I may be tired, but cannot find the binomial theorem listed? I cannot seem to come up with the 0.34 and 0.23 values, can you assist, either walk me though it or direct where I can find the method?

The Binomial distribution is explained in detail on page 96. In the example here P(D | H1) is the probability of 3 wins in 5 matches where the probability of a win is 0.6. That is just the Binomial distribution where n=5, p=0.6 and r=3, which is:

10 times (0.6 to the power of 3) times (0.4 to the power of 2). That is 0.34 to 2 decimal places.

(Of course if you dont want to do the Binomial computations by hand you can do them very easily in AgenaRisk.