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However, if it comes up "heads" when tossed, you might win something in which case the observed event is causal though heads/tails remain complementary

No, they are actually mutually exclusive (either-or). One wins, the other one loses. They eliminate each other.

If-then is conditionally complementary. They re-informce each other.

No, they are actually mutually exclusive (either-or). One wins, the other one loses. They eliminate each other.

The two sides of the coin remain complementary no matter which side you are facing.

That you, as the observer, can only face one side of the coin at a time (i.e. from tossing a coin) - is that which is mutually exclusive, you can only see either heads or tails.

This conversation itself is an excellent example of the perils of the observer problem. The coin observer probably realizes that the coin has two sides, one of which he cannot see while facing the other. But that insight is not always carried over to other issues - such as predestination v free will, Triune God, other doctrines/traditions, etc.

If-then is conditionally complementary. They re-informce each other.

No, "if then else" would be a conditional complementary. "If then" without the "else" does not preclude that anything which fails the "if" cause would not also have the same effect, "then".

For instance, I might say "if my husband is home then the air conditioner will be on." But that doesn't mean the air conditioner will be off if my husband is not home.

No, [complementarities] are actually mutually exclusive (either-or). One wins, the other one loses. They eliminate each other.

The "elimination" is entirely temporary, lasting only as long as the observed event.

I'm not sure you've grasped what Bohr meant WRT his theory of complementarity: "Even though the wave and the particle behavior of an object are mutually exclusive, we need both to completely understand its properties."

Must run away for now but will be back soon.