Gacha Probabilities - June 30 - July 3

The results are in from the June 30 - July 3 Double 5-star Chance Gacha Event! If you participated, thank you for contributing to the survey (created by 小為) to provide the Line Rangers player community with helpful information.

The Results

Our friends at LINE Rangers 台灣社團 have concluded their survey once the event finished and they were able to collect 329 sets of data from participants, a total of 3449 results (raw data is here) from Gacha. Results were:

• 3★%: 1008 (29.23%)
• 4★%: 1001 (29.02%)
• 5★%: 1440 (41.75%)

This 5 star result is very similar to what the previous results were from their mid-June study which were:

• 3★%: 30.56%
• 4★%: 21.55%
• 5★%: 47.89%

The Analysis

Authors 小為 and 楊濟安 of LINE Rangers 台灣社團 posted this new article about their findings with some more information and analysis on the numbers. Contained within this box is their article interpreted in English. 

The results being 3★ 29%, 4★ 29% and 5★ 42%, by lumping the 3★ and 4★ odds together (an average together of 58% of the samples), we can say that the Gacha is only slightly biased towards 3 and 4★.

Now let's move on to some more in-depth useful information. 

1. How many times do you need to play to receive one super ranger? 

  - The authors defined super ranger as one of the ten 5★ rangers that everyone typically wants to get: KSM, Susu, Cherina, Luis, Hitman, Prince James, Dwight, Dumpy, Dancer King Boss (DKB), Hip Hop Brown. There are a total of 24 5★ rangers on the roster now (Ola is no longer obtainable). Let us assume that the odds of each ranger are the same within their star grade. The chance of you receiving one of these shiny 10 rangers is 10/24 * 41.75% = 17.40% during the event. You'll need 100/17.40=5.75 spins of the Gacha on average before you can expect to receive one of the 10 super desirable rangers. 

2. How much do I need to spend on average to get a level 80 Susu?

  - For this question, we're going to have to assume again that the chances to receive each of the 5-star rangers are equal.

   Susu is 1 out of 24 of the available 5★ rangers. Multiply 1/24 by our 41.75% to obtain 5★ and you'll get a 1.74% to receive Susu, which will take approximately 57.5 Gacha spins for 1 Susu. You need 5 Susus to max out so that means you actually need about 287.5 spins.

    Well, 287.5 spins means you have to play the 5+1 48 times (4800 rubies). I don't know how much they charge all the other regions in the world but in US Dollars on the Android Google Play market during the Ruby Event we can get 494 rubies for roughly $49. In order to get 4800 rubies, we'd have to buy almost 10 packs, which costs $491 USD! It's possible that you get unlucky and have to spend more, but there are those who scored Susu on their first few spins. The average is simply for illustrative purposes.

    That said, I sincerely hope that if you were aiming to get Susu, that you did all your Gachas during this past event because if you don't do it during the double chance event, chances are you'll end up spending a great deal more money. But then again, these are averages based on some reality, some assumption, so take it all with a grain of salt.

3. Should I spin with 20 rubies or 100 rubies? 

   - This is a popular question and to answer it, we won't talk about the part that luck plays, we will only discuss probabilities. 
    This question involves the concept of independent events. If we assume that the 6 results from playing 100 rubies are each independent events, this means that one spin of the Gacha has no bearing on the result of the next spin of the Gacha. The authors believe that the 6 results from 100 rubies Gacha are independent events because a lot of people reported getting four 4-stars and one 5-star, or three 5-stars and three 4-stars. This kind of result would not be possible if the game developer had set the 100 rubies Gacha to be dependent events. For instance, if we believe the Gacha is set up to predetermined dependent results, then we should often get results of three 3-stars, two 4-stars and one 5-star, with some variability but not to the extreme of some people getting four or five 4-star rangers in one shot of 100 rubies. So if we assume that both the 100 rubies and the 20 rubies Gacha are independent events then we can use the July results of 41.75% to do some calculations.

For this example, we'll just assume that the chance of you receiving the ranger you want is 1 out of 100 for sake of illustration. 

    - If you used 20 rubies x5, the chance of you getting the ranger is 5%. 

    - If you used 100 rubies, the chance of  you getting the ranger is 6%. 

Based on 41.75% chance to get a 5-star ranger, we have a 17.54% of getting one of the desirable super rangers. 

    - If you use 20 rubies five times to spin 5 times you will average only 0.877 desirable rangers (which is to say playing 5 times can possibly yield you zero desirable rangers). 

    - If you use 100 rubies once to spin 6 times, you will average 1.05 desirable rangers (which is to say you'll get at least 1 desirable ranger on average in the bundle of 6).

    The difference is slight, but it lies in the fact that 100 rubies gives you that one extra spin. Remember the answer we got to question 1 above: you need to spin 5.75 times on average before you can expect to get a desirable ranger. Playing 100 rubies puts you inside the chance to get one since you are spinning 6 times. In this light, playing the 100 rubies game is relatively better. This was deduced based on the information that was collected from the data set. Of course, your personal experience may deviate from this because this is the "average."

4. Should I spin while there is no double chance event?

The short answer is no, of course not. Here's why:

   - Since we have a 41.75% to get a 5★ ranger during the double chance event, then it goes to reason that without the event, our chances are roughly 20.88%. 

Our chances to get a desirable super ranger: 

   - With double chance event is 17.4%, averaging 5.75 spins to get 1 ranger

   - Without double chance event is 8.7%, averaging 11.5 spins to get 1 ranger

This makes it pretty obvious that during the double chance event your odds of getting something good are much higher. The authors recommend, as I also do, please resist the urge to scratch the itch while there is no double chance event going on! For if you do, you're very likely going to spend some time with this guy.

Go away, Pew. We still do not love you.

Concluding Thoughts

I've stated this before and I think it is important to repeat this: The 41.75% number was an average from a vast pool of results. It is possible that you played and rolled on some very different results than the average. And surely you have seen on the internet instances where people have rolled insanely good results. But this is why this is the average. 

The other consideration that often makes players sad after playing Gacha is the fact that your personal set of "desirable" rangers may be a lot smaller than than 17.4%. Maybe all you want are Susu, Hitman and Cherina. In that case, you're rolling on much smaller chance and the chances of you getting something you don't want are much, much higher. 

Astute players will notice that supposing 5 star chance remains the same in the future, as long as LINE continues to release more new rangers, the chances of us getting each ranger will be lessened each time. This is made especially clear when you compare the difference in the odds of Susu (1.74%) and last month's Ola Brown (2.39%) which translated to an average difference of $148. This really does put players who have been playing for a long time in a worsening situation. For instance, myself, I have almost all of the rangers on the roster (not all are masters) and the ones I still need are just a tiny percentage. The chances of me getting what I want keeps diminishing. It's a tough situation, but I can understand that as a game maker, they need to keep pushing out newer, better, shinier products for people to want to buy. For me, the breaking point is near, but for many others, there's still plenty of incentive to buy in. 

Last but not least, a special thanks to 小為 for pooling all this information for us to share.