Custer wasn't dumb. He was quite able and his decision to not bring gatling guns or artillery with him on patrols is quite rational. The typical native nomadic camp usually had 30-100 fighters in it. They moved around a lot over a patrol area that was massive. Even with horses, covering it and finding the native population was difficult. It required speed, knowledge of which water sources were drinkable and which were alkaline. It required luck as well.
Gatling guns and cannon would be required to keep up with the cavalry. This just was not possible given the wilderness areas that needed to be traversed. He would have had no success with his patrols without speed. Often the patrols needed to operate for as much as 72 hours straight to make contact.
Finally, there was a change in the native tactics in the month leading up to Little Big Horn. The population of natives had accepted a spiritual prophesy by Crazy Horse. It was a very rare occurrence. The small groups started to find each other and form larger ones. The Battle of the Rosebud just prior to the Big Horn showed the natives were now fighting back harder. An interesting intelligence failure is that the behavior change wasn't reported. It would have been expected to be reported but there were various personal and inter-cavalry reasons why it wasn't.
When Custer came across the main body he was running on no sleep for days. His wings were sent out to flank. He didn't realize he was striking a force 100 fold greater in size than the average previous encounter. In the distance you see the encampment but you can't judge how big it really is other than larger than normal.
The normal engagement tactics took into account the fact that the natives would flee upon first contact so if you were going to defeat them you needed to hit them quickly from multiple sides and then combine, stand, and fight. These tactics worked for 11 years.
Those tactics worked with the Springfield single shot rifles the Army used against the aged rifles the natives often had. However, due to the prophesy, the natives started to gather much more advanced weapons. They had a mix of repeaters and longer ranged rifles. They typical 7th cavalry load was 15 rounds of ammunition.
Two more factors: about 15% of the 7th Cavalry were warriors in that they were trained, dedicated, and ready to fight. The Army wasn't a great deal in 1870's. That fact meant it drew in people who had little other choice and who were ready to desert their post if they could when they got what they wanted (usually just being moved out West where there was opportunity).
The final intelligence failure is that the attack was launched without advanced scouting. This meant that, not only was the size of the encampment greatly underestimated, but that the topology of the land wasn't appreciated and that the plan of combining the wings back on the center just wasn't even possible in the timespan of the battle.
However! If they had done the scouting. If they had known that the natives were standing their ground. This intelligence would have been useful. It would allow for a scouting party to find the main body and stick with it, sending couriers with detailed information. As it was, they weren't going anywhere. This was a gigantic festival for the natives and they were going to be there a while.
However a great Centennial defeat of the natives would have required a force that probably didn't exist in the West at that time. Even larger battles that would follow such as the Dull Knife Fight, only created minimal casualties. In order to defeat the natives the Army could either do what it did which was a slow hunting of remaining groups or the development of faster deploying support firepower. That would have required a lot of innovation.
I think this game will be a fun What-if!
