[pzhon]

[ QUOTE ]
Team A has an advantage at

0 < p < 0.542310724269960960
and
0.960204909275475293 < p < 1

[/ QUOTE ]
[img]/images/graemlins/diamond.gif[/img] The range has to be the reflection about 50% of the complement. If p gives side A an advantage, then 1-p gives side B the same advantage by reversing the result of each throw, but you concluded that probabilities around 50% give A an advantage as do both very high and very low probabilities.
[img]/images/graemlins/diamond.gif[/img] You left out a few terms. There should have been 6*7=42, as there are 6 scores in {0,1,2,3,4,5} and 7 in {0,...,6}. You left out most scores of the form 0 to n. You'll find that your probabilities for win, lose, and tie don't add up to 1.

The surprising thing to me is that your calculated start of the upper interval disagrees with mine, 0.96020505749108031144, only by about 1/10 million, even though the disagreements are much larger for lower values. The reason is that the omitted terms are all very small when p is large, since they contain (1-p)^5, but the derivative of the advantage is relatively large.