TÍNH XÁC SUẤT THỐNG KÊ TỈ LỆ RA SSR CHARACTER Ở MỖI BANNER GAME CAPTAIN TSUBASA
Lâu lâu lại có đợt Klab ra cùng lúc nhiều banner, mà có vẻ banner nào cũng có hàng ngon. Với người chơi, nếu ta có 200ball thì quay banner nào tỉ lệ ra hàng cao hơn? Đây là câu hỏi thường trực nhất với mọi người chơi, và mình làm post này để mọi người có thêm cơ sở quyết định. Nếu ai đã đọc post giải thích về RNG&Gacha ở đây, thì sẽ hiểu rằng trong game gacha, người chơi chúng ta thường sẽ nắm phần thua, sẽ nhiều lần phải đổ máu mà không nhận được kết quả gì. Một khi cái pool mà klab khởi tạo rất lớn, thì dù số ball của bạn có lớn đến bao nhiêu, cũng như muối đổ bể.
Tuy nhiên, chúng ta hãy thử áp dụng toán thống kê vào đây, thử tính xem xác suất ra hàng ở banner nào sẽ nhiều hơn, là cơ sở để xuống ball cho banner đó.
*Công thức đơn giản như sau:
-Công thức 1: p_total = 1 – (1 – p)^n
hoặc
-Công thức 2: p_total = 1 – (1 – p_1)^n * (1 – p_2) * (1 – p_3) * (1 – p_4).
trong đó:
Công thức 1: áp dụng cho các banner thông thường (VD: banner DC, banner Dream fest)
Công thức 2: áp dụng cho các banner step-up (VD: banner WC, banner MisugiT hidden)
p_total : là tổng tỉ lệ tích luỹ ra cầu thủ đang tính
p: tỉ lệ công bố của klab với cầu thủ cụ thể
n: số lần single-pull (quay 5 ball hoặc 1paid ball)
p_1: tỉ lệ ra hàng ở các step thường
p_2, p_3, p_4: tỉ lệ ra cầu thủ ở các step-up guaranteed
*Các công thức trên được thành lập là bởi:
-Tất cả chúng ta đều mong muốn ra tối thiểu 1 cầu thủ xịn nhất (hàng mới nhất) trong kì banner
-Tuy nhiên, rất khó để có thể tính được tỉ lệ khi nào ra 1 cầu thủ xịn, 2 lần của nó hay 3 lần của nó (ra đúp).
-Nên, tốt nhất là tính ra tỉ lệ “không ra hàng”, rồi lấy tổng 100% trừ đi, sẽ ra còn lại là “tổng tỉ lệ tích luỹ ra tối thiểu một cầu thủ đó”.
-Chú ý: tỉ lệ này đúng cho cả single-pull và multiple-pull, sở dĩ sử dụng đơn vị là single-pull để dễ quy đổi và nhất quán giữa các banner khác nhau, cũng như có thể tính toán với số ball lẻ (VD 50 ball hay 55 ball, đều là 1 lần multiple-pull, nhưng sẽ là 10 và 11 single-pull).
VD minh hoạ:
Tổng tỉ lệ tích luỹ ra MisugiT Hidden ở banner 3 step (tức 3 lần multiple pull đầu tiên):
Trong đó:
step1: 0,5%
step2: 0.5%
step3 (guaranteed): 16.665%
=>p_misugi = 1 – (1 – 0.005)^29 * (1 – 0.16665) = 20.33%
Công thức trên chỉ đang áp dụng với 3 step, chứ ko thêm từ step thứ 4 trở đi.
Tổng tỉ lệ tích luỹ ra SalinasA ở banner 6 step (tức 6 lần multiple pull đầu tiên):
Step 1: 0.25%
Step 2: 0.25%
Step 3 (guaranteed): 2.778%
Step 4 (guaranteed): 5.555%
Step 5: 0.25%
Step 6 (guaranteed): 16.667%
6 step có tổng cộng 60 lần single-pull, nhưng có 3 step (3,4,6) là guaranteed, vì vậy sẽ chỉ có 57 single-pull là theo tỉ lệ 0.25% mà thôi.
=>p_salinas= 1 – (1 – 0.0025)^57 * (1 – 0.02778)*(1-0.05555)*(1-0.1667) = 33.65%
OK, bây giờ nếu trong túi chỉ có 200 ball, và muốn quay banner DC, thì tổng tỉ lệ tích luỹ ra Ishi DC là bao nhiêu?
Số lần Single-pull = số ball/5 = 200/5 = 40 lần
Tổng tỉ lệ tích luỹ ra Ishi DC (giả sử 0,42% như các banner DC khác) trong 40 single-pull (tức 4 lần multiple pull): p_Ishi = 1 – (1 – 0.0042)^40 = 15.49%
Nếu số ball lên 500 ball ~ 100 single-pull, tỉ lệ sẽ lên
p_Ishi = 1 – (1 – 0.0042)^100 = 34.35%
Mình làm một bảng thống kê tỉ lệ ra Ishi DC tương ứng với số ball có thể:
*Nhìn vào đây anh em sẽ nghĩ đến việc: nếu tôi có 10.000 ball thì gần như chắc chắn có được con Ishi DC đúng không? Câu trả lời là gần như thế, chứ ko chắc chắn. Số đen đủi thì sẽ rơi vào 0.02% còn lại kia. Vẫn chưa hiểu tại sao lại có thể đen như vậy thì mời đọc lại bài học cơ bản về RNG&Gacha ở đây!
*Nếu anh em nào không tiện dùng máy tính hoặc excell, thì có thể sử dụng công cụ online sau đây: https://stattrek.com/online-calculator/binomial.aspx
Công cụ này áp dụng được cho các banner thông thường (ko steps up), như banner DC, Dream fest,… Cách nhập liệu là:
Bài viết của mình tham khảo từ bài gốc này trên reddit, anh em có thể đọc để hiểu hơn:
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