Random Number Generator

A uniform discrete draw over the integers min through max should give every value the same probability, 1/(max - min + 1). The expression floor(u * (max - min + 1)) + min does that by slicing the continuous interval [0,1) that Math.random returns into equally wide buckets, one per integer, then shifting the bucket index up to the minimum. The +1 is what makes the range inclusive at both ends: without it the maximum could never be produced. Because the underlying double carries a 53-bit mantissa, the buckets stay effectively equal in width for any range narrower than roughly 9 quadrillion values, so bias from the mapping itself is not a practical concern at ordinary scales. Two limitations matter more. First, Math.random is pseudo-random: it advances an internal state with a deterministic algorithm, and in V8 that algorithm is xorshift128+, whose state can be reconstructed from a modest number of consecutive outputs. It is fine for dice, shuffles, sampling and raffles, and unsuitable for passwords, session tokens, or anything an adversary benefits from predicting - crypto.getRandomValues, seeded from operating-system entropy, is the correct tool there. Second, each value here is drawn independently, meaning draws happen with replacement. Requesting six numbers from 1 to 49 therefore produces at least one repeat about 27 percent of the time, which is not how a physical lottery draw behaves.

Before computers, statisticians drew randomness from physical devices and published the results as books. The RAND Corporation built an electronic roulette wheel driven by a pulse source and issued A Million Random Digits with 100,000 Normal Deviates in 1955, which served as a standard sampling reference for decades. Algorithmic generation began at almost the same moment: John von Neumann described the middle-square method in 1946 for Monte Carlo work on ENIAC, remarking that anyone producing random digits by arithmetic means was living in a state of sin. D. H. Lehmer proposed the linear congruential generator in 1949, and it went on to power the standard rand functions of Fortran and C. Linear congruential generators turned out to have structure. George Marsaglia showed in 1968 that their outputs, plotted as points in several dimensions, fall onto a small number of hyperplanes, and IBM's RANDU became the notorious example. Makoto Matsumoto and Takuji Nishimura answered this in 1997 with the Mersenne Twister, whose period is 2 to the 19937 minus 1, later adopted as the default generator in Python, R and MATLAB. Marsaglia's shorter xorshift family followed in 2003. Browsers inherited this lineage directly: V8 replaced its older MWC1616 generator with xorshift128+ in 2015, while the Web Crypto API added crypto.getRandomValues to give JavaScript a separate, entropy-backed path for security work.