---
title: 'The Year 11779 Oshi Mark Problem'
description: 'When will we run out of 2-emoji oshi marks?'
pubDate: 'Oct 24 2024'
heroImage: 'https://files.catbox.moe/8gr7k2.jpg'
---
import Latex from '../../components/Latex.astro';

(This is a problem that lives rent-free in my head)

The oshi mark is are emoji(s) that VTuber fans will often put in their social media usernames to represent their support for a particular VTuber. These are typically chosen during or before a VTuber's debut stream, you'll often see many VTubers changing their usernames to include them too!

Seems like a good idea, until you realize that there is a finite number of emojis...

## Definition
As of writing this there are 3790 emojis in the Unicode standard. I know that platforms like X have may have their own standards (Twemoji), but for the sake of this problem let's assume that we're using the Unicode standard.

This also includes skin-tones, which may or may not be appropriate to use in this context as well. However, this is just all theory anyways so let's include them and take this as a best-case scenario.

## Problem
Ideally, VTubers all want a unique oshi mark to represent them. Of course,  in the early days of VTubing a single emoji would be enough to represent a VTuber. However, as the industry grows and more VTubers debut, the chances of a VTuber getting a unique oshi mark decreases...

So the fix is intuitive, let's just use 2 emojis for each new VTuber. This is fine, in fact its the solution we're on right now, but how long until we run out of 2-emoji oshi marks?


<Latex formula="\binom{3790}{2} = \frac{3790 \times 3789}{2} = 7,171,755" />
We then assume that all 1-emoji oshi marks are taken, so add that to the total number of 2-emoji oshi marks and we end up with 7,175,545 VTubers.

### Predicting Growth
We can predict VTuber growth in a fairly crude manner using Holodex. I wrote a Java wrapper for the Holodex API a while back, so I was easily able to spin something up quick.
```java
import com.pinapelz.Holodex;
import com.pinapelz.HolodexException;
import com.pinapelz.datatypes.Video;
import com.pinapelz.query.VideoQueryBuilder;

import java.time.LocalDate;
import java.time.format.DateTimeFormatter;
import java.util.HashMap;
import java.util.List;
import java.util.Map;

public class App {
    public static void main(String[] args) {
        try {
            Holodex holodex = new Holodex("API_KEY");
            VideoQueryBuilder query = new VideoQueryBuilder().setTopic("Debut_Stream").setLimit(100);
            List<Video> videos = holodex.getVideos(query);

            Map<LocalDate, Integer> dateCountMap = new HashMap<>();
            for (Video video : videos) {
                System.out.println(video.title);
                LocalDate date;
                try {
                    date = LocalDate.parse(video.published_at, DateTimeFormatter.ISO_OFFSET_DATE_TIME);
                } catch (NullPointerException e) {
                    continue;
                }
                dateCountMap.put(date, dateCountMap.getOrDefault(date, 0) + 1);
            }

            double average = dateCountMap.values().stream().mapToInt(Integer::intValue).average().orElse(0.0);
            System.out.println("Average number of debut streams per day: " + average);

        } catch (HolodexException ex) {
            throw new RuntimeException(ex);
        }
    }
}
```

The above code takes the first 100 streams that are tagged as a "Debut_Stream" and then finds the average number of debut streams per day.

Running the code outputs:
```
Average number of debut streams per day: 1.9565217391304348
```

Let's just call it at 2 new debut streams per day roughly. This means that we can expect 730 new VTubers per year.

There are some numbers online that suggest that there are around [https://blog.gamesight.io/vtuber/](49 500 VTubers as of June 2023), so let's
estimate that there are probably around 52 000 VTubers by the end of 2024.

So that means 7,125,545 unique 2-emoji oshi marks remain assuming all VTubers have an oshi mark:

Using the growth rate previously calculated: This means that in 9754 years, 4 months, and 2 days we will run out of 2-emoji oshi marks... (oh no!)

### Conclusion
On February 26th, 11779 we will run out of 2-emoji oshi marks, and will need to start using 3-emojis instead. So sleep well at night knowing that we have a long time before we run out of 2-emoji oshi marks.