Uniform Distribution
A probability distribution where every value in a range has an equal chance of being selected.
In uniform distribution, each outcome is equally likely. For random integers 1-10, each number has a 10% chance. Good random generators produce uniform distributions. Biased generators might favor certain values, which is problematic for games (unfair) and simulations (inaccurate). Test your random source for uniformity.
ExampleA fair die roll is uniformly distributed over 1-6
Monte Carlo Method
A computational technique using random sampling to obtain numerical results, often for complex problems.
Monte Carlo methods run many simulations with random inputs to estimate outcomes. Used for: risk analysis (financial modeling), physics simulations (particle behavior), optimization (finding best solutions), integration (estimating areas/volumes). The more iterations, the more accurate the estimate. Requires high-quality random numbers.
ExampleEstimating pi by randomly throwing darts at a square with inscribed circle