(1) Maybe, but we lose the entire element of surprise going for the gate at all which is why I didn't mention it this time when I suggested a night attack. It's more effective to just kill the sentries and climb the walls quietly to take out the defenders as they sleep then to open the gate to let our men in and wake up every soldier in the castle in the process forcing a fight. We then have to storm the fort against alerted men and fighting close quarters inside a building isn't what we're trained for.
(2) Either way it's only going to be our men in the fighting so why open the gates at all? We have ladders we can get 50 men onto the wall in a couple of minutes with no need to go near the gates at all and it maintains the element of surprise for us to use.
(3) Also, how does it half the chance? Our men go in different places and so have to sneak past a larger number of sentries, being 2 smaller groups doesn't make any difference if you have to get past twice as many people. Thats twice as many sets of eyes to spot one of those groups.
1. The gate is our objective. It was said in the mission statement. Killing someone is not completely silent, even marksmen such as ours cannot instantly kill sentries simultaneously in the middle of the night. No matter what we do, we have to open those gates.
2. Opening the gates gets our men inside the castle faster than using ladders all around the fort. You yourself just said that it was an increased chance of detection with more men, so sending 50 with ladders is not going to raise the alarm? It takes more than a few minutes to run 100 yards, prop the ladder against the wall, then climb up it. All the while, the sentries are watching. Even if we send five men with each ladder, it would still take at least ten to fifteen minutes to get all of them on the walls, and then they're spread out.
3. Yes, smaller groups do make a difference. The human eye sees motion in darkness, so the less movement=less detection. As well, having two sets of men increases
the chance of success as one getting caught wouldn't affect the other group.