Hi bkuehlhorn,

Let’s look at a scenario. Assume the prize is behind door #2 and goats are behind doors #1 and #3.

Scenario #1 for always switching:

1. You choose door #1

2.The host opens door #3 , because the prize is behind door #2, and asks if you want to switch.

3.You decide to switch to door #2

4.YOU WIN!

Scenario #2 for always switching

1.You choose door #2

2.The host opens door #3 or door #1 , because the prize is behind door # 2, and asks if you want to switch.

3.You decide to switch to door #1 or door #3

4.YOU LOSE.

Scenario #3 for always switching

1. You choose door #3

2. The host opens door #1 , because the prize is behind door #2, and asks if you want to switch.

3. You decide to switch to door #2

4. YOU WIN!

From the possible scenarios above where the prize was behind door #2 and you opted to always switch, you would’ve won 2/3 times from switching and lost 1/3 times for switching or vice versa you would’ve won 1/3 of the time by sticking with your choice and lost 2/3 of the time for sticking with your choice.