you correctly picked the car door to begin with ( in , chance)then the host left random goat door closed if you picked goat door ( in , chance)the host specifically chose the car door to leave closed the choice of which doors to open isn' randomthe host knows to leave the car door closed it' almost certain that you didn' pick the car door to begin withso you should switch to the other door another way to think of it is that you have , boxes and one box contains prize you guess which box the prize is in and the host puts it in your hands do you think the prize is in your box or one of the other boxesyou don' need the host to open of the boxes that don' contain prizethe amount of choice is the same as with the , doors the odds that you guessed correctly in the beginning are in , while the odds that you did not (and that the prize is in one of the other boxesis near certain in , more information about the monty hall problem can be found at the program in action when you run montyhall pythe output will look like thisthe monty hall problemby al sweigart al@inventwithpython com --snip-+++ +++pick door or (or "quitto stop) +++( oo / /| |goat||+++door contains goatdo you want to swap doorsy/ +(oo / /| |goat||++car___/ __o ++(oo / /| |goat||+monty hall problem