Lazy Liz's Escape
Lazy Liz is stuck in a dry well that's 210 meters deep. Each day, she flips a coin. If it lands on heads, she works on climbing out of the well and is able to climb up 10 meters. If it lands on tails, she lazes the day away and ends up sliding down the well 10 meters. Of course, if she is at the bottom of the well, she can't slide down any further, so she just lazes the day away. Currently, she is just 10 meters away from the top of the well. What is the expected number of days it will take her to climb out of it?
Details and assumptions
If she flipped a head on the first day, it takes her 1 day to climb out of the well.
She does not slide down 'overnight'.