Addendum and Dunkin Donuts and Life

 I need to add a few things to yesterday's post that are obviously missing. It's been bothering me all day please just bear with me.

First, I never even calculated the expected value of the random binomial method. That can be defined as: 

    np = 100 * (0.3) = 30 * 60k Bell Profit = 1,800,000 Bells

 Just from that, its clear this method isn't expected to profit as much as our linear method.  

 Second, one simulation?? I have let you, the reader, down. Let's see 1,000 simulations. 

 

  

 Mmmm a nice sweet normal(ish) curve. The mean of our simulations was a little greater than the expected value, coming in at 1,811,8200 Bells. Still worse than burying 10k Bells, the conclusion stands!

 

Ok thank you for bearing with me, it was really bothering me that I left those out. 

 

I got dunkin donuts again this morning. I really think it's the best commuter coffee you can get. It's just the perfect level of tolerable to wake me up on the train and not good enough to make me feel like I'm wasting a good cup of coffee on a boring work commute.  

  

I've been listening to To Love Somebody by Holly Humberstone on repeat. I can't wait for her new album, I'm sure I'll be normal about it. 

Optimizing New Horizons Money Trees

The money trees in Animal Crossing New Horizons are a great way to continuously gain bells with pretty much no effort. Just bury 10K Bells in the glowing spot each day and reap 30k Bells from the spot when the tree fully grows in 3 days. 

But according to the Animal Crossing Wiki, there's actually a 30% chance that, upon burying more than 10K Bells, your money will be tripled when the tree eventually grows. 

Nookpedia.com chart of money tree return rates in acnh

 So would the optimal method for planting money trees actually be to plant 30k each day? You wouldn't make a profit every time a tree grows, but when you do make a profit it would be 40k Bells greater. I wanted to quickly explore this thought. 

The Methods

Let's quickly define our 2 methods of Bell yield mathematically. 

 

Guaranteed (Linear) Yield Method

 This is a linear function where, each day a tree grows, the player is able to gain 20k Bells. 

   y = 20x 

(we can multiply the result by 1000, I do not want to keep typing out that many zeros.)

 

Random (30k) method

This is a cumulative binomial function!  The player plants 30k Bells each day and has a 30% chance to profit 60K Bells or a 70% chance to make nothing (never losing any Bells). 

 

To clarify, 30k bells is the minimum number of bells that can be returned if a player plants 10k or more bells (see chart above). If a player buried more than 30k bells each day they would incur losses each day they did not succeed in getting the 3x return on buried bells.

 

For this experiment let's initially look at a window of 100 days. We can define our function then as

    X ~ Bin(100, 0.3)
 

Outcomes!  

I threw a simple simulation together in R and plotted the cumulative profits of both methods over the 100 days in our experiment. 

 

...and yeah it doesn't look great for the random method. 

bell yield over 100 simulated days

After simulating 100 days of both discussed methods, the first linear method ends squarely at 2,000,000 bells. The Random Method reaches 100 days with 1,560,000 bells. 440,000 Bells short! 

 

With this simulation it's pretty easy to recommend burying 10k Bells each day and not worrying about anything else. 

 

Finally I will leave you with a simulation of 15k, 20k, and 25k bells compared to the linear method just to see how much worse they are than even the 30k method.

 

all much worse! yikes!

 

I Like Recipe Stories

 I like it when I find a recipe online and there's a story at the beginning of it. There I said it. Cooking is a social task! Learning about the recipes that bring people comfort in bad times or remind someone of an exciting moment in their life feels really special, even intimate. For that reason I find it really beautiful when I find a recipe online with a cute story at the start. 

It's one of the reasons I love getting the Cook's Illustrated magazine. There's always a spread with a nice recipe and the author's experiences with the recipe! Here's a page from the most recent issue with a crab rangoon recipe. 

Along with a straightforward recipe, there's a whole article on the history of the dish and the author's personal connection with it. I love it! Cooking is a social activity and it feels so cold and wrong to simply pull a recipe online. It's lovely to hear why the author liked it, or their experiences in cooking it.

That isn't to say its always good. Many times the sections preceding a recipe are SEO slop, with headers like "easy [recipe name]" immediately followed by a header like "[recipe name] for dinner" with essentially the same information under it. I'm not a fan of those, it makes the recipe feel robotic and alien. It's the same with AI generated recipes, but respectfully if you are asking a chatbot for a recipe it may be too late for you.

Completely aside I was looking at my camera roll for photos of food and I realized I have a truly insane number of photos of dunkin cups.

  

dunking donuts 

It's snowing a little today, I watched the Smosh reddit stories and traveled far away to get my cat a very specific flavor of food because she will not eat anything else. I love her. Thank you for reading, I think this is a week of blog posts. Wherever you are reading from I hope you are having a lovely day!