Category: Statistics

Summary: Mapping the boundary where alternating history-dependent Parrondo games switch from losing to winning.

Parrondo’s paradox shows that two individually losing games can combine into a winning strategy. This experiment studies the history-dependent version, where one game changes its bias according to the previous two outcomes, and asks for the detailed boundary in parameter space separating net loss from net gain under alternation.

The script sweeps the coin-bias parameters, simulates repeated play, and records mean drift, variance, and fine-scale features of the winning-losing boundary. Rather than demonstrating the paradox in a single setting, it builds a high-resolution phase map.

That broader map is useful because boundary geometry can reveal subtle interactions between memory and bias that are hidden in isolated examples. The experiment is especially interested in whether the boundary develops nontrivial curvature or fine structure.

Method: Repeated Monte Carlo simulations of alternating history-dependent Parrondo games over a two-parameter grid.

What is measured: Mean drift per round, variance of cumulative gain, boundary location in parameter space, and fine-structure diagnostics.