What are some quick ways to determine the relationship between any two random types? It's good to have a function-based understanding of intertype relations, but for determining them quickly, something even more immediate would be nice. Some relations are fairly apparent (quasi-identical, contrary, dual, conflicting, etc), and most of the rest aren't bad, but I have trouble with illusionary and semi-dual. The "easy-to-remember charts" at socionics.com are okay but not ideal (http://socionics.com/rel/charts.htm). I guess it also depends on which naming convention you use. I still think of things mostly with the four-letter acronyms, but it seems like intertype relations would probably easier with the three-letter acronyms, especially since the base function for introverted types is more apparent.
For the four-letter acronyms, here's what I currently do when I'm in a hurry (not very elegant, I know):
Quasi-identical: j vs. p (last letter differs)
Contrary: E vs. I (first letter differs)
Conflicting: all letters differ
Super-ego: middle two letters differ
Mirror: same ego functions / first and last letters differ
Dual: first three letters differ
Activity: pair of introverts or extroverts from the same quadra
Look-a-like: between perceiving types, perceiving function differs, between judging types, judging function differs
Comparative: between perceiving types, judging function differs, between judging types, perceiving function differs
Semi-Dual: same base function as your dual / is the dual of your comparative (and the comparative of your dual)
Illusionary: same base function as your contrary / is the dual of your look-a-like (and the look-a-like of your dual)
Supervision and Benefit: if the two types are from adjacent quadras and differ in j/p, they will have a relationship of supervision or benefit. If one is E and one is I, it's supervision, and if both are E or both are I, it's benefit. To determine direction, there are two "rings" of benefit/supervision that point in opposite directions. I just remember them by remembering which one I'm in.