<p>Assuming block finding is a Poisson process with rate 1 per 10 minutes.</p>
<p>In that case, the number of blocks found per given finite time interval would be described by a Poisson distribution. For 20 minutes, a Poisson distribution with lambda = 20 minutes / 10 minutes = 2.</p>
<ul>
<li>No blocks in 20 minutes: ~13.53%</li>
<li>1 block in 20 minutes: ~27.07%</li>
<li>2 blocks in 20 minutes: ~27.07%</li>
<li>3 blocks in 20 minutes: ~18.04%</li>
<li>4 or more blocks in 20 minutes: ~14.29%</li>
</ul>
<p>Due the memorylessness of the Poisson process, it doesn't matter when you start the clock for your 20 minutes. These hold for whatever window of 20 minutes you look at.</p>

CC BY-SA 4.0
2022-05-18T03:15:13.620Z
2022-05-18T03:15:13.620Z
Pieter Wuille
<p>I know that block interval in bitcoin blockchain is exponential distribution. Now I want to know what is the probability that maximum of 3 block will be mined in the next 20 minute?</p>

<mining-theory><proof-of-work>
Probability of mining maximum of 3 block in next 20 minute
ali-sezar
# Probability of mining maximum of 3 block in next 20 minute

(Asked by: username_0 on 2022-05-18)

I know that block interval in bitcoin blockchain is exponential distribution. Now I want to know what is the probability that maximum of 3 block will be mined in the next 20 minute?

**Tags:** mining-theory, proof-of-work


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## 1 answers

### Answer by username_1 on 2022-05-18. Score: 4 | Accepted answer

Assuming block finding is a Poisson process with rate 1 per 10 minutes.

In that case, the number of blocks found per given finite time interval would be described by a Poisson distribution. For 20 minutes, a Poisson distribution with lambda = 20 minutes / 10 minutes = 2.

* No blocks in 20 minutes: ~13.53%
* 1 block in 20 minutes: ~27.07%
* 2 blocks in 20 minutes: ~27.07%
* 3 blocks in 20 minutes: ~18.04%
* 4 or more blocks in 20 minutes: ~14.29%

Due the memorylessness of the Poisson process, it doesn't matter when you start the clock for your 20 minutes. These hold for whatever window of 20 minutes you look at.


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