Whenever the peasant has to make a choice of which way to go he has 3 choices and no way of knowing which route to take. Assume he chooses randomly and work out the probability of him reaching chamber A and the probability of him reaching chamber B. The clever princess has seen the map and worked out which chamber he is more likely to end up in so she waits there knowing that then the story is more likely to end up happily ever after.

Xing Cong gave the solution that the princess should wait in A because the probability of the peasant arriving in A is 5/9, and he sent this diagram.