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QBism regards quantum mechanics as an addition to probability theory. Theaddition provides an extra normative rule for decision-making agents concernedwith gambling across experimental contexts, somewhat in analogy to thedouble-slit experiment. This establishes the meaning of the Born Rule from aQBist perspective. Moreover it suggests that the best way to formulate the BornRule for foundational discussions is with respect to an informationallycomplete reference device. Recent work [DeBrota, Fuchs, and Stacey, Phys. Rev.Res. 2, 013074 (2020)] has demonstrated that reference devices employingsymmetric informationally complete POVMs (or SICs) achieve a minimalquantumness: They witness the irreducible difference between classical andquantum. In this paper, we attempt to answer the analogous question forreal-vector-space quantum theory. While standard quantum mechanics seems toallow SICs to exist in all finite dimensions, in the case of quantum theoryover the real numbers it is known that SICs do not exist in most dimensions. Wetherefore attempt to identify the optimal reference device in the first realdimension without a SIC (i.e., $d=4$) in hopes of better understanding theessential role of complex numbers in quantum mechanics. In contrast to theircomplex counterparts, the expressions that result in a QBist understanding ofreal-vector-space quantum theory are surprisingly complex.

Quantum mechanics? It's all fun and games until someone loses an $i$