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First time I made the correct choice and had a successful outcome
Then for completionists sake I wanted to fail
Next two times I made the wrong choice but still succeded.
You have a 9/10 chance that switching is correct
You unluckily or luckily as some would say, got that 1/10 chance that it would be wrong to switch.
I stayed the second time and got it wrong.
I switched the third time and got it right.
I'm not liking these random chance "decisions" in this game.
https://www.youtube.com/watch?v=tvODuUMLLgM
Personally I cant stand the problem and its infuritating to me but this is a great simple explaination of the problem and the game theory behind it.
With just 3 doors it's harder to see any benefit, but with 10 like in the game it's easier. Let's imagine we have 100 doors though, and only 1 contains the prize.
You pick a door. There's a 1% chance you got it right. 98 empty doors open, and you can now switch. You'd think it's a 50/50 shot right now, and without knowing about the other 98 doors you'd be right, but look at it a different way. What is the chance that the prize was NOT in the door you picked originally? 99%. The other door is the only one left that wasn't picked originally. There's a 99% chance that it has the prize.
Basically all the doors that get opened cause the one that's left to acumulate the chance from them.
edit: I spoke too soon
If you actually had to repeat a scene ~200 times it would be pretty rage inducing.
If you chose correctly (1/10 chance) then 8 incorrect lockers open and a random incorrect locker is left.
If you chose wrong (9/10 chance) then 8 incorrect lockers open up, and the correct one is left.
So nine times out of ten, you'll pick the wrong door at first, and switching will give you the correct one. If you think you blindly picked the correct door the first time without any help, then don't switch.
Essentially, switching is like choosing every other door all at once. Not switching is just one door and that's it.