Great explanation Mike!!! Two quick comments:
(1) If you are very comfortable working with conditionals and with diagramming split boards, then actually I think it is often helpful to use a conditional to create split boards. For example, in this game, we can use the last rule to divide the game into two scenarios: One where males are assigned to Veblen South, and one where males are not assigned to Veblen South. In the scenario where males are assigned to Veblen South we now know everything except the assignments in Richards South and Tuscarora South- one of them is males and the other is females, but we don’t know which one is which. That’s a lot to know about one of two scenarios. In the other scenarios, the only additional piece of information we have is that males are not assigned to Veblen South- i.e. females are assigned to Veblen South. If you are very comfortable working with conditionals and with diagramming split boards, you will know that this doesn’t tell us anything about who gets assigned to Weblen North.
Another reason why it is often helpful to use a conditional to create split boards if because you are, in effect, drawing the rule into your master diagram(s), which makes it much less likely that you will forget about the rule.
(2) If you have a biconditional (for example, the following rule is a biconditional: males are assigned to Veblen South if but only if males are assigned to Wisteria North), you should definitely use it to diagram split boards. The biconditional generally tells us that two things are either in together or out together, so that creates THE two scenarios: The case where the two things are in together, and the case where the two things are out together.