  To resolve disputes or determine the order of things, people commonly use
binary choices such as tossing a coin, even though it is obscure whether the
empirical probability equals to the theoretical probability. The geomagnetic
field (GMF) is broadly applied as a sensory cue for various movements in many
organisms including humans, although our understanding is limited. Here we
reveal a GMF-modulated probabilistic abstract decision-making in humans and the
underlying mechanism, exploiting the zero-sum binary stone choice of Go game as
a proof-of-principle. The large-scale data analyses of professional Go matches
and in situ stone choice games showed that the empirical probabilities of the
stone selections were remarkably different from the theoretical probability. In
laboratory experiments, experimental probability in the decision-making was
significantly influenced by GMF conditions and specific magnetic resonance
frequency. Time series and stepwise systematic analyses pinpointed the
intentionally uncontrollable decision-making as a primary modulating target.
Notably, the continuum of GMF lines and anisotropic magnetic interplay between
players were crucial to influence the magnetic field resonance-mediated
abstract decision-making. Our findings provide unique insights into the impact
of sensing GMF in decision-makings at tipping points and the quantum mechanical
mechanism for manifesting the gap between theoretical and empirical probability
in 3-dimensional living space.
