The way I understood why it’s beneficial to switch your choice after the host opens a door showing you a goat is as below

Assume that door 1 has a goat , door 2 has a car and door 3 has a goat behind it. There are 3 trials possible in the Monty Hall scenario

Trial 1 Contestant chose door 1(which is a goat). Host opens door 3(because he has to) and asks if contestant would like to switch. If he switches, then he wins the !

Trial 2 Contestant chooses door 2, host can open door 1 or 3 doesn’t matter. Host asks contestant if he’d like to switch and if he does then he loses.

Trial 3 Contestant chooses door 3(which has a goat). Host opens door 1(he has to) and asks if contestant would like to switch to door 2. Contestant switches to door 2 and wins a cat!

So 2/3 times contestant wins when switching his/her original choice.

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