- Aug 19, 2015

- 18

- 37

First, a theoretical note: It can trigger with one very puny, but very lucky XT miner solving 750 blocks in a row. A miner triggered fork can happen at any time, regardless of criteria, in theory.

So, when we say lucky, what do we really mean?

**Assumption**

First, some assumptions. We're going to define our problem in terms of:

- A time period (defined in number of blocks):
**N** - A target ratio of blocks:
**t** - An actual ratio of hashrate:
**r**

- If hash rate is increasing, then the net hashrate percentage when the fork triggers is higher than the average over the entire time period (more miners are on board than you'd get with steady state mining, which is a good thing).
- If hash rate is decreasing then the fork is strictly less likely to trigger than in the preceding time period. It's more likely the fork would already have triggered.

**The math**

The total number of blocks with the flag (which we'll call

**) is a random variable following a binomial distribution.**

*X*We can calculate the chance of a fork happening in a given

**blocks by just calculating the cumulative probability function's value for**

*N***times**

*N***.**

*t*So what are the probabilities?

- At 75% of hashrate we have a 51.7% chance of finding at least 750 blocks in the 1000 block span.
- 74.9%: 48.8% chance
- 74%: 24.8% chance
- 70%: 0.0025% chance
- Plug your own numbers here if you're curious about other percentages.

Now, this is for a single span of 1000 blocks. What if hash rate percentage stays at 70%

*forever*? How long until we see a fork?

You may be tempted to just consider each separate 1000 block span independently (2000 blocks is 2 independent spans of 1000), but that will underestimate the probability, since the 750 can happen using part of one and part of the other.

You may instead consider each overlapping 1000 block span (so 1001 blocks is 2 independent spans of 1000), but the results of those are not independent, and so you'll massively overestimate the likelyhood of success.

Since I don't know a good math formula for this, I decided to simulate the damn thing. PM me if you want the code, but the approximate results are below:

- At 75% of hashrate we would expect to take around 1269 blocks to trigger the fork
- 74.9%: 1303 blocks
- 74%: 1870 blocks
- 72.5%: 5901 blocks
- 70%: 301127 blocks

*TL;DR*: At anything less than 70% of steady hashrate, triggering a fork would take at least 6 years, and gets exponentially less likely as miner share decreases.