Probability of a successful attack Attacker
two dice three dice four dice five dice six dice seven dice eight dice
Defender one die 83.8% 97.3% 99.7% *100% *100% 100% 100%
two dice 44.4% 77.9% 93.9% 98.8% 99.8% *100% *100%
three dice 15.2% 45.4% 74.3% 90.9% 97.5% 99.5% 99.9%
four dice 3.6% 19.2% 46.0% 71.8% 88.4% 96.2% 99.0%
five dice 0.6% 6.1% 22.0% 46.4% 70.0% 86.2% 94.8%
six dice 0.1% 1.5% 8.3% 24.2% 46.7% 68.6% 84.4%
seven dice *0.0% 0.3% 2.6% 10.4% 26.0% 46.9% 67.3%
eight dice *0.0% *0.0% 0.6% 3.7% 12.2% 27.4% 47.1%

okay, copying and pasting charts doesn't work.

http://en.wikipedia.org/wiki/Kdice

Cool, there is more that can potentially be done, there is value in creating a risk/reward calculator that takes into account whether it's worth going on a run with a tall stack x squares away, whether the payoff is better to try and connect or to leave alone under different circumstances, etc.

That chart will save me some time.

the odds of you gaining a territory are in direct oppostion to the overall need for that territory by a factor of 4
.
.
inversely ... the odds of gaining a territory that you do not strategically need are 10 to 1 in your favor