
Speculating on the Animal Crossing Turnip Market - kho
https://insignificantbits.com/2020/05/02/turnips/
======
madrox
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](https://en.wikipedia.org/wiki/Secretary_problem)
[2]
[https://en.wikipedia.org/wiki/Optimal_stopping](https://en.wikipedia.org/wiki/Optimal_stopping)

~~~
underanalyzer
Afaik the 1/e solution is only optimal when you don't know anything about the
distribution being draw from (but also why it's amazing). Since the author
knows the probability distribution the prices are being draw from you can do
much better with a little dynamic programming.

~~~
dmurray
It's also solving a different problem: it maximises the when probability that
you get the absolute best match, rather than maximising the expected value of
your choice.

~~~
ISL
Furthermore, I suspect it requires that each measurement is independent and
identically-distributed.

If your measurements are correlated (as prices generally are -- if they were
lower than average yesterday, they are more likely to be lower than average
today), the secretary-problem approach will not work.

------
Spivak
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.

~~~
ruytlm
See also the Turnip Exchange[0], which has set up automated queue systems for
people to visit other people's islands to buy and sell turnips, and now
appears to be expanding into other AC:NH trade.

It's been super impressive to watch how quickly the devs there have built out
really useful features, and managed the growth in interest - pretty sure the
Turnip Exchange Discord is >22,000 people.

[0]: [https://turnip.exchange/](https://turnip.exchange/)

~~~
tsukurimashou
considering their patreon currently gives them $11k a month I'd say yes they
have interest.

------
tablethnuser
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.

~~~
dehrmann
As someone who is only vaguely aware of AC, this reads like you're insane.

------
ganonm
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".

~~~
scast
Absolutely. I just focused in finding good weight allocations for the given
risk, but changing the objective function given to the negative of the sharpe
ratio should get you good allocations that maximize the sharpe ratio.

You'll notice I am returning the expected return and variance of the returns.
I didn't talk about it too much (besides a high level risk vs. returns at the
end) because I didn't want to introduce another concept, but you can readily
compare the sharpe ratio using those.

I did a quick analysis (which I had put here but I can't properly format it)
here:
[https://gist.github.com/scast/d7ab3a0f5c5458c11d8624cc73806d...](https://gist.github.com/scast/d7ab3a0f5c5458c11d8624cc73806d40)

------
TrinaryWorksToo
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.

~~~
ganstyles
This doesn't sound fun. :/

~~~
jchw
I think it's amusing that you mention this, because 'time traveling' appears
to be a huge sticking point among fans, with some coming out vigorously
against it, almost violently, and 100% in earnest. I've seen people say things
like "If you time travel in AC, please unfollow me now." and going as far as
writing articles about how time traveling makes you a bad person.

I think it's absolutely fascinating. I'm not by any means a person with
credentials to be doing psychoanalysis, but what it seems like is some people
are hurt by the fact that other people are able to accomplish more and benefit
from it while they are playing 'fair and square' for almost no practical
benefit. It seems like a mix of jealousy and harm to their own feeling of
accomplishment.

Which relates to this comment for this reason: I'd argue _nothing_ in this
game is really _fun_ on its own. It's a busy work simulator. The only real
reward is the end result of having done the work. So I think people derive
_fun_ from this game in ways that are unusual for video games. Cheating here
feels more like "cheating" in real life, to some.

And if you watch different people play this game, you will see that kind of
thing play out. Different people get _entirely_ different things out of Animal
Crossing games.

I'd argue folks who are ending friendships and getting genuinely angry over
time traveling have an unhealthy attachment, but it feels like unhealthy
attachment over fiction and leisure has been on the rise over the past
...decade? or so, and so maybe that's not anything in particular to do with
Animal Crossing (though, maybe it is partially to do with quarantine, right
now.)

~~~
zimpenfish
> other people are able to accomplish more

By cheating, tho'. It's the same as saying people who get rich by dodging
taxes or defrauding people are "accomplishing more" than people who play 'fair
and square'.

(Personally, I don't care if people time travel and island-hop to grind
turnips all day - it affects nothing about my game and my experience.)

> folks who are ending friendships and getting genuinely angry over time
> traveling have an unhealthy attachment

Or they might feel that someone who is ok cheating at a zero-stakes, zero-
effect game might not be a great person after all. It's the difference
between, say, cheating your taxes purely because you want to be rich vs
dodging your taxes because you have to feed your family.

~~~
jchw
> Or they might feel that someone who is ok cheating at a zero-stakes, zero-
> effect game might not be a great person after all. It's the difference
> between, say, cheating your taxes purely because you want to be rich vs
> dodging your taxes because you have to feed your family.

I don’t cheat at Animal Crossing. No real reason not to, I just don’t feel
like it. I am not in a rush or anything. But to me, Animal Crossing is (and I
mean, to be fair, literally is) a computer program and “cheating” is really
just “using in unintended ways” that are not really much different from
modding games (that are not intended to be.)

I can’t tell if you are playing devil’s advocate or not but I view this
argument as being pretty much projection. I think everyone should feel guilt-
free to explore video games and the arts however they enjoy so as long as
nobody is directly being harmed by it. I personally would bet the farm and
some change that there’s no correlation between cheating in Animal Crossing
and “not [being] a great person.”

And I’m not saying this as though I view video games as purely being software
and experience absolutely no emotion. I am pretty much saying that for Animal
Crossing, but there are plenty of games where I felt very immersed and felt
empathy/sympathy for characters the way I would in other realms of fiction and
indeed, real life. I couldn’t do “genocide route” in Undertale, for example.
But, that also does not mean that I engage in this stuff as if it’s real,
because of course, it’s not. It’s fiction. It’s walled off into its own space
where I can explore and experience things in ways that I probably wouldn’t and
maybe would not want to in real life. I certainly do not condone my actions in
Grand Theft Auto as good, but I assure you I am no closer to committing such
offenses in real life.

(Aside: I think the video game violence debates are equally fascinating as a
subject matter, on that note.)

I am also not at all suggesting how you consume this content has no bearing on
reality, but I am certainly saying I believe it’s very non-trivial and fair to
handwave as being too complicated and personal to make pure blanket statements
about.

I went a bit rambley here, sorry. My thoughts on this subject matter are
complicated, although it isn’t really something I hold too personal,
especially because the reality is I play exceedingly few video games anymore.

I don’t really condemn anyone for their opinion on this either, but I do feel
it is a good moment to reflect and broaden the horizons (pun intended)
regarding how people consume and enjoy games. Again, watching people play this
game has been absolutely fascinating, no two people I’ve seen appear to get
the same exact thing out of it!

~~~
zimpenfish
> I can’t tell if you are playing devil’s advocate or not

Not really - I can well believe that someone could/would view another person
who "cheats" (their opinion) at zero stake games to be a less worthy person. I
wouldn't personally condemn someone for "cheating" Animal Crossing - I'd think
they were missing the point of the game per my perspective, mind, and it would
definitely confuse me about their outlook.

Same as if someone cheated at Monopoly or Scrabble whilst playing board games
at home, I guess.

> I think everyone should feel guilt-free to explore video games and the arts
> however they enjoy

In an ideal world, yes. (I do try but having been a ridiculously cynical and
judgemental arsehole for many a year, it is taking some time to adjust.)

> no two people I’ve seen appear to get the same exact thing out of it!

I think that's the beautiful thing about Animal Crossing.

~~~
f00_
Are you against wave-cheating in ssbm?

~~~
zimpenfish
I'm assuming SSBM is Super Smash Brothers Melee (had to look it up)? Never
played it or any variety of Super Smash Brothers for that matter. As such, I'm
not entirely sure I'm qualified to give an opinion ... but that never stopped
anyone on HN.

Assuming you mean "wavedashing" (the only vaguely relevant thing I could
find), and given that
[https://www.ssbwiki.com/Wavedash](https://www.ssbwiki.com/Wavedash) claims it
was explicitly left in as a mechanic during development, no, I'd not consider
that a "cheat".

Would you?

~~~
jchw
If the developer’s opinion is actually what matters most to you, then you may
find it interesting that the developers of Animal Crossing seem to have a
rather tepid view on time traveling. Many have interpreted them as having said
time traveling is not cheating, although I am not sure exactly what that is
concluded from; still, it does seem as though they acknowledge it as valid, if
still unintended, a way to play the game:

>“Adding all the seasonal events by updates wasn’t our way to shun away time
travel by any means,” Kyogoku said. “But Animal Crossing is a game that users
are able to play and enjoy throughout the year.”

Of course though, this worldview is pretty hard to really get behind because
it’s even more arbitrary than usual. Some of the developers may dislike time
travel and others might endorse it.

Moreover, opinions of the developers may even shift. On the topic of
Wavedashing, Sakurai expresses discontent for it:

> While Sakurai noted that wavedashing was widespread in an interview with
> Nintendo Power, he disliked the technique, as he felt it had led to a
> significant degree of separation between beginning and advanced players.

All in all, even trying to be very generous and non-presumptive, I am having
trouble seeing the argument as having a rational basis. It seems like one born
and mostly justified only from emotional response.

~~~
zimpenfish
> the developers of Animal Crossing seem to have a rather tepid view on time
> traveling

That may be but it's not a mechanic that's specifically in the game itself, is
it? Which means you can't (honestly) equate it to wave dashing to make a
point.

> I am having trouble seeing the argument as having a rational basis.

Which argument? The one that time travel in Animal Crossing is "cheating"? In
that case, go nuts, time travel all you want! But at least allow others their
opinion on the topic.

------
zimpenfish
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.

------
voz_
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?

------
bobblywobbles
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.

