Probabilities and Dragons

Probabilities and Dragons

Chasing the Gacha

Rolling on the Gacha is part of the game. It’s the fastest way to get more powerful team. FMA and YYH collabs have both released with really strong singular chase cards, unlike the Dragonbound gacha where most of it is useful.

However, chasing these comes at a monetary cost. Mobile games that utilize Gacha have been required to reveal rates. Puzzle and Dragons has done a good job in revealing exact rates for specific units. I learned a hard personal lesson of the “I’m not that unlucky” thought process. I used about 600 stones (half were free) chasing Ed before finally getting him.

A healthy gaming habit is setting limits for the Gacha. I was okay with reaching for Ed because I hadn’t spent in about a year prior to that. I would rather see more people play for longer, spending within their limits, rather than going broke and rage quitting. That’s not healthy for the community nor yourself. If you feel like you are at risk, or know someone who is at risk, I strongly recommend reaching out to addiction help groups.

I’ve done some charting out for probability drops, based on number of rolls. I also did the reverse of how many rolls needed to hit the probability.

Probabilities and Tables

Rolls Made
End User Probability 3 10 20 40
0.60% 1.789% 5.841% 11.340% 21.394%
1.50% 4.433% 14.027% 26.086% 45.368%
2.50% 7.314% 22.367% 39.731% 63.677%
15.00% 38.588% 80.313% 96.124% 99.850%

Selected some of these numbers based on published rates in the general REM and collab rates. I want to caution people that think that “oh if I drop 40 rolls, it’s a 64% chance I will get Yusuke.” It’s not. It’s a 64% chance you will get a 6* roll from the YYH collab, so you could roll Kurama or Raizen.

Looking at it another way:

Rolls needed 
End User Probability 50.00% 75.00% 95.00%
0.60% 115.1776089 230.3552178 497.7893437
1.50% 45.86236545 91.7247309 198.2138457
2.50% 27.37785123 54.75570247 118.3251044
15.00% 4.265024282 8.530048564 18.43312827

To have a 50/50 shot at diamonds for YYH, you are looking at at least 1 pack and then some. Having somewhat reasonable chances you’re probably closer to the 3 pack range. If you are chasing, it’s going to be about 120 rolls, or about 600 stone for a 5 stone machine. Coincidentally, the same number I used for Ed.

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