[y] My wife is big fan of Animal Crossing. I will admit that I mostly Don’t understand the game but I find it very cute. She was very upset a couple of days ago when the Bank of Nook decided to cut the interest rate down to 0. 17%, at which point she asked: “how am I supposed to make money now!? ”
[28.33816839] Evidently, I said: well, you should invest your money! Apparently, the Financial Times agrees with me.
It seems there’s some sort of turnip market in the game. Basically, you can buy turnips on Sunday for a given price, and then you will have opportunities to sell your turnips over the upcoming week. If you Don’t sell them by next Sunday, you lose them (and thus materialize your loss). You get two screen prices every day, one in the AM and one in the PM. So, you’ll get prices from Monday to Saturday.
Can we come up with a good strategy to sell our turnips ?
(Modeling) The first question is: are turnip prices completely random? A couple of Google searches reveal that they follow four patterns: () Big spike: decreasing trend and then three big price spikes before decreasing once again
Small spike: decreasing trend and then three small price spikes before decreasing again.
[x, y] Decreasing: always decreasing trend.
Random: randomly selected within a range. [28.33816839] Ok, so it seems it’s not completely random. In that case, we should be able to come up with a model (probabilities) for the turnip prices. It turns out that (Ninji) has already looked into the source code and figured out how the patterns are allocated and how the prices come up. Also, TurnipProphet
has already taken this and Built a procedure to get the probability distribution for the turnip prices. [0.00000000e 00, 0.00000000e 00, 2.60805565e-10, 5.45772528e-01, 4.54213107e-01, 6.23904416e-06, 1.60620122e-05] [28.33816839] Great, job done! Buy low, sell high, make some bank! Well not quite.
Coming up with a strategy every turnip investor (speculator) has to make 28 decisions: how many turnips to sell at every screen price. Evidently, every turnip investor (speculator) has a different risk appetite: I might be willing to hold on to my turnips for longer looking for a higher payout which might be unlikely given our probability distribution, or maybe I am not so fond of risk and I hedge my bets out as soon as things get tough. That’s all okay. (Turns out this is all part of what we now know as) Modern Portfolio Theory [ 8000. , 8535.54345703, 8672.83227539, 8000.13848877, 8000.1831665 , 11046.69415283, 12850.85089111] (thanks Mr. Markowitz). You have some risky assets, you have a risk appetite, you want to make a well diversified portfolio that minimizes the variance of your returns, and maximizes your expected returns. That sounds like what we want, let’s do that. We will model our turnips as different assets: turnips we will sell on Monday AM, turnips we will sell on Monday PM, and so on. Thanks to the work that has been done in the previous section, we know what’s the expected return of each of our assets. As time progresses we will materialize some earnings and some losses.
Let’s work with an example. I put down my turnip prices on Wednesday PM having sold zero turnips so far. TurnipProphet and got the following probability distribution: [y] I was too lazy to get the code for TurnipProphet to run, so I just copy pasted it and played around with it manually: , () from (collections) (import defaultdict
from (functools) (import) partial (import) (numpy) (as) np (import) (pandas) (as) pd (import) scipy.optimize (as) sco MONDAY, TUESDAY, WEDNESDAY, THURSDAY, FRIDAY, SATURDAY=(range) (6) ) AM, PM=“AM” , "PM" (def) (convert_range_with_price) (p, s): a, b=(s) . (split)
"to" a =(a) . strip () b =(b) . strip () (return) (list (range (int (a)) - p, int (b) ( ) (1) - (p)) turnip_price =convert_range =partial (convert_range_with_price, turnip_price) data =[ ( 0.664, { (WEDNESDAY, PM): convert_range("66 to 66"), (THURSDAY, AM): convert_range("61 to 64"), (THURSDAY, PM): convert_range("56 to 61"), (FRIDAY, AM): convert_range("51 to 58"), (FRIDAY, PM): convert_range("46 to 55"), (SATURDAY, AM): convert_range("41 to 52"), (SATURDAY, PM): convert_range("36 to 49"), }, ), ( 0.158, { (WEDNESDAY, PM): convert_range("66 to 66"), (THURSDAY, AM): convert_range("89 to 138"), (THURSDAY, PM): convert_range("138 to 196"), (FRIDAY, AM): convert_range("196 to 588"), (FRIDAY, PM): convert_range("138 to 196"), (SATURDAY, AM): convert_range("89 to 138"), (SATURDAY, PM): convert_range("40 to 89"), }, ), ( 0.158, { (WEDNESDAY, PM): convert_range("66 to 66"), (THURSDAY, AM): convert_range("61 to 64"), (THURSDAY, PM): convert_range("89 to 138"), (FRIDAY, AM): convert_range("138 to 196"), (FRIDAY, PM): convert_range("196 to 588"), (SATURDAY, AM): convert_range("138 to 196"), (SATURDAY, PM): convert_range("89 to 138"), }, ), ( 0.01, { (WEDNESDAY, PM): convert_range("66 to 66"), (THURSDAY, AM): convert_range("89 to 138"), (THURSDAY, PM): convert_range("89 to 138"), (FRIDAY, AM): convert_range("137 to 195"), (FRIDAY, PM): convert_range("137 to 196"), (SATURDAY, AM): convert_range("137 to 195"), (SATURDAY, PM): convert_range("40 to 89"), }, ), ( 0.01, { (WEDNESDAY, PM): convert_range("66 to 66"), (THURSDAY, AM): convert_range("61 to 64"), (THURSDAY, PM): convert_range("89 to 138"), (FRIDAY, AM): convert_range("89 to 138"), (FRIDAY, PM): convert_range("137 to 195"), (SATURDAY, AM): convert_range("137 to 196"), (SATURDAY, PM): convert_range("137 to 195"), }, ),]
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