Fulmination chain

I've had 2 pieces of tier 18 for a week or so now. The elemental 2-set bonus states:

Your Earth Shock has a 45% chance not to consume any Lightning Shield charges and to have its cooldown instantly reset.

What this means is that when you earth shock, to drop your lightning shield stacks into a fulmination, a proc allows you to instantly cast it again for the same effect. The extra cast also gives the set bonus another chance to proc, meaning you can get lucky and chain multiple earth shocks/fulminations in a row.

These are independent events, meaning two procs in a row, resulting in 3 earth shocks, has a 0.45 x 0.45 = 20.3% or roughly 1 in 5 chance of occurring. This continues as follows:

4 in a row - 9.1%
5 in a row - 4.1%
6 in a row - 1.8%
and so on.

The first time I had 6 earth shocks in a row I was briefly shocked, until I got a moment to think about it and realised you could easily experience that a couple of times in a raid night. When I had 9 in a row, I thought I probably wouldn't beat that for a while. But on our heroic iskar attempts, I had a new personal record of 11 earth shocks in a row.

This did cause a 'holy shit' moment, where I had to bring up the calculator and figure the probability of that happening - 0.034% or a roughly 1 in 2940 chance. I hope to beat that at some point, although I suspect it might be a once in a raid tier level event.

For now I will save my thoughts on the set bonus until after I get my fourth piece and I can see the interaction with the 4 set bonus.

A quick final note, last night I ran LFR to get the last 5 Tomes of Chaos I needed to form the legendary ring Nithramus. I look forward to trying it out, but I am only aware of 2 others in our raid team having it so far, so the full effectiveness won't be visible just yet.