Buying silvers on 3 greatly inhances the chance of hitting 4 +
So 9 turns is a reasonable estimate.
But that's buying a card, which was deemed unnecessary at the start.
So I tried some super simple simulation via proxy on
Dominiate to answer Asper's question: "Can I reach $4 seven times before you reach $8 twice?"
Here's the code for the Salt strategy:
{
name: 'PureSalt'
requires: ['Great Hall']
gainPriority: (state, my) ->
if state.supply.Colony?
[
]
else
[
"Great Hall" if my.coins > 3
"Silver"
]
}
Great Hall is a proxy for Salt the Earth here. It buys StE with 4+ and Silver otherwise. Obviously I can't run this thousands of times to see what wins, but I can run single games a few times and check the game log to see when the 7th Great Hall is purchased.
Results from 10 trials:
10
10
9
10
9
8
10
11
10
11
Mean: 9.8
Mode: 10 (5 times)
It hit a speedy 8 turns once, a slow 11 turns twice.
Now here's a naive Smithy bot that rushes Provinces.
{
name: 'RushSmithy'
requires: ['Smithy']
gainPriority: (state, my) -> [
"Province"
"Gold"
"Smithy" if my.countInDeck("Smithy") < 2 \
and my.numCardsInDeck() >= 16
"Smithy" if my.countInDeck("Smithy") < 1
"Silver"
]
}
When does it buy the second Province? 10 trials:
10
13
8
11
8
8
10
10
8
8
Mean: 9.4
Mode: 8 (5 times)
It hit a speedy 8 turns a whopping 5 times, but a slow 11 turns once and an abysmal 13 turns once.
It's close, but it looks to me like going for Provinces has an edge here. Pure Salt is more consistent while the rush can be pretty blistering to 2 Provinces. However, these are both naive approaches, and I'd guess that the rush has overall more control and flexibility which will give it the edge when played responsively. OTOH, buying the 2nd Province vs. the 6 StE buys is only achieving an equal score, so that's a point in Salt's favour.
There's lots of strategic wiggle room here for optimization though -- the rush might be using something worse than Smithy, both parties could be buying/trashing Duchy, the Province rush could potentially make use of Salt the Earth as well.
But I think my argument stands. You shouldn't neglect buying cards even if you intend to Salt all the way down. You should certainly take Silver at least, and you will probably be better served by buying at least a few other things as well.
Edit: I also just noticed the second Smithy rule in the rush bot that is unlikely to be optimal. I just edited down the SmithyBM bot and didn't give it much thought, but I'm guessing that getting the second Smithy earlier or not at all may be better (with the current rule, it's probably a waste of time when it happens).