Bitcoin Forum

What is the probability that the next block will be found within 10 minutes from now?

Or within 1 minute?
Or 10 seconds?
Or 1 second?

Bitcoin's designed to put out a new block every ten minutes. And it's going good. Difficulty controls it and most of the blocks are mined 10 minutes apart.
There are a few exceptions when two blocks are found very fast, in a row, and that's just called luck.

There's no probability actually. It just averages around 10 minutes per block.

This could be an interesting read for you too: https://bitcointalk.org/index.php?topic=135982.0

It's a Poisson process, with a mean of 10 minutes. So...

63.212%

9.516%

1.653%

0.167%

+1 to Foxpup.  :)

Foxpup, that's a killer response ;)

Now THAT is a killer response!

http://weknowgifs.com/wp-content/uploads/2013/03/billy-dee-williams-clapping.gif

       https://i.imgur.com/EqRJH.gif

Technically speaking the chances are somewhat better then this because additional miners have apparently been added to the network (net of miners that have been removed, in terms of hashrate). The above percentages would be correct in the event that the apparent hashrate was exactly the same as it was when the difficulty last changed

It might be a good idea to also mention that the probability that 0 blocks are found within the next 30 minutes is 4.978%. Then maybe people would stop complaining when we get the occasional over 30-minute block.

Those longuns are easy to predict.... they happen about the once every few weeks that I decide to send a transaction :D

you must send when I send.
rambling on the side:
I always thought it might be an interesting energy savings experiment to run a farm but only mine at near the peak of the distribution/time chart. could you save a ton of power and hash more effectively vs power. (of course you'd have to be solo mining and we're a bit past that heh, otherwise your just submitting less shares at an equal pace for the offtime)

What do you mean? I think you're wrong here.

The probability of you finding a block in any time period of fixed length should be independent of what everybody else does (if we ignore difficulty changes).

Wouldn't a number closer to 50% make sense for the 10 minute mark?

Only in as much as it would be a lot easier to make Pi equal 3.0000000

Of course not. 10 minutes is the mean, not the median. The median (the point where 50% are higher and 50% are lower) is 6 minutes and 56 seconds. It should be expected that the median will be much smaller than the mean because there is a lower bound to the block time (zero) but no upper bound. It is possible to have a block time to be 20 minutes longer than average, but it is obviously not possible for the block time to be 20 minutes shorter than average (because it would be less than zero). Thus there a few very long block times that aren't (and can't possibly be) matched by very short block times, and this skews the average.

Thank you for the details. I used to score really high on tests, but seem to have been dragged back towards the median.   :D

You can also express that percentage as "on average, once every 25.1 days we should see 30 minutes with zero blocks found."

Holy guacamole. How to tell a BitCoiner with statistics background versus a newblet.

Take a bow, sir.
http://media.tumblr.com/740f90580de520b93afdcb2bae632857/tumblr_inline_mtcf2wUtbw1rwwk99.gif

How much information is typically in a block? I'm still a novice

...

Poisson distribution, but approximates its continuous cousin the exponential distribution.  For me it is easier to think in terms of the exponential.

When I am waiting on a confirmation for a transaction just done, the rule of thumb I use is (very similar math to Foxpup's) is that a confirmation (let's just use a simple rule of a solved block = a confirmation, not always true) will come in a median of the 6.32 mins:

10 (minutes) - 10(1/e) = 10 - 10(0.3678) = ~ 6.32 minutes (median) even with the designed 10 minute average.  Where "e" is that pesky number that shows up in the most unusual places (and is approximately 2.71828).

What seems to happen to me a lot is that confirmations (time until next solved block) seem to take 20 - 25 minutes rather often...:

P(> 20 mins) = 1/e^2 = some 13.5%, wow, I'm unlucky.  So don't look for me in Vegas...

:)

...

Here's a chart I did for curiosity back on Nov 27 of last year tracking the times between blocks (info from blockchain.info):

https://drive.google.com/file/d/0BxnHmH-02CQIZ2VqeFBzQVhIb1U/view?usp=sharing

Where minutes between blocks are the Y-Axis and the 112 or so consecutive blocks on the X-Axis.

The mean and standard deviation of that data set (both in minutes):

9.92920354
7.700552872

(Sorry I could not figure out how to post the image right into here)


EDIT: My understanding of the exponential distribution (probably the Poisson as well) is that the standard deviation should (approximately in reality) equal the mean, in this data set that is not true...  Please correct me if I am wrong, smile,,,

Of course there is.

The block time is actually an exponentially distributed variable, which is a continuous process (rather than a poisson distribution which is discrete, although they're closely related) with mean = 10 minutes.
This implies the probability of the next block being found in t minutes from now, is 1-e^-t/10 (with e≈2.71828183 or e^x = exp(x)).

The reason the actual mean is probably a bit lower than 10 minutes, is because the total hash rate is almost continuously increasing, whereas the difficulty (which is supposed to keep the mean at 10 minutes) is based on the previous 2016 blocks.

Very well explained sir https://i.imgur.com/9YlZkFV.gif

In general, the probability of the next block being found in t amount of time, when the average block time is b, is 1-exp(-t/b) (you can express t and b in minutes, seconds, fortnights, whatever you prefer).

One more interesting observation: as already mentioned, the probability of the next block not being found within 30 minutes, is e^-30/10 ≈ 4.98%

However, when this occurs, e.g. no block as been found for 30, or 40, or 60 minutes, then at that point the next block is still expected to be found 10 minutes after that.

In other words, at any given moment (no matter how short or how long ago the last block was found!) you can expect the next block to still take 10 more minutes.

How'd you arrive at those values if you mind me asking? Anyone can explain?

Great topic....we don't get good topics like this much anymore.

well..somehow most of my transactions take more than 10 mins for confirmations.. no clue y is that..but it seems like every time..over 10 mins.! very occasionally under 10 mins..!! I put fee as 0.0001..

Some people study statistics, some study art.  It's all good.

I'd say it's just luck.

I asked the same question, and it led me to read about Poisson random processes, and the exponential distribution, which is the related time-interval probability density function. To get the probability that a block will be found within whatever amount of time, call it "t", you integrate the probability density function from "t" to infinity to get the probability that it takes longer than "t" and subtract that from 1 to get the probability that it takes less than "t".
Call the Expected block interval time "Beta" = 10 minutes or 600 seconds. (It does not matter, as long as the same units are used throughout), and call the inverse of the expected block interval time "Lamda".
The probability density function is:   Lambda * e ^{-Lambda * t}
The probability that "x" (the time to find a block) will be larger than "t"  =  Integral(from "t" to Infinity) of Lamda * e ^{- Lambda * t} dx,  which fortunately, simplifies to e^-Lamda*t
The probability that "x" will be less than or equal to "t" is therefore = 1 - e^-Lamda*t
This is the equation that gives these values:
 P(x <= 10 minutes) = 0.63212 or 63.212 %
 P(x <= 1 minute)    = 0.09616 or   9.616 %
 P(x <= 10 seconds) = 0.01653 or 1.653 %
 P(x <= 1 second)    = 0.001665 or 0.1665%

I think that because finding the winning hash of a block is a Poisson random process, no matter how long it took to find a block, the expected value of time to find the next block is 10 minutes, but as time goes by since the last block was found, it is more and more likely that a block will be found.  The probability that a block will be found in less than time "t" is given by  1 - e ^-Lambda*t,
where Lambda = 1 / Expected Block Interval Time; (for Bitcoin, Lambda = 1/10 minutes or 1 / 600 seconds)
So for example, if you want to be 99.9% sure when the next block will be found, you can set 0.999 = 1 - e ^-(1/10)*t and solve for t.

      0.999 - 1  = - e ^-(1/10)*t           // subtract 1 from both sides
      1 - 0.999  = e ^-(1/10)*t             // multiply both sides by -1
 ln( 1 - 0.999) = -(1/10)*t                                  //  take natural logarithm of both sided
 ln( 1 - 0.999) * 10 = -t                                      // multiply both sides by 10

    t = 69.08 minutes, =  about 1 hour 9 minutes 5 seconds

So, you can say, that after a block has been found, it is 99.9% certain that the next block will have been found within the next hour nine minutes and 5 seconds.

If you want to be 99.999% sure, the same calculation yields 115.13 minutes or 1 hour 55 minutes and 8 seconds
 -
 

Probability of BTC price over $1000 within 11 months is 2,199,114,855/700,000,000 (which comes out to exactly 3)

Probability goes from 0 to 1. What you say makes no sense.

Yeah so if the probability was 0, and now it's 3, then that's 3 times more likely (p = 0 x 3 = 3.141592654)

http://inmyskinnygenes.com/wp-content/uploads/2014/02/Trolls.jpg

Just use the ignore button.

You're right, he must be trolling.  Nobody could have misunderstood my comment that badly, so I shouldn't have responded to him as if he was a legitimate poster.

Now I don't know if you're being sarcastic or a troll or what. 0 x 3 = 0. Simple math.

It's a humour-joke, referencing a previous post in this topic