Yousif et al. (2022) proposed a computational model to investigate the processes and biases involved in human random number generation (RNG). Their original two-parameter model includes a repetition parameter and a side-switching parameter representing influences of the immediately preceding number on the choice of the next number. We propose two changes to the model. First, we replace the side-switching parameter with a more general and less task-dependent distance parameter, which accounts for the tendency to select subsequent numbers that tend to be either closer to or further away from the previous number on the selected response pad. Second, we extend the computational model by adding a third parameter to account for the human tendency to select subsequent numbers with greater probability the longer the respective number has not been previously selected, following the pattern of the well-known gambler’s fallacy. This new “cycling” parameter takes into account the most recent and all previous selections. The generalized distance parameter, and particularly the new cycling parameter, improved the fit of the model to human-generated sequences and the rate of successful predictions of the next choice from 14.09% to 26.47%, significantly exceeding the expected chance value of 1/9 = 11.1%. Model-driven simulations also showed that the extended three-parameter model could better account for systematic patterns that can be observed in human RNG tasks. The improved model could be useful in many contexts where human biases in RNG tasks are analyzed.