What many descriptions of the problem leave out is that it is critical that Monty knowingly picks a door with a goat. If Monty chooses at random, then the winning odds do indeed increase to 50% if he happens to open a door with a goat behind it.

The randomized variant, by the way, tends to garner roughly the same degree of "you're completely wrong" responses when given to people who know just enough about the normal Monty-hall problem not to be fooled by it.