Okay, I think I have a method that is O(X*9^X). Which means that given a large enough starting X, it should beat X^64.
disclaimer: I don't fully understand what you're doing, so maybe I talk nonsense.
If you call the size of the starting hand X with both strategies, then yes, your strategy out-scales the currently dominant one.
But I don't think that's really a fair comparison. In your strategy, the limiting factor is starting hand so you should write your profit as a function of that.
In "our" strategy the limiting factor is this number of actions you get to play.
About your strategy: Why are you including the Overlord, Crown & Mint? It seems to be equivalent to just using King's Court and Black Market straight away.
I don't see a way to draw more than 14 useful cards at the start of your turn (5 regular, 5 from tactician, 4 from expedition), which would allow for 25 black market plays.
You can easily add ~70 Silvers to that hand (opponent playing a lot of KC Swindler, always hitting Rocks and replacing with Rocks) but that doesn't really help.
The real limiting factor is that you have no way of replacing these silvers with the much more useful banks.
am I missing something? Any chance Adventurer can help your plan? It draws Crowns, but not Overlords or Black Markets.
Hmmm, I thought that because you're always writing like starting hand and number of coins for Black Market buy, that your strategy is a function of that number, as well as the exponent on that number being hard capped by number of Actions i.e. X^2^(2*A), where A is at most 6. Like, if your strategy has 20 starting cards, you can do something like 2^256 times as well as starting with 10 cards, because you can use your 6 actions to square 12 times. So it makes sense to use starting cards as X, since your gains are limited by starting cards in hand as well.
Another thing is your limit on Black Market plays is Actions available, mine is cards in hand, which is a heck of a lot higher. However, your Black Markets square and mine just multiply by 3.
The Overlord trickery was mostly because I thought of it and it seemed cool. However, there's also the issue of the initial seed money being low, which I didn't think of using Rocks+trashing to solve before. So KC/Black Market is probably better.
With that, you need like 1/3 of your cards to be King's Court, but you play the other 2/3 of your Black Markets three times, so you get up to 2X plays of Black Market. If I is your initial money from $ token, Silver in starting hand, etc. then you get an I*3^2X ending hand of Silvers, and O(I^2)O(81^X) gains using Raid.
Expedition is unlimited with Travelling Fair and Platinum, so that's out unless there's a different better end payload than squaring(which, if you do it out, is like doubling the hand size).
Properly done out:
Setup: Play Tactician. Opponent, on a Tactician turn, plays 3 King's Courts and 5 Swindlers. He then plays Tactician and buys Messenger for Rocks and Mission. For the next hand, he plays 3 King's Courts and 4 Swindlers, Outpost, and Tactician, and the third he plays 3 King's Courts and 5 Swindlers, buying Messenger for Rocks. Total, that's 14 Swindlers tripled for 42 Silver in hand. (No Watchtower because another Black Market is just loads better.)
Then, we have a hand of 4 King's Courts and 6 Black Markets. So that's 3^18*3*42 ending Silver, 3^18*3*42/7*3^18*3*42 gains is a paltry 10^20....
Main issue really is X is different, because different cards are being used to reach it. If X was like 760 it would work... but the loss of stuff like Haunted Woods and Council Room might just be too great to bear.