Trading Post AINEC.
You might have an argument for Vault in a Province game.
Interesting that you think so - I thought Vault would be better in a Colony game since:
- a Trading Post is (besides the Trashing) good for getting Silvers, which will slow you down in the end of the Colony game, and
- a Vault is an automatic Gold every turn, and doesn't need that much (a gold + something) to get a platinum.
The thing about Vault in a Prov game is that it pretty much combos with itself. Any time you draw a vault you at least get a gold and then every time you draw a vault and a gold or two silvers you get a province. The engine can start as soon as turn three and Prov>>Dutch(if prov <4)>>Gold>>Vault>>Silver has about a <14 turn goldfish off of a first turn vault.
I spent some time working the simulations to try to make a first turn TP bot that could beat the first turn Vault bot but was unsuccessful. Best I could come up with was a 38%.
As far as a colony game testing is showing that vault nudges out TP by the tiniest of fractions when both are ~optimized. Upgrade is worse than either by far. The TP bot essentially bought TP first turn then turned into a vault bot. I also tried making it into a TP>Big money deck however this was much much worse. I then tried throwing in a steward or two at various points in the game however they only lowered the win% a few points.
Of course, as is obvious, if the buy orders are off (or if the robots are bad at playing cards) then the results could be far different. I also didn't include any other kingdom cards as none seem to synergize with the first turn fives.