A 3-1 ratio based on a simple numerical total of troop numbers has not only thus limited use as a general rule-of-thumb guide for military planning, but is useless for analytical purposes .
Simply put, while there are many historical cases where an attacking force with a 3-1 numerical advantage succeeded, there are also many cases where attackers won with less than a 3-1 advantage, and even with a numerical inferiority
On the Eastern Front during World War II, for example, the German Army regularly conducted successful attacks against numerically superior Soviet forces. To the point that the conclusion must be: in the average modem battle, the attacker’s numerical strength is about double the defender’s.
This is because the attacker has the initiative and can initiate combat at a time and place of his choosing and in the manner of his choosing. The attacker can mass his forces at critical points on the battlefield to gain the advantage in strength which he believes necessary to assure the success of the attack.
A battle usually does not take place unless each side believes it has some chance for success. Otherwise, the attacker would avoid taking the initiative. The defender, if he could not avoid battle by withdrawal, would make every possible effort to reinforce the prospective battle area sufficiently to have a chance for successful defense.
One circumstance in which a battle occurs without the tacit agreement or acceptance of the defender, is when the attacker achieves surprise. Alternatively, surprise by a defender (for instance, by ambush) may result in a battle taking place before the prospective attacker is ready.
Most military men are aware of the rule of thumb that an attacker can count on success if he has a three-to-one numerical superiority, while a defender can expect success if his inferiority is not less than one-to-two.
But the side achieving surprise can count on the effects of surprise multiplying its force strength by a factor ranging between 1.5 and 2.5 (or even more in some cases). Thus, an attacker expecting to achieve surprise would be willing to attack with less than a three-to-one superiority.
Another factor which can influence an attacker to seek battle with less than a three-to-one superiority is confidence in the superior quality of his troops. This accounts for many instances in which the Germans attacked in World War II with less than the desirable numerical superiority, and for the similar instances of Israeli attacks in the Arab-Israeli wars without great numerical superiority.
That's why I said the battle tactics are more important, and the actual terrain and fortress in question. 5 people could overtake a fort if they were sneaky enough.
A lot. At Monte Cassino the German strongholds withstood even American super heavy artillery. They had to be taken by the infantry. Artillery does not fight. It never did.