At the end of 2 nd week the state vector is
Px 1

x (2) =
Px (1)
=
|.25
.20
.25
.30|
|.25|
=
|.2550 |
|.20
.30
.25
.30|
|.20|
=
|.2625 |
|.25
.20
.40
.10|
|.25|
=
|.2325 |
|.30
.30
.10
.30|
|.30|
=
|.2500 |

Note that we can compute x 2 directly using
x 0 as
x (2) = Px (1) = P(Px (0) ) =
P 2 x (0)
Similarly, we can find the state vector for 5 th , 10 th , 20 th , 30 th , and 50 th observation periods.
x (5) =
P 5 x (0) =
.2495
.2634
.2339
.2532
x (10) =
P 10 x (0) =
.2495
.2634
.2339
.2532
x (20) =
P 20 x (0) =
.2495
.2634
.2339
.2532
x (30) =
.2495
.2634
.2339
.2532

x (50) =
.2495
.2634
.2339
.2532

The same limiting results can be obtained by solving the linear system of equations P P = P using this JavaScript. It suggests that the state vector approached some fixed vector, as the number of observation periods increase. This is not the case for every Markov Chain. For example, if
P =
0
1
1
0
, and

Good read, but I’m missing something here…It’s probably that:

You say “The first 100 points of Critical Rating increase Critical Chance by %”

To which I could reply “So…what?”

The bigger problem here is how much dps per point you get from crit rating vs power, because crit as in crit chance is always nice, problem is, what you have to sacrifice in order to get it.

And while I’m not expecting you to write an in-depth analysis for each spec to account for auto-crits and surge increases, something like “A 5 min parse using only auto-attack with 0 crit is 800 on average, while with 100 crit and 72% surge it is an average of 820” would be more convincing than “100 crit rating gives % crit chance”.

Don’t get me wrong though, what you explained you explained well, it just lacks some kind of a real scenario to demonstrate it.