Gacha Probabilities - June 2014

The results are in from the June 19 - June 21 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 349 sets of data from participants, a total of 5782 results (raw data is here) from Gacha. Results were:

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

This 5 star result is over twice what the previous results were from their May study which were:

• 3★%: 49.22%
• 4★%: 30.17%
• 5★%: 20.60%

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. Note: The numbers on the article were as of late hours of June 19 when the data up to that point was reflecting an average of 43.85%.

If you played the 5+1 Gacha with 47.89% odds of receiving a 5-star ranger, this translated to about 2.88 5★ rangers out of 6 balls for every 100 rubies played. They went on to answer some really good questions based on the 43.85% result that they got at the time of the writing of their post. Wherever possible I'll use their math and adapt it with the end-result number of 47.89%.

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

  - They defined super ranger as one of the eight 5-star rangers that everyone typically wants to get: KSM, Dancer King Boss (DKB), Sorcerer Cony (SoCo), Bernard, Hip Hop Brown, Dumpy, Dwight, Ola Brown. There are a total of 20 5-star rangers on the roster so the chances of you receiving one of these shiny 8 rangers is actually 19.16% during the event. 100/19.16=5.22 spins of the Gacha on average before you can expect to receive one of the 8 super desirable rangers. 

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

  - For this question, we're going to have to assume that the chances to receive each of the 5-star rangers are equal (side note from Panic: we know this to be untrue because Line Game Support has directly told me that the odds for each of the rangers is preset, and they have said that "rarer" rangers have a lesser chance. I understood this means in reality some rangers are really preset to be less likely to pop out). 

   So, anyway, Ola Brown is 1 out of 20 of the available 5★ rangers. Multiply this by our 47.89% and you'll get a 2.39% to receive Ola Brown, which will take approximately 42 Gacha spins for 1 Ola Brown. You need 5 Ola Browns to max out so that means you actually need about 210 spins.

    Well, 210 spins means you have to play the 5+1 35 times (3500 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 3500 rubies, we'd have to buy just over 7 packs, which costs $343 USD! Unfortunately, it sounds about right... And if you happen to be unlucky, you'll spend more. 

    That said, I sincerely hope that if you were aiming to get Ola Brown 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 question involves a concept that we've touched on before when I shared the May event's results on this blog, which is whether or not the 6 results you get from spending 100 rubies are 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 we assume they are independent events and we can use the June results of 47.89% 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 47.89% chance to get a 5-star ranger, we have a 19.16% of getting one of the desirable super rangers. 

    - If you use 20 rubies five times to spin 5 times you will average only 0.958 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 1.14 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 5.22 times on average before you can expect to get a desirable super 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 47.89% to get a 5★ ranger during the double chance event, then it goes to reason that without the event, our chances are roughly 23.95%. 

Our chances to get a desirable super ranger: 

   - With double chance event is 19.16%, averaging 5.22 spins to get 1 ranger

   - Without double chance event is 9.58%, averaging 10.44 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 do not love you.

Concluding Thoughts

I've stated this before and I think it is important to repeat this: The 47.89% 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 19.16%. Maybe all you want are Ola Brown, KSM and Dwight. 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. 

Now, the last thing that is bothering me is the fact that this event's results differed greatly from last month's. June's double chance event was seriously more than twice more lucrative (and from my personal experience, I tend to agree with the results). Such a large difference cannot be a mistake on the survey because they had over 5700 samples. May's results were done with over 2000 samples, which should still be quite accurate. So I don't think the numbers are wrong. I think this was a deliberate change in the presets by the game developers. With the release of Team Battle Mode and Endless Mode, I believe they really want people to participate and they want people to feel competitive. Nobody likes losing over and over and that can make a PvP battle fizzle out very quickly. I'm guessing that's why they've more than doubled the odds to get 5 star rangers, so people will be more likely to jump into the new modes.

So in the end, I do apologize that I did not get this post out sooner because perhaps it would have swayed some players to take more advantage of the event while it was still possible to get the best odds at Ola Brown. However, now that the "new" non-event probability for 5-star rangers is roughly 23.95%, I wonder if it will stay that way until some other significant event happens (like new area release or new ranger release). Did they increase the non-event chance from 10% to 23.95% when the "major update" came out on June 19? Nobody knows for sure when the change in the odds was made. LINE has no obligation to tell us. We can only try to figure it out with our collective effort. Hopefully this provided some deeper understanding of the gamble that is Gacha. Special thanks to 小為 for pooling all this information for us to share.