Anthony Legros

Gacha collectible card game

An experimentation in drop rates and shop pricing


Economic Designer


Microsoft Excel




During the specialization and research class we got into teams and had to find a common thread with which we could use to make a game or an experiment together. Our team honed in on the subject of gambling, loot boxes and gacha games. For me it was great because I got to experiment with distribution curves, drop rates and store monetization.

At the end we had to do a redaction summarizing our findings and creations.

Pascal’s triangle.

Pascal’s triangle in Excel.

Experimentation with curves:

For this project we needed to learn or explore things related to our specialized domain. And I wanted to experiment with loot tables and drop rate chances with curves.

I was inspired by normal distributions or “bell curves” obtained by Pascal’s triangle as a beginning point.


I took only values of the downward slopes to give me the numbers in blue for the following reward structure: Common -> Uncommon -> Rare -> Epic -> Legendary -> Ultra rare.

I then also created variations of those curves in yellow, and completely unrelated new curves in purple.

The result:

I compared all the functions for 10, 25, 50 and 100 boxes being opened. I found that for a collectible card game Pascal's triangle slope is way too steep, and the numbers in purple more appropriate, especially for the relatively small scope of our project. Drop rates of less then 1% are really difficult to overcome, and were a bit too rare.

Shop prices

I also made the expected values of different price points for the real money currency for the game. Expected value is used in bulk grocery shoping but also digital currency like Fortnite’s V Bucks, or Roblox’s Robux


Here is the complete 100 page PDF we made together:



Concept artist:



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