When locked in combat with an enemy each knight has even odds of winning or losing. Knights, being chivalrous, prefer single combat and will not double up on their enemies. The extra knights in the larger army will wait until there is a free enemy to fight.
[Essentially the killing power of the larger army is proportional to the size of the smaller army.]
When the dust settles the smaller army is eliminated. How many knights (are expected to) remain in the larger army?
Generalize for two armies of size A and B where A>B.
A couple things i should clear up
