A-to-Z Mathematical & Regulatory Slot Glossary
The industry's definitive encyclopedia of slot machine mathematics, statistical distributions, cryptographic PRNG architectures, and international regulatory standards.
Poisson Distribution in Respin Mechanics
A discrete probability distribution expressing the probability of a given number of respin events occurring in a fixed interval of play.
In Hold & Win and streak respin mechanics, the probability of landing k reset symbols within a fixed window of 3 respins conforms to Poisson and geometric distributions. As grid density increases, the probability of hitting an unpopulated tile decays exponentially, which models the tension curve before bonus termination.
P(X = k) = \frac{\lambda^k e^{-\lambda}}{k!}Lambda represents the expected rate of bonus scatter occurrences across the active reel grid per respin cycle.
On a 15-cell grid with 12 positions filled, the Poisson probability of landing at least one remaining symbol on the next spin drops to under 8.4%.
- The game does not intentionally make the final coin harder to hit; the decay in hit rate is a pure geometric outcome of fewer open reel tiles.