Speculating on the Animal Crossing Turnip Market

I was surprised that there was no mention of the secretary problem [1]. Optimal stopping has a whole host of problems and means of evaluating them [2]. I'm curious how this solution compares to just using the 1/e rule.

Generally, the 1/e rule in this situation implies you should evaluate prices until Wednesday afternoon for the max sell price up to that point, and then sell the next time you see a price higher than that max (or Saturday afternoon whichever comes first). You won't always get the best price this way, but you'll perform better than any other know strategy. This strategy works with friends, too, as you can account for their prices in this strategy.

The only reason this may not be the best strategy here is that there are ways of having some information about future prices.

[1] https://en.wikipedia.org/wiki/Secretary_problem [2] https://en.wikipedia.org/wiki/Optimal_stopping

One detail I didn’t see that affects the risk profile is that every island in AC is their own market and you can buy and sell turnips on other people’s islands.

You can afford to be far more risky than the model suggests if you have a few friends or an active Discord group because on any given day you can almost surely find an island with a profitable price if you need it in a pinch.

Nintendo was late to dip their toes into f2p game economies and it shows with the poorly balanced bell economy in (farmville-like) Animal Crossing.

Turnips are a terrible way to make bells in the single-player game. You have to buy a stack of them for around 10,000 bells and then wait all week for the market to pop. Let's say you see it pop to 130-160, which is a fairly common range in my experience. For all the hassle of buying and storing turnips (AC's inventory management is high effort and turnips have additional restrictions) you might net 6,000 bells per inventory space. Thing is, Animal Crossing regularly generates bugs and insects which sell for 2,000-8,000 bells. They are also one inventory space, and they are available all the time with no expiration or holding strategy needed. There are also abundant resources like iron ore, where a crafted stack of 30 ore in one inventory space will net you 22,500 bells in profit. Turnips are low value per inventory slot.

To get around this, players coordinated online. Sometimes turnips hit a jackpot price in the 300-600 bell range. So that stack is suddenly worth 60,000 and now we see inventory efficiency worth playing with turnips. All you have to do is join an online group and someone will be having a jackpot day every day. You do have to share profits with the host but the scheme is still worth it.

This is a big economy mistake. 60,000 bells is quite a lot of money in AC, and a backpack full of turnips turns into 2,400,000 bells which is enough money to bypass most of the game. Avg item price is magnitude 3-4 so these are effectively free now. All from doing a single turnip scheme. Of course players will do this with multiple backpack loads and become deep millionaires living off bank account interest.

Nintendo's second mistake was to fix this exploit by attacking a symptom and not the root cause. They reduced interest rates by a magnitude, making it balanced for ppl with huge savings accounts and worthless for anyone playing the game as intended. We of course see the folly in this approach in OPs blog where his wife was punished for playing the game as intended. She is now incentivized to join the turnip schemers, making the problem worse.

Nintendo should either cap the amount of turnips you can sell on a friend's island, reduce the turnip value for island visitors, or disallow visitors selling turnips altogether. Then the bank accounts can remain as is.

Anyone with experience tuning f2p economies would have seen this leak a mile away and prevented it from ever happening. Now Nintendo only has bad options since removing player assets is never an option. Once you leaked you leaked.

Musings from a former f2p economy designer.

The Sharpe ratio should be mentioned here. It allows an apple to apples comparison between the performance of different assets in terms of expected return against variance (risk). In an efficiently priced market, assets will be priced to lie on a straight line of unit return vs unit risk. The line itself passes through the y-axis (zero risk) at a point called the 'risk free rate'. This is a hypothetical point but a close proxy in the real world is e.g. US treasury bills. In the game, I assume the bank always pays interest on deposits so it _is_ the risk free rate (0.05%).

Plotting the different strategies, then fitting a straight line (passing through the risk free point) would allow us to say "strategies falling above the line have market beating Sharpe ratios and strategies falling below are underperforming".

I found an island selling for 500 bells and time travelled to sunday and went back and forth selling turnips until I got bored. Netted 15,000,000 bells that way.

I tried one of the Stalk Market Predictors based on Ninji's decompiled algorithm and it was awful. Didn't get a single day right as we went through the week. Suggested a high of 500-600 on Friday, highest all week was 163.

Which isn't down to the code, I should add, but more that they don't (yet?) know how many times the random generator can be spun outside of the turnip price price setting which obviously makes their predictions very finger in the wind.

Neat little writeup. I'd love to play with the algo and data. OP, if you see this, care to publish a notebook / code on Github?

Well written article. If I was better versed in math I might be able to pose questions on the article, but it is a straightforward explanation.