Answer to POW #6:

The most likely value of the total is 13.

The elegant way to argue this is to point out that on the last roll of the die (the one that will take your total over 12), whatever total you get, you could also have rolled to get a total of 13. (In other words, you can get a final total of 13 from a second-to-last total of 7, 8, 9, 10, 11, or 12.) (Solution courtesy of Len Van Wyk)

You can also run a computer simulation to calculate the probabilities of various final totals (thanks to Ed Lee, who did this):
P(13) = 0.27926
P(14) = 0.23700
P(15) = 0.19231
P(16) = 0.14559
P(17) = 0.09737
P(18) = 0.04847

Source: Halmos