Question: Sadistic Tendencies
You are captured by a Russian spy and tortured for information. Every time you fail to answer his question adequately, he plays the following game: First, he draws a number randomly between 1 and 4. This becomes the comparison value.
He then draws a number from between 0 and 4. If it is greater than or equal to the comparison value, you get a lash with a wet noodle, and he draws again. He continues this until he draws a number that is less than the comparison value, at which point he continues his interrogation. If he draws a 3 as the comparison value, what is the expected number of lashes you will receive for that question? What is the expected number of lashes you will receive per question?