Pull them all ! : Examining basic probability in Gacha games

DISCLAIMER: I am not sponsored by any of the games listed in this article.

Unsurprisingly, microtransactions and add-ons have been popular in mobile games for over a decade. Whether you are a Whale or a F2P (free-to-play), you have played a Gacha mobile game.

What are Gacha games?

The first history of gacha games in the gaming market dates back to the 2010s. Ever since then, the trend has no signs of stopping. Gacha is when players can pull or spend in-game currency for items.

The most popular appeal of gacha games is getting special playable characters to use in the game. People have spent thousands of dollars on gacha games to collect every character, weapon, and collectible. They are called whales; a person who spends a ton of money in-game purchases. The term whales originated in MMO gaming and has remained a controversial topic. On the opposite spectrum, some free-to-play players don't spend money on in-game purchases.

Examining probability

This article is going to cover basic probability in various gacha games on games.

Here are the Gacha games I currently play.

  • Honkai: Star Rail
  • Tears of Themis
  • Obey Me (OG version in this article, not NB)

To start with a disclaimer, this is only for F2P players. I did not pull on every banner and spent months and weeks saving in-game currency without spending money on microtransactions. I will cover Honkai Star rail since it's the easiest to calculate probability in their gacha mechanic.

Here are some basic terms:

  • Pulls: Draws an amount. The player can receive based on what is available. Most Gacha games will have two options. 1 - pulls a single time or 10 pulls which has 10 draws each time. The most popular choice for players is the 10-draw option.
  • Pity: The minimum amount you need to pull on before a player has a chance to gain a rare item or special character related to that banner. There's soft pity, hard pity, and 50/50. Pity is reset after a player draws the limit. Each gacha game has a different pity system and pity is separate for each banner.

Pull Breakdown

Honkai Star Rail

For Honkai Star Rail, I did not pull on Ruan Mei or Argenti banners since I planned to pull for Dr.Ratio.

Overview of Dr.Ratio banner

Featured characters on the banner have a drop rate boost.

5 Star - Featured: Dr Ratio. 50% chance out of all 5-star characters

4 Star - Featured: Sushang, Natasha, and Hook. 50% chance out of 4-star characters

Note: I pull 10, meaning 10 draws per pull. Every 10 warps guarantees a 4-star character or 5-star character. Dr. Ratio is a free 5-star given to players. Pulling on his banner can increase his Eidolon level.

I had a total of 10 pulls which means I had 100 draws.

Warp 5 -Star 4-Star 4-Star Light Cone 3-Star Light Cone
1 0 1 Sushang 0 9
2 0 0 1 9
3 0 1 Natasha 0 9
4 0 0 1 9
5 0 1 Natasha 0 9
6 0 1 Hook 1 8
7 1 Dr.Ratio 1 Hook 0 8
8 0 0 1 9
9 0 1 Sushang 1 8
10 0 1 Sushang 0 9

I managed to pull Dr.Ration on my 7th warp, meaning I did not lose the 50/50 pull since I obtained him. In 70% of my pulls, I managed to pull at least one of the featured 4- Stars. In each pull, it was between 80% and 90% of receiving light cones. Now if you are unlucky, there is a chance to lose the 50/50 and not even get the featured 5-Star on the banner.

Other games

Some games offer a free pull after a certain period. However, this is often for a single pull. The drop rates vary from each game. Tears of Themis has limited-run events where you can obtain items. Obey Me has ranking awards based on the amount of points you earned during an event. The higher the ranking, the better rewards a player can obtain.

In conclusion, I decided to examine the basic probability in gacha games. Gacha gaming has earned over a billion dollars - that's a lot of money. It is common for more studios to make gacha games their main source of generating revenue.

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Jamie Larson