Wouldn't that newton's-second-law your own conker just as hard though? As the aggressor you get to choose the points of contact, which must be where the accuracy comes in. If you can strike your opponent downwards you're more likely to knock them off the string and lead to Stamps.
While obviously all three laws do apply to a usual conker match (if not, the radiation from the plasma sheath and relativistic shrapnel is probably the bigger concern that the result of the match), I think the third law is the one you mean: For every action, there is an equal and opposite reaction.
Conkers are usually oblate spheroids and the dangling one has its largest radius spot on top usually - thinking back I never thought to string one differently not sure if that was allowed. So the person taking the hit can aim to hit with the shortest radius section of their conker on the flat spot of the other. There's also the skill of an accurate hit - someone who misses a lot or hits away from center glancing blows is not going to win very much.
Also the nut being hit is restrained by the string whereas the hitting nut can go in any direction or simply rebound. Cracks may start at the hole in which case being hit is worse than hitting on average.
