Mac is idly tossing two dice when he decides to see how many tosses it would take to go from 1 to 6 in order. The rules are to toss the two dice until one or the other or both show a 1. Then, toss until a 2 shows. However, if both a 1 and a 2 show at the same time, both can be used.

He then tosses for a 3 and similarly for other numbers. What is the expected number of tosses to go from 1 to 6?