A platform cooling arrangement in a turbine rotor blade having a platform at an interface between an airfoil and a root, wherein the rotor blade includes an interior cooling passage that extends from a connection at the root to the approximate radial height of the platform, wherein, the interior cooling passage comprises a high-pressure coolant region and a low-pressure coolant region, and wherein a pressure side of the platform comprises a topside extending circumferentially from the airfoil to a pressure side slashface. The platform cooling arrangement may include: a platform cavity formed within the pressure side of the platform, a high-pressure connector that connects the platform cavity to the high-pressure coolant region of the interior cooling passage; a low-pressure connector that connects the platform cavity to the low-pressure coolant region of the interior cooling passage; and a pin bank formed within the platform cavity that includes radial pins.