You pick one of three options, giving you a 1/3 chance of being correct, 2/3 odds you picked incorrectly.
The host removes an option and give you the option to switch.
Your options then are -
Keep the same door: you win 1/3 of the time (your first guess was right)
Switch doors: you win 2/3 of the time (your first guess was wrong)
It really just comes down to, do I think I was right the first time, which was 1/3 odds, or wrong the first time, 2/3 odds.
You pick one of three options, giving you a 1/3 chance of being correct, 2/3 odds you picked incorrectly. The host removes an option and give you the option to switch.
Your options then are -
Keep the same door: you win 1/3 of the time (your first guess was right)
Switch doors: you win 2/3 of the time (your first guess was wrong)
It really just comes down to, do I think I was right the first time, which was 1/3 odds, or wrong the first time, 2/3 odds.