Table or lookup functions, TF, are part of System Dynamics models since the very beginning fifty years ago. TF formulation, dynamics and multidimensionality are analyzed and suggestions for their improvement are presented. TF spread nonlinear dynamics to other variables involved and simplify structure, allowing the concentration on problems. Relationships between nonlinear varying eigenvalues and TF’ patterns are established, which open the door for SD’ software improvements and further research. A general shape, synthesizing typical TF’ patterns, plots a normal curve that the Central Limit Theorem of statistics proves as the distribution of any accumulation (level) of random variables. The random face of SD, uncovered by Agent Base Simulation, converges into this normal curve, which gives statistical grounds to lookup relationships and improves policy design by fine-tuning estimation.