# The probability that the entire network generates at least two blocks within 10 minutes?

We know that Bitcoin network on average generates one block per 10 minutes.

Is there a formula to compute the probability that the entire network generates at least two blocks within 10 minutes by using current hashrate of the network and current difficulty level ?

Thanks

Since current hashrate and current difficulty level should be matched up usually, we can disregard them. (Although, we could easily accommodate them if they are diverging as well.)

Finding blocks is a Poisson Process.

The chance to find at least two blocks in ten minutes is "all cases" excluding the cases where we find 1 and 0 blocks: `P(2+) = 1 - P(1) - P(0)`

``````P(0) ≈ 0.368
P(1) ≈ 0.368

→ P(2+) ≈ 0.264 = 26.4%
``````

I've described the formula here: How can we be sure that a new block will be found?

• Thanks for useful information. Thus, it means that the probability that the network generates exactly 2 blocks in 10 minutes is 36% ? (maybe I'm wrong ...) – Questioner Sep 18 '16 at 19:21
• @sas: No, exactly two blocks in ten minutes would be 18.4%. – Murch Sep 18 '16 at 19:23
• Thank you very much for your helpful information. Now the question is that if network would include 2 mining pools (pool_1 and pool_2) with the hashpower of 49% and 51%,respectively, then the probability that in 10 minutes, 2 blocks would be generated such that the first block is generated by pool_1 with hashpower of 49% ? Thanks – Questioner Sep 18 '16 at 20:08
• 0.184×0.49? However, the network is fundamentally broken then: pool_2 can just ignore all blocks by pool_1 and still produce the longest chain by itself – Murch Sep 18 '16 at 20:12
• Yes, but we assume that pool_2 is honest and pool_1 is selfish. So, the probability under this condition is 0.184×0.49? – Questioner Sep 18 '16 at 20:16