Some thoughts on trying to resolve yesterday's problems intuitively, without having to resort to Bayes' theorem, which takes the fun out of everything.

The original Monty Hall seems less counter-intuitive this way : Because the host has to open an empty door after your initial choice, switching doors will always give you the contrary result (try a tree diagram it helps). Since there is a 2/3 chance of getting it wrong the first time, switching gives you a 2/3 chance of getting it right. You are betting against your first choice, really.

The three-card swindle seems much easier to resolve intuitively, without knowledge of conditional probability. If you open a black card (or red) and bet that the other card is black (or red) as well, you are essentially betting that the two cards are suited. That happens 2/3 of the time (because there are two suited pairs, as opposed to a mixed one).