This calculator helps you determine the probability of obtaining a desired potential line on your equipment, or calculate the estimated number of cubes needed to reach a target success rate. Enter any two values (Rate, Rolls, or Target Probability) to solve for the third.
Maplestory Cube Calculator
Detailed Calculation Steps
Maplestory Cube Probability Formula:
The calculation is based on the Binomial Probability Model for independent trials. To find the probability of getting the desired potential line (at least once) after N cubes, we use the inverse of the probability of *not* getting the line on any of the N rolls:
$$P_{\text{success}} = 1 – (1 – R)^N$$Where:
- $P_{\text{success}}$ is the Desired Success Probability (as a decimal, e.g., 0.90)
- $R$ is the Single Roll Rate (as a decimal, e.g., 0.005)
- $N$ is the Number of Cubes/Rolls
Formula Source: Maplestory Potential System | Official Cube Rates Disclosure
Variables Explained:
- Target Line Success Rate (R): The probability (as a percentage) of any single cube roll resulting in the exact potential line you want (e.g., 30% Boss Damage, 12% STAT). This rate is typically published by Nexon.
- Number of Cubes/Rolls (N): The total count of cubes you plan to use or have used, representing the number of independent trials.
- Desired Success Probability (P): The overall probability (as a percentage) that you will succeed in getting the target line *at least once* within the specified number of rolls.
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What is Maplestory Cubing?
Cubing refers to the process of using consumable items called “Cubes” (such as Red Cubes, Black Cubes, or Master Cubes) on equipped items to re-roll their Potential stats. Potential grants powerful bonuses like increased ATT, STAT%, Boss Damage, or Critical Rate. This system is crucial for achieving end-game power.
The process is fundamentally based on chance, as the outcome of each cube is determined by a vast set of probabilities. Understanding these rates is vital for budgeting real-life money or in-game Mesos, and this calculator helps turn those opaque probabilities into actionable estimates of expected investment.
How to Calculate Maplestory Cube Probability (Example):
Let’s find the number of cubes needed to have an 85% chance of getting a 0.7% line:
- Identify Known Variables: The Target Line Success Rate ($R$) is $0.7\%$ (or $0.007$ in decimal). The Desired Success Probability ($P$) is $85\%$ (or $0.85$ in decimal).
- Determine the Inverse: The probability of *failure* (not getting the line) is $1 – 0.85 = 0.15$. The probability of *failing* on a single roll is $1 – 0.007 = 0.993$.
- Apply the Formula (Solving for N): We use the rearranged logarithmic formula: $N = \frac{\log(1 – P)}{\log(1 – R)}$.
- Calculate: $N = \frac{\log(1 – 0.85)}{\log(1 – 0.007)} = \frac{\log(0.15)}{\log(0.993)}$.
- Result: $N \approx \frac{-0.8239}{-0.003046} \approx 270.5$ Cubes. You would need approximately 271 cubes to achieve an 85% chance of success.
Frequently Asked Questions (FAQ):
A: The probability of getting a specific line exactly once after N rolls is a more complex calculation. This calculator focuses on the practical question: “What is the chance I achieve my goal line if I roll N times?” which is the chance of achieving it *one or more* times.
A: Yes, if you use the published tier-up success rate as the “Target Line Success Rate (R)” and solve for the “Number of Cubes/Rolls (N)” needed to hit a high “Desired Success Probability (P)”.
A: Most players aim for a 90% to 99% success probability when calculating cube quantities, as this significantly mitigates the risk of unlucky streaks (colloquially known as “dry spells”).
A: EPS (Epsilon) is a small tolerance value used in the code to check if all three inputs are mathematically consistent when a user provides all three values. Due to floating-point math imprecision, we can’t check for exact equality (e.g., A=B), so we check if they are very close (e.g., |A-B| < EPS).