taken from the wikipedia page linked above. this lended a huge hand to my grasping the concept

It may be easier for the reader to appreciate the result by considering a hundred doors instead of just three. In this case there are 99 doors with goats behind them and 1 door with a prize. The contestant picks a door; 99 out of 100 times the contestant will pick a door with a goat. Monty then opens 98 of the other doors revealing 98 goats and offers the contestant the chance to switch to the other unopened door. On 99 out of 100 occasions the door the contestant can switch to will contain the prize as 99 out of 100 times the contestant first picked a door with a goat. At this point a rational contestant should always switch.