So, I ran a bunch of simulations today (
http://rspeer.github.io/dominiate/play.html)...
First, and least importantly my opponent did indeed get lucky.
My opponent went for Ironworks-Advisor, which I thought would be too slow.
Advisor-BM doesn't sound that good, but enough Advisors from Ironworks could make it enough. I wouldn't be surprised if it was better than I thought, but I do think Mine-BM should be better.
Mine-BM is way better than IW/Advisor. I could not find anyway to increase Advisors above a 35% win rate or so against unoptomized Mine-BM.
Now, the important questions:
I could be wrong here, but Mine/BM strikes me as very weak BM. In two base-only BM games I once played with a friend, I found Chancellor/BM to be substantially more effective.
The presence of Market Square supports Mine due to the on-trash effect and the fact that it can be a cantrip in case of emergencies, but I don't know if it will contribute more than silver in the long run.
On a generic board (i.e. no other cards bought), simulation suggest Mine-BM and Chancellor-BM are almost equal. I got 52.5%-47.5% for MineBM vs. ChancellorBM after several thousand runs. My strategy of Chancellor+Mine-BM was also about equal, scoring 49% against Mine-BM. Those difference are small enough that tweaking the algorithms (or making better decisions when terminal collide in Chan+Mine) could make the difference. However, with Harem on the board, Mine-BM is clearly better (57-43) due to the ability to mine Silver into Harem.
The other strategy offered up by several here was Ironworks-BM. Without Harem, IW-BM beats Mine-BM 55-45. With Harem on the board, Mine wins 51.5-48.5, again close enough that tweaking the Harem rules\other things coudl make the difference easily.
IW+Mine scored 49% agaisnt Mine. I would lean toward that as the best strategy. In reality you can use IW to gain Market Square in those cases, whereas the simulator will either use Mine or gain Silver with IW. Market Square isn't implemented in the sim and even it is was, it probably wouldn't play it very well (i.e. decideing when to draw v.s when to hold for Gold/other reasons). Thus, I can't say if it helps or not in the general case (but surely helps when obtained for free).
Knights also aren't implemented, but I doubt they can compete (unless Anna/Michael is on top). I tried adding Bridge to most strategies and at best it was neutral. I do not think it is worth getting. Adding a second Mine also seemed neutral at best.
Overall, all non-Advisor strategies offered here are pretty darn close. That would explain the lack of consensus.
Best algorithm I found:
{
name: 'MineBM'
requires: ['Mine', 'Harem']
gainPriority: (state, my) -> [
"Province"
"Harem" if 0 < state.gainsToEndGame() <= 5
"Duchy" if 0 < state.gainsToEndGame() <= 5
"Harem" if my.countInDeck("Gold") >= 2
"Estate" if 0 < state.gainsToEndGame() <= 2
"Gold"
"Mine" if my.countInDeck("Mine") < 1
"Silver"
]
}