So... basically [any typos duly accredited]:
[A]WIN LOSE [C]LOSE
I choose A and door B is opened.
I don't switch to C and win the car.
I switch to C and lose the car.
I choose A and door C is opened.
I don't switch to B and win the car.
I switch to B and lose the car.
I choose B and door C must be opened.
I don't switch to A and lose the car.
I switch to A and win the car.
I choose C and door B must be opened.
I don't switch to A and lose the car.
I switch to A and win the car.
[A]LOSE WIN [C]LOSE
I choose A and door C must be opened.
I don't switch to B and lose the car.
I switch to B and win the car.
I choose B and door A is opened.
I don't switch to C and win the car.
I switch to C and lose the car.
I choose B and door C is opened.
I don't switch to A and win the car.
I switch to A and lose the car.
I choose C and door A must be opened.
I don't switch to B and lose the car.
I switch to B and win the car.
[A]LOSE LOSE [C]WIN
I choose A and door B must be opened.
I don't switch to C and lose the car.
I switch to C and win the car.
I choose B and door A must be opened.
I don't switch to C and lose the car.
I switch to C and win the car.
I choose C and door A is opened.
I don't switch to B and win the car.
I switch to B and lose the car.
I choose C and door B is opened.
I don't switch to A and win the car.
I switch to A and lose the car.
In all instances, twice I don't switch and win, twice I
do and win.
No advantage - the odds remain 50/50.
However, whilst this scenario separates WIN [A] from LOSE
, it amalgamates the LOSE possibilities, essentially:
ABB
BAB
BBA
The true situation is:
ABC
ACB
BAC
BCA
CAB
CBA
Thus:
CAR GOAT1 GOAT2
CAR GOAT2 GOAT1
GOAT1 CAR GOAT2
GOAT1 GOAT2 CAR
GOAT2 CAR GOAT1
GOAT2 GOAT1 CAR
Does separately distinguishing GOAT1 from GOAT2 make any
difference whatsoever?
Consequently:
CAR GOAT1 GOAT2
I choose CAR and GOAT1 is opened.
I don't switch to GOAT2 and win CAR.
I switch to GOAT2 and lose CAR.
I choose CAR and GOAT2 is opened.
I don't switch to GOAT1 and win CAR.
I switch to GOAT1 and lose CAR.
I choose GOAT1 and GOAT2 must be opened.
I don't switch to CAR and lose CAR.
I switch to CAR and win CAR.
I choose GOAT2 and GOAT1 must be opened.
I don't switch to CAR and lose CAR.
I switch to CAR and win CAR.
CAR GOAT2 GOAT1
I choose CAR and GOAT1 is opened.
I don't switch to GOAT2 and win CAR.
I switch to GOAT2 and lose CAR.
I choose CAR and GOAT2 is opened.
I don't switch to GOAT1 and win CAR.
I switch to GOAT1 and lose CAR.
I choose GOAT1 and GOAT2 must be opened.
I don't switch to CAR and lose CAR.
I switch to CAR and win CAR.
I choose GOAT2 and GOAT1 must be opened.
I don't switch to CAR and lose CAR.
I switch to CAR and win CAR.
GOAT1 CAR GOAT2
I choose GOAT1 and GOAT2 must be opened.
I don't switch to CAR and lose CAR.
I switch to CAR and win CAR.
I choose CAR and GOAT1 is opened.
I don't switch to GOAT2 and win CAR.
I switch to GOAT2 and lose CAR.
I choose CAR and GOAT2 is opened.
I don't switch to GOAT1 and win CAR.
I switch to GOAT1 and lose CAR.
I choose GOAT2 and GOAT1 must be opened.
I don't switch to CAR and lose CAR.
I switch to CAR and win CAR.
GOAT1 GOAT2 CAR
I choose GOAT1 and GOAT2 must be opened.
I don't switch to CAR and lose CAR.
I switch to CAR and win CAR.
I choose GOAT2 and GOAT1 must be opened.
I don't switch to CAR and lose CAR.
I switch to CAR and win CAR.
I choose CAR and GOAT1 is opened.
I don't switch to GOAT2 and win CAR.
I switch to GOAT2 and lose CAR.
I choose CAR and GOAT2 is opened.
I don't switch to GOAT1 and win CAR.
I switch to GOAT1 and lose CAR.
GOAT2 CAR GOAT1
I choose GOAT2 and GOAT1 must be opened.
I don't switch to CAR and lose CAR.
I switch to CAR and win CAR.
I choose CAR and GOAT1 is opened.
I don't switch to GOAT2 and win CAR.
I switch to GOAT2 and lose CAR.
I choose CAR and GOAT2 is opened.
I don't switch to GOAT1 and win CAR.
I switch to GOAT1 and lose CAR.
I choose GOAT1 and GOAT2 must be opened.
I don't switch to CAR and lose CAR.
I switch to CAR and win CAR.
GOAT2 GOAT1 CAR
I choose GOAT2 and GOAT1 must be opened.
I don't switch to CAR and lose CAR.
I switch to CAR and win CAR.
I choose GOAT1 and GOAT2 must be opened.
I don't switch to CAR and lose CAR.
I switch to CAR and win CAR.
I choose CAR and GOAT1 is opened.
I don't switch to GOAT2 and win CAR.
I switch to GOAT2 and lose CAR.
I choose CAR and GOAT2 is opened.
I don't switch to GOAT1 and win CAR.
I switch to GOAT1 and lose CAR.
A summary of those six possibilities:
LOSE/LOSE/WIN/WIN/LOSE/LOSE/WIN/WIN/WIN/LOSE/LOSE/WIN/WIN
/WIN/LOSE/LOSE/WIN/LOSE/LOSE/WIN/WIN/WIN/LOSE/LOSE
I both win and lose the car on 12 of 24 outcomes.
Strictly 50/50; so why should I switch?
In answer to my query, 'Does separately distinguishing
GOAT1 from GOAT2 make any difference whatsoever?', I note
that any differentiation seems to be irrelevant.
Doubtless, as an acknowledged layman, I'm unaware of
inherent, fundamental, statistical criteria which
substantiates accepted proof why we should always change
our initial selection - two-thirds of the time we would
win the car.
An explanation _why_ the above cited data is spurious
would be much appreciated.
James Easton.