I thought about a different version of this puzzle: A finite stalemate game.
Can anyone think of a situation where it is optimal for both players to not gain anything for n turns, then gain something the (n+1)st turn? I'm thinking pin game, but I think the pinned player wants to buy stuff there to help drain piles...
Do we count coin tokens as "anything"? How about VP tokens? Or Masq as "gaining"?
For instance Tr/Kc(from Bm deck)/Monument x2 gains 6 VP a turn. An opponent with 10 villages/Fortress(from Bm deck)/Bish x4 will gain 12 VP a turn once they are setup. If the opponent has enough clutter (e.g. curses and the like) and enough of a VP lead that the Monument player is then best setup to milk 6VP a turn while the Bish player hits 3 or fewer and then pile out when they are ahead before the Bish player again overtakes them.
The Bish player should buy to 3 pile IFF they can end the game before Monuments overtake their starting lead or once they have re-overtaken the Monument player.
So something like a 5:20 starting VP balance, but P2 can only average 1 Bish per turn. After 3 turns we'd expect something like 23:23. This would go to 29:24 until the Bish player can start hitting double and triple Bish plays. Eventually Bish will be hitting 12 per turn so Monument wants to end the game before that is decisive. You can even do this with just Bish or monument. P1 has to start with more points than P2, but earn fewer per turn for some period of n turns, but have deck acceleration so he eventually earns more points than P2.
Another option would be something like reliable-ish, but fragile engines for both players with 5 Bakers/5 Candlestick makers for each player. Optimal play might be for each player to hoard their coins until they can purchase a game winning amount of green (which then nerfs their engine). Optimal play for both would be to hope the other guy whiffs rather than starting buying and piling later.
Another option is waiting for an opponent to whiff on drawing a key reaction card like Moat. For instance, say we both have engines that run on Kc -> Kc -> Moat and both have two cursers. If you buy green, it lowers the odds that you will have a Moat in hand. When you don't have Moat in hand, you likely gain 6 curses (breaking your engine). Optimal play might then be to wait & hope that the other guy misses one of his 5 Moats before you do. Eventually one guy whiffs and he gets 6 Curses and then 4 more in a few more turns. At that point the lucky player can safely buy green without having his deck break.
You each have 1 copper in deck (you both trashed the rest with Mint), Tr, and Pirate ship (both have zero tokens). You can now buy nothing but coppers & curses. However, if you buy coppers you greatly increase the odds that the other guy will hit on Pirate ship (making it worth $1) and allowing him to buy good cards.
There are likely many other variants where your best bet is to play your deck & do nothing until the other guy gets horrid shuffle luck. Basically doing nothing gives you 50% odds that you crumble first, but buying anything else gives >50% odds of crumbling first. Eventually someone whiffs and then it is in one or more players interest to buy more cards.