In free space, how does the gain of two three-element, horizontally polarized Yagi antennas spaced vertically 1/2 wavelength apart typically compare to the gain of a single three-element Yagi?

When you stack two identical antennas, such as two three-element Yagis, and feed them in phase, the effective radiated power in the main direction essentially doubles (assuming optimal spacing and minimal losses). In the decibel scale, a doubling of power corresponds to an increase of 3 dB. Because you are only doubling the radiating area and power focus, you only gain 3 dB over the single antenna. To achieve a 6 dB increase (which represents a quadrupling of power), you would need to stack four identical Yagi antennas, not just two. Therefore, adding a second identical antenna yields a theoretical maximum gain of 3 dB higher than using a single antenna alone.