discovered by blackbombchu

Chateau Romaini, Gold dust, and a big poe can all be sold for 200 rupees. You can actually get the money from selling it without getting rid of it, enabling you to sell it again by equipping an empty bottle then pressing the c-button for the empty bottle after saying "I'll take it." You have to be very precise how long after you say "I'll take it" you press the bottle button or you will lose the item you sold. Suppose you have an empty giant's wallet and the number of rupees already deposited in the bank is a multiple of 500, then each selling is 7 seconds long so the fastest way to get that heart piece is to sell it 3 times on each trip to the curiosity shop. The next add on of 100 rupees already deposited in the bank before you start selling the 200 rupees item, makes the fastest way be to omit the third selling on one of you trips, the next one after that omits the third selling from another trip, then omits the third selling from another trip, then omits the third selling from another trip, then removes an entire trip while adding the third selling back onto all the other trips. The result is the following time save of getting the heart piece for each add on of 100 rupees already in the bank:

- 7 seconds saved for 100 rupee add on to 0 more than a multiple of 500 rupees
- 7 seconds saved for 100 rupee add on to 100 more than a multiple of 500 rupees
- 7 seconds saved for 100 rupee add on to 200 more than a multiple of 500 rupees
- 7 seconds saved for 100 rupee add on to 300 more than a multiple of 500 rupees
- 20 seconds saved for 100 rupee add on to 400 more than a multiple of 500 rupees

Here's the optimal way to sell the item for each number of rupees left to be deposited that's a multiple of 100 from 100 to 5,000 where a blue box indicates the time between sellings and a purple box indicates the selling time. Alternatively, you could release a fish before and recapture it at the end of each selling to make the not getting rid of the 200 rupee item a lot more reliable as shown in https://www.youtube.com/watch?v=mg64QIZyOAc, making each selling 22 seconds long. If you're doing it that way, then if you have an empty giants wallet and the number of rupees already in the bank is 200 more than a multiple of 400, the fastest way to get the bank heart piece is to sell the item twice on each trip to the curiosity shop. The next add on of 100 rupees already in the bank makes the fastest way be to remove an entire trip and add a third selling to 3 of the other trips, the next add on of 100 rupees removes a third selling from one of the trips, the next one after that, removes the third selling from another trip, and the next one removes a third selling from another trip leaving no third selling on any trip. The result is the following time save for each add on of 100 rupees deposited in the bank:

- 22 seconds saved for 100 rupee add on to 0 more than a multiple of 400 rupees
- 22 seconds saved for 100 rupee add on to 100 more than a multiple of 400 rupees
- 5 seconds saved for 100 rupee add on to 200 more than a multiple of 400 rupees
- 22 seconds saved for 100 rupee add on to 300 more than a multiple of 400 rupees