Rubik's Cube Probability Calculator
What are the odds of solving a Rubik's Cube by randomly turning it? With 43,252,003,274,489,856,000 possible states (that's 43 quintillion!), the numbers are astronomical. This calculator shows the probability of randomly stumbling upon the solved state in N moves. Even making one random move per second for the age of the universe, you'd have essentially zero chance. Discover why learning actual solving methods beats random luck by a factor of quintillions.
How We Calculate This
Probability = 1 - (1 - 1/M)^N where M = 43,252,003,274,489,856,000 states. For small N relative to M, this approximates to N/M. Time for 50% = 0.693 × M / attempts per second. Uses numerically stable logarithm calculations.
Frequently Asked Questions
How many states does a Rubik's Cube have?
A standard 3×3 Rubik's Cube has exactly 43,252,003,274,489,856,000 reachable states. That's about 43.25 quintillion combinations. This number was mathematically proven by analyzing the group theory of cube rotations.
Could a computer solve it randomly faster?
A supercomputer making a trillion attempts per second would still need about 1.4 billion years for a 50% chance of randomly hitting the solution. It's far more efficient to use an algorithm - computers can solve cubes optimally in under a second.
What is God's Number?
God's Number is 20 - the maximum number of moves needed to solve any Rubik's Cube position. This was proven by Tomas Rokicki and others in 2010 using massive computer analysis. No matter how scrambled, optimal solving needs at most 20 moves.
What are the actual odds of random solving?
Effectively zero for any reasonable number of attempts. The expected number of random moves to solve is roughly 43 quintillion, making random solving practically impossible. This is why every cube solver uses systematic methods.
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You might also find these calculators helpful: Statistics Calculator, and Asteroid Hit Odds Calculator.
This calculator is for educational purposes about probability. Random cube solving is not a recommended strategy. Learn proper methods at speedsolving communities instead!