>>12 These are both about the three door monty hall problem, and thus not relevant to OP. I'm not sure what the point of labeling the goats is supposed to be, but lets roll. Goat A, Goat B, Car C. At your initial pick, you can choose A, B, or C. If you pick A, the host opens door B and gives you the option to keep A or switch to B&C. If you pick B, the host opens door A and gives you the option to keep B or switch to A&C. If you pick C, the host opens A or B and gives you the option of keeping C or switching to A&B. The fact that in the case where you initially pick C, the host may open either of A or B doesn't change that the Monty Hall choice is still either to stick with C or switch to A&B.

These are both about the three door monty hall problem, and thus not relevant to OP.

I'm not sure what the point of labeling the goats is supposed to be, but lets roll. Goat A, Goat B, Car C.

At your initial pick, you can choose A, B, or C.

If you pick A, the host opens door B and gives you the option to keep A or switch to B&C.

If you pick B, the host opens door A and gives you the option to keep B or switch to A&C.

If you pick C, the host opens A or B and gives you the option of keeping C or switching to A&B.

The fact that in the case where you initially pick C, the host may open either of A or B doesn't change that the Monty Hall choice is still either to stick with C or switch to A&B.