The Statistics of Villager Hunting

Also known as: how the hell did I get so lucky that one time?

For those of you who are subscribed to my YouTube channel, you should know that on my very first villager hunt, I found one of my dreamies, Eugene, in three tickets.

Here's the episode in case you missed it. Sorry for spoiling it.

I've been on two other villager hunts, neither one turning out so well. On the third, I came up empty after 45 tickets, and on the second, I found Anicotti (shudder). I don't think I can figure out just how I got so lucky other than sheer chance, but I can figure out just how lucky I got.

The villager you find on a specific island is decided randomly, but each one isn't an equal 1 in 391 chance. First, the game picks one of the 35 species in the game. Second, it picks a villager from that species. That means your chance of finding a specific villager are 1 in 35 times the number of villagers in that species. Before my November villager hunt, I actually calculated my chances of finding one of my dreamies in the 30 tickets I had. Today, I will redo them for you since I left the notebook I did them in at home.

My four dreamies at the time were Raymond, Eugene, Ribbot, and Sprocket. (My list has definitely changed since then as villagers have gained and lost my favor and, more importantly, stopped being dreamies and started being realities.) I started by calculating the chances of finding each villager individually:

Raymond is a cat. That means the chances of finding him are 1 in 35*22 (23 cats minus Kabuki, whom I already have)=1 in 770 or 0.13%.

Eugene is a koala. That means I had a 1 in 35*9 koalas chance of finding him. That's 1 in 315 or 0.32%.

Ribbot is a frog. That means I have a 1 in 35*18 frogs chance of finding him. That's 1 in 630 or 0.16%.

Sprocket is an ostrich. That means I have a 1 in 35*10 ostriches chance of finding him. That's 1 in 350 or 0.29%.

I also included the percentages for the specific villagers because I want to add them together. I call this the Dreamie Constant, the chance of finding any of my dreamies in a single ticket. That number is 0.9% or about 1 in 111.

Of course, with 30 tickets, which is what I had, that number increases to 21 percent. This is where real-life math comes in. In my stats class last semester, we learned about binomial distributions where the only two possibilities are success and failure. In this case, success is defined by finding a dreamie, and the chance of success is 0.009. This is done by multiplying the Dreamie Constant by the chances of not finding a dreamie to the power of the number of tickets spent previously for each ticket and adding all those numbers together. I have R open on my computer right now to do all that for me.

The command I gave R is dbinom(1,30,0.009), meaning I'm asking for the chance of having exactly one success (dreamie) in 30 trials (tickets), and that number is 0.207.

Now for the chances of finding Eugene in 30 tickets just as a stepping stone between finding any dreamie in 30 tickets and that mind-blowing three-ticket villager hunt. The command is now dbinom(1,30,0.00317). That number is 0.087, or 8.7 percent.

Last but not least, the question we've all been asking, what sort of odds did I have to beat to find Eugene in three tickets or fewer. The R command becomes dbinom(1,3,0.00317). The answer is 0.00945.

I had a 0.9% chance of finding Eugene in three tickets. That's close to the same as finding any dreamie in one ticket, but considering that Eugene is one cool cat (er, koala), I'd say I like those odds. Of course, if you look at my calculations at the top, you'll notice that Eugene is the dreamie I had the highest chance of finding, but I'll still take him. I also left out calculations for the chance of finding more than one dreamie, but when will I ever pass up the first one?

Last, for the record, my dreamie list is currently Raymond, Del, Bangle, and Carmen. My secondaries are Sherb, Mira, Ribbot, Sprocket, Coco, Hopkins, and Stitches, and my Jacksons are Zell, Tammy, and Bubbles.