EuAgxAl11−x phases adopting the BaHg11-type structure (space group Pm3̅m, Z = 3) were synthesized with high yield by arc melting a mixture loaded as “EuAg3.5Al7.5” and annealing at 500 °C for 40 days. This phase has a very narrow phase width around EuAg4.0Al7.0; and it is unstable at 600 and 700 °C, at which it transforms into other phases. Magnetometry indicates that Eu is divalent, which gives the valence electron concentration per Ag/Al atom as 2.45 e−/atom, higher than in the BaCd11-type phases in the Eu−Ag−Al system (2.10−2.30 e−/atom). First principles electronic structure calculations, using a computational model structure built by simulating the crystallographic results as well as maximizing the number of heteroatomic (Ag−Al) contacts, can explain why the cubic BaHg11-type structure is favored at higher valence electron concentration than the tetragonal BaCd11-type structure.