Ternary iron-boron-based bulk metallic glasses ͑BMGs͒ were explored exhibiting capability of thick amorphous casting at least 1 mm in rod diameter or 0.5 mm in plate thickness, excellent soft magnetic properties with saturation magnetization 1.56 T and coercivity smaller than 40 A / m, and electrical resistivity larger than 200 ⍀ cm. The BMG alloys represented by the formulas M a Fe b B c are based on two simple selection rules: ͑1͒ M is an element with an atomic radius at least 130% that of Fe; ͑2͒ M possesses eutectic points with both Fe and B, and the M-Fe eutectic is at the Fe-rich end. Among more than 30 candidate M elements, Sc, Y, Dy, Ho, and Er fulfill BMG capability at the composition range, in at %, 3 Ͻ a Ͻ 10, 18Ͻ c Ͻ 27, whereas a + b + c = 100. It is very remarkable that with a tiny addition of M, such as 4 at %, the critical cooling rate to form an amorphous state is abruptly lowered by more than four orders of magnitude as compared with Fe-B binary alloys, and a bulk amorphous state is achievable with only three elements ͑conventional ones 4-7 elements͒. These alloys are promising as core materials for transformers.