Battle of the Little Bighorn
Part of the Black Hills War, Indian Wars

Date: June 25 – June 26, 1876
Location: Near the Little Bighorn River, Big Horn County, Montana
Result: Native American victory

Combatants:
Lakota, Northern Cheyenne,Arapaho v United States

Commanders:
Sitting Bull,Crazy Horse v Lt. Col. George Armstrong Custer

Strength:
Native Americans - (949 lodges), probably 950-1,200 warriors.
7th Cavalry - 31 officers, 566 troopers, 3 civilians, ~35-40 scouts

Casualties:
Native Americans ~200 killed (according to Yellow Horse, Red Horse and Little Buck Elk)
7th Cavalry ~268 killed (16 officers, 242 troopers, ~10 civilians/scouts), ~55 wounded

"Within roughly three hours, Custer's force was completely annihilated. Only two men from the 7th Cavalry later claimed to have seen Custer engage the Indians: a young Crow whose name translated as Curley, and a trooper named Peter Thompson, who had fallen behind Custer's column, and most accounts of the last moments of Custer's forces are conjecture. Lakota accounts assert that Crazy Horse personally led one of the large groups of Lakota who overwhelmed the cavalrymen. While exact numbers are difficult to determine, it is commonly estimated that the Northern Cheyenne and Lakota outnumbered the 7th Cavalry by approximately 3:1, a ratio which was extended to 5:1 during the fragmented parts of the battle. In addition, some of the Indians were armed with repeating Spencer and Winchester rifles, while the 7th Cavalry carried single-shot Springfield carbines, which had a slow rate of fire, tended to jam when overheated, and were difficult to operate from horseback.

The terrain of the battlefield gave Lakota and Cheyenne bows an advantage, since Custer's troops were pinned in a depression on higher ground from which they could not use direct fire at the Indians in defilade. On the other hand, the Lakota and Cheyenne were able to fire their arrows into the depression by lunching them on a high arching indirect fire, with the volume of arrows ensuring severe casualties. U.S. small arms might have been more accurate over open distances, but the fighting on this occasion was close combat where rate of fire and reliability of a weapon were more important attributes."

Source - http://en.wikipedia.org/wiki/Battle_of_the_Little_Bighorn

By the bye Little Hawk as you do not bother to check things, and for the sake of accuracy the Officer Commanding at Rourke's Drift was Lt. John Rouse Merriot Chard, Royal Engineers.

Custer's men fired few bullets because of the early type of fixed case ammunition supplied for the 1873 model Springfield Carbine had a copper cartridge. A serious flaw, if the gun had to be fired rapidly over an extended period the copper cartidge case would expand due to the heat of the breech causing the gun to jam, this problem disappeared when brass was used for the cartridge case. To give the impression that the Indians were better armed is erroneous, although some were armed with better rifles the majority were armed with lances and bows and arrows, the latter seemed to have done the damage. Custers men ill-disciplined, badly trained and very poorly led. Even armed as they were, in the position occupied, they only needed to form up in close order to repel a vastly superior force, deployed as Custer's men were, in extended skirmish lines they did not stand a chance as at no time could fire be concentrated, i.e. it was virtually everyman for himself from the outset.

In terms of studies there are two actions fought by British troops (Infantry) that should never have turned out the way they did. The Guards action in defence of Hougemont during the Battle of Waterloo and the defence of Rourke's Drift. The troops at Hougemont and at Rourke's Drift were the opposite of those Custer commanded, they were professional soldiers, highly disciplined, very well trained and in the actions mentioned well led.