Danny76, the 3 round burst came about exactly like I said. Source: "Dirty Little Secrets of the Vietnam War" by James F. Dunnigan, Albert A. Nofi. They cite the study in the book.
I understood that this study concluded that "three-shot groups provide an optimum combination of ammunition conservation, accuracy and firepower" and also led to development and testing of the "duplex" round for use in combat rifles during the Army's ACR competition in the '90'
The H+K G11 specifically cited it's 3 round burst function, stating the third round would have left the barrel by the time the recoil had caused significant effect on accuracy, and simply gave a spread of rounds better ensuring a first shot hit.
I was unaware that there was any reasoning as to the number of rounds required to kill the enemy, which at best is vague, and has too many contributing factors to be pared down to the difference between one and 3 rounds.
How far away was the enemy? was he behind cover? was he wearing body armour? did his equipment contribute to either causing greater injury? (e.g grenade detonation), or offering protection (cigarette case from wife over heart chestnut) where were the bullet strikes? was he in a vehicle? what were the weather conditions? did the wounded soldier have access to immediate first aid.
Of course, if you can get 2 or 3 rounds onto target, you stand a better chance of putting the guy down than with just one hit, or with no hits in the case of full auto spraying, but I would suggest that was the point I was making in my previous post