Double sided gambler's ruin for combat odds?

#1
Suppose that one unit has an attack factor of 4 and health factor of 4. The other has a defense factor of 3 and a health factor of 2. When either has lost all of its health factor, he loses. The basic odds of winning are easy, 3 to 2 or 3/5= 0.6. The odds of losing 4 times in a row are easy: (1-0.6)^4 = 0.0256. The odds of the defender winning 2 times in a row are 0.4^2. But what are the odds that the defender will lose 2 times before the winner loses 4 times?
 
#2
But what are the odds that the defender will lose 2 times before the winner loses 4 times?
One easy but boring way in this simple case is to list all the possibilities of which (I think) there are 10 this time. Loss possibilities are dd, add, dad, aadd etc up to daaad, then calculate and add. Looking at the list will probably give you an idea on how to tackle bigger cases.