Did we ever explain the Monty Hall problem with logic?
In short, you have 2/3 chance of selecting a coconut when you first choose a door. Every time you select a coconut with your first choice, the host (when removing one of the other two doors) MUST leave you with the yacht, which means when you change under these conditions (which is 2/3 of the time the best thing to do), then you win the yacht.
It's easy to think it's still 50:50, but that assumes the host RANDOMLY removes a door, in which case 1/3 of the time, there would be nothing to win.