Keep in mind that forward directionality is tied in with the choice of Mid pattern. That is, the pattern of the Mid mic determines the maximum achievable forward directionality of the stereo configuration. But because that maximum forward directionality is achieved at a ratio of 100% Mid / 0% Side, it's equivalent to just the Mid in mono and not useful for stereo. As the proportion of Side is increased the forward directionality of the Mid mic is traded off for increased stereo width, until at a ratio of 0% Mid / 100% Side there is no remaining forward directionality influence by the Mid mic at all. You just have Side with opposite polarity to each speaker.

So using an omni Mid means no forward directionality and the sum of the combined patterns will always omnidirectional. With an omni Mid the virtual patterns will vary across the entire first order pattern range from omni through bi-directional, but the angle between the resulting virtual patterns is always 180 degrees apart regardless of what Mid:Side ratio is used. So when using an omni Mid and a 50:50 Mid/Side mix, the result *is *crossed cardioids, but with an angle between them of 180 degrees rather than a more typical stereo X/Y angle.

The inverse situation happen when using a bi-directional Mid. In that case the virtual patterns always remain fig-8 at all Mid:Side ratios, and only the angle between the virtual 8's changes.

Using other Mid patterns lands somewhere between those extremes, with both virtual patterns and virtual angles varying with mix ratio, up to the maximum possible forward directivity as determined by the Mid pattern.

So, one way to determine what Mid pattern to use is to consider how much forward directionality you want given your recording position. If you need to minimize pickup from behind, use the most directional Mid you have available. If you want to minimize pickup from the sides, use a bidirectional mid along with a minimal amount of side in the mix ratio.