to me the expected value of "when will the next block be found" is 5 minutes, as @Norway alluded to.

This would be the case if a miner found a block within the last 10 seconds, or if the previous block was found several hours ago.

 

[Peter R]

@Mengerian:

OK I did a quick simulation to help convince you.

Here is some explanation for how I'm simulating a single measurement

And here's where I run the experiment multiple times, average the measurements, and compare it to the inter-block time.

 

[Zarathustra]

Yes, the last block has been found 5 minutes ago and the next one will be found in 5 minutes, on average.

 

[Mengerian]

@Peter R Hmm, that is indeed counter-intuitive!

Is that Mathematica?

Maybe my stumbling block is over the "expected" time of blocks relative a particular time.

It's easier to conceptualize the "expected" number of block within a particular time interval. For example that the "expected" number of blocks in a 1-hour time interval would be 6.

So could we say the if we choose a random time t_0, that the "expected" number of blocks in the 10 minutes leading up to t_0 is 1? And that the number of blocks that we expect to find within the next 10-minute period is 1?

 

[Mengerian]

I think I realized my mistake.

Some blocks are farther apart in time than others.

If you just look at all the inter-block intervals in a particular period, enumerate them and average them, you will indeed find that the average inter-block time is 10 minutes.

But, if you choose a random time on the time-line, the probability of choosing a time between blocks that are farther apart is higher than the probability of choosing a time between blocks that are close together. So if you're randomly sampling points in time, you will get more samples from block intervals that are farther apart than form block intervals that are close together.

So this explains why, sampling random points in time, if you just take a bunch of measurements and average them, you get a result greater than 10 minutes.

 

[adamstgbit]

Imagine you are throwing dice. Everybody would agree, that after a n=few hundreds throws, we would approximately see every number with an fraction of 1/6 * n. Now, if we've thrown a six for 20 times in a row, would you say, that at the next throw, the possibility for a six is lower than 1/6?
No, the chance for every number is still 1/6 at the next throw. Regardless of what you've thrown in the past.

i understand the science behind it now.
and i have new found appreciation for the technical marvel that is minning bitcoin.

but the gambler inside me can't help but FEEL that a block is more likely to be found if one hasn't been found in the last 10mins.

 

[AdrianX]

Here is a question for the algorithm people.

Does any one have data on how many times a individual miner tries the exact same calculation more than once between blocks, or is each attempted calculation between blocks an original attempt for the golden nonce?

IE. when a miner is trying to trow a 6 and he throws a 4, how many times does a miner throw the dice with the exact same velocity trajectory, environmental pressure distance from the ground, in the same environment with the same gravitational pull etc, that would result in him repeating the exact same through that resulted in throwing a 4?

 

[Norway]

@Peter R
There's a bus leaving every 10 minutes. You don't have a watch, so you just meet up at the bus station at a random point in time. How long is the average waiting time for the bus?

 

[Peter R]

@Mengerian: yes that is exactly right! If you pick a time at random, you're more likely to pick a longer-than-average block period because they last longer. I still find it weird how that average is exactly twice the interblock average (if you average enough trials).
[doublepost=1501456346][/doublepost]Yes it is Mathematica.
[doublepost=1501456720][/doublepost]@Norway: 5 minutes for the bus question; it's not a memoryless process.

 

[Norway]

@Peter R
The bus drivers don't care about time. They somtimes stop to eat. They sometimes talk with passengers etc. They don't have a scedule. They have a random behaviour. But on average, it's 10 minutes between each bus. Do you think it's still 5 minutes on average waiting time?

EDIT: Reading up on memoryless processes. This is not a good example of that.
EDIT2: Bitcoin is actually used as an example of a memoryless process on Wikipedia. To the moon! https://en.wikipedia.org/wiki/Memorylessness

 

[Mengerian]

@Peter R " I still find it weird how that average is exactly twice the interblock average (if you average enough trials)."

Yeah, that is interesting. It must be a property of processes where the events are randomly distributed and independent from each other.

One can imagine other distributions where this is not the case, for example if you had 100 minute window with 9 blocks found in the first minute, and one block found in the 99th minute. In that case, for a random point in time, your "expected" time between blocks would be something close to 99 minutes.

Or if blocks come every 10 min like clockwork, then the expected time between blocks would be 10 minutes.
[doublepost=1501458159,1501457484][/doublepost]@Norway, I think the expected waiting time would be something longer than 5 minutes.

If the buses show up exactly every ten minutes according to a schedule, then your expected waiting time will be 5 minutes.

But, if there is some randomness, then sometimes the buses will be close together, and sometimes they will be far apart. If you just show up at a random time, it will be more likely that you are in one of the longer gaps between buses. And in these longer gaps, your waiting time will likely be longer, which will outweigh the times you happen to just miss one bus, but catch one that is close behind it.

In an extreme case, imagine the buses travel in clumps of two. So every 20 minutes, two buses go by very close to each other. You can see that in this case, you can expect to wait 10 minutes on average.

 

[Norway]

@Mengerian Yes, reading up on memorylessness now. The random busdriver is a bad example (wrong).
[doublepost=1501458679][/doublepost]It's better for me to think in terms of dices.

 

[Norway]

The future Bitcoin Cash price is double at hitbtc.com compared to viabtc.com. It's been like that for several days now. A great arbitrage without risk except for the risk that exchanges are risky in general and the fork might not happen.

 

[AdrianX]

Bitcoin mining is not memoryless to my observation. In the example @Norway referred to with the hallway of safes below.

Imagine that an eccentric man walks down the hallway, stopping once at each safe to make a single random attempt to open it.

Bitcoin mining is different. There is a gold coin in some of the safes. The man workes each safe until he opens it he checks to see if there is a coin and then moves on. Every 2 weeks the distribution of coins changes to ensure on average the discovery of coins happen at random every 10 minutes.

Every safe is not tried once, every safe is opened and the man knows empirically it's empty. He has memory that all the empty safes are empty.

​

 

[NewLiberty]

A little late to the party, but if I'm understanding the gist of the bet, if "now" is t=0, the answer is t=15, but if "now" is t=-10, the answer is t=5?

Expected Value is a mathematical term E[X]=r((1-p)/p)
It gives a measure of the center of the distribution of a variable
It is not the same as the average.

Both betters were right about different things.
Both were wrong to make such a bet.

Mining is almost memoryless. Nonce are not reused so it is not perfectly memoryless, only so close to memoryless as to be memoryless for practical purposes.

 

[AdrianX]

Woot. gold collapsing bitcoin up @NewLiberty returns things are looking up.

 

[Norway]