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@neu
Original -> 2nd choice after 1 box removal
001 -> 01-/1-0
010 -> 10-/-01
100 -> 01-/0-1
Original choice is 1/3 chance
if you change you mind after one box is removed the new chance is 1/2
I think.. I may have got it wrong.
Edit: I have, got it wrong, this is correct:
If you dont change you mind chance of winning is still 1/3.
After one loosing box is removed the chance of either box having a win or loss is equal, 2/3.