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Usually, by the time I can withdraw 100 Krowns, my troop is self-supporting anyway- missions, loot and maximizing trade runs, but I might do it for some cushion after a large purchase like a trade post or a pile of skill books.
Tavern income, Krownwise, is only supplemental for me as I make most of my money through trade. There's a guide somewhere around here that lists which towns sell what and which towns pay the most for a given commodity. By end-game, my teams often have over 100K in cash regardless of tavern income.
Edit: It's apparently 100 copper coins per 20 krowns on Extreme difficulty.
As you said, the most efficient is probably to withdraw twice per shift (-10 on the conversion rate) until the conversion rate is 100:96 before you withdraw for the current shift. For that particular shift take out just once to lower the conversion rate by 5, hitting 100:91. Next shift you'll be back to 100:100 again, and you repeat the process.
So, withdraw twice for four consecutive days, withdraw only once on the fifth day, repeat. This'll net you an average of 172.8 krowns per day.
Once you get 400 Copper Coins (or more) per shift and you're not saving them for anything, you just withdraw them all at once whenever the conversion rate hits 100:100, which will net you an average of 185.625 (or more) krowns per day. Waiting for 100:100 ratio before mass withdrawing is (very) marginally more efficient than just withdrawing it all every day.
When you are first starting the game, you can get closer to 1 : 1 for a while. But the devs clearly decided on 10 : 3 as the exchange rate they thought "fair"/acceptable for the amount of gold that can be made.
Even at 10 : 3, it's around 1000 gold per service once your tavern is upgrade. And really, the entire game economy is balanced around *not* having the Tavern. Nothing was changed after the Tavern release to make things more expensive. You don't need to try to maximize the exchange rate. At 10 : 3, you will make more gold than you can spend. I don't even take missions or trade anymore in my current late-game run, and I'm pushing past 90K gold, just from selling loot and my Tavern.
IMHO, just forget about the exchange rate. Use your copper to develop/build the Tavern, and any gold you get is gravy. Your'e not supposed to be getting a 1 : 1 exchange, except when you first get started.
Actually, it is 20 crowns, not 30. At least on expert/expert.
The exchange rate may also depend on the economic difficulty then?
Oh, that's interesting. I didn't realize that the difficulty option affected the Tavern's exchange rates.