Figure 2.

a) Plot of $\mu (n)$ and ${\sigma }^2(n)$ comparing theory (lines) and simulation (circles), realizing the strong Parrondo effect. Parameters are $p=0.39$, $p_1=0.02$, $p_2=0.6$, $r=r_1=r_2=0.2$, and $\gamma =0.5$. b,c) $\mathrm{\Delta }\mu =0$ fair isoclines in ${\varphi }_1$‐${\varphi }_2$ parameter space for differing $M$ and $\gamma$, comparing theory (lines) and simulation (circles). Parameters are $p_1=0.35$ and $r=r_1=r_2=0.1$, with $M=4$ for (b) and $\gamma =0.5$ for (c).