I was curious about how the probabilities actually ended up playing out when trying to get stuff to +15, mainly due to the downgrading, so I did some quick simulations. Figured it wouldn't hurt to share the test results.
HD Ore Rates:
10 -> 11: 100% (I simulate using normal ores here)
11 -> 12: 20%
12 -> 13: 16%
13 -> 14: 16%
14 -> 15: 15%
Here were roughly my results
10 -> 12: 5 HD ores, 5 non-HD ores (duh)
10 -> 13: 37.5 HD ores, 26 non-HD ores
10 -> 14: 214 HD ores, 136 non-HD ores
10 -> 15: 1220 HD ores, 760 non-HD ores
I reran each trial quite a few times and the numbers ended up being fairly consistent.
And here's a rough breakdown of the percentages, meaning there's around a 7.5% chance of getting to +15 in under 100 HD ores
The unluckiest a run ever got was around 15,300 HD ores
Source code for verification and if anyone wants to test on their own: