Mr. Markov either wins or loses at a card table. His result on a given day is related to his result the day before.
If he loses today, there is a 50% chance he would lose tomorrow.
If he wins today, there is a 30% chance that he would lose tomorrow.
How often would he lose on two consecutive days? Assume an infinite horizon so the first day result is irrelevant.
(Note: Losing three days in a row counts as losing on two consecutive days twice)