Is there an upper limit of how much money you can throw in a gold hole?

Question

Sometimes you can dig up gold, and then put back an amount in that hole. Then, a couple days later, you get back 3 times the amount.

I've been putting 99,000 bells in these holes, but my SO is telling me that after an amount, you will not get the full amount you put in times 3. And I'm pretty sure I've been doing the 99000 bells for more than 3 days, but I never shaked a tree

Is that true? Is there an upper limit to the number of bells you can put in a gold hole and after that you will not be getting 3 times the amount?

Answer 1

Yes and no. When you plant 10,000 bells, you will always receive 3 bell bags with the amount you planted. Above 10,000 bells, you may receive either 3 bell bags containing the amount you buried, or 3 bell bags containing 10,000 bells.

Supposing there is a p_full chance for a full payout, the expected profit for any amount b planted above 10,000 bells is:

(1 - p_full) * (30k - b) + (p_full) * (b * 2)

According to some data mining, there is a 30% chance for a full payout, so if you consistently plant 99,000 bells, you have an expected profit of 11,100, vs the guaranteed profit planting 10,000 bells of 20,000.

The expected profit function can be reduced to 21,000 - 0.1 * b, a linear function with negative slope. 10,000 bells is the optimal amount to plant.