Warmatrix

The battle of Mobei, fought in 119 BCE, was part of the Han-Xiongnu War. The Han, fed up with Xiongnu raids along their northern border, launched a few grand military campaigns into Mongolia. The nomads did what they always did when confronted with a superior force: they simply retreated to the north of the Gobi Desert, calculating that the barren land would deter any further advance. But the Chinese were determined to score a victory, set up a massive logistic organization and followed their enemy.
The Chinese army was very large: 100,000 cavalry and 200,000 infantry according to Chinese historians, though in reality it was probably three times smaller. It advanced in two columns of equal size, the primary under general Wei Qing and the secondary under his nephew Huo Qubing. The Han emperor Wu favored the younger general and had assigned the best troops to him, hoping that he would use them to crush the main force of the Xiongnu chanyu. He was originally advancing on the western side, but false information from a captured warrior led the Chinese to believe that the main Xiongnu army was in the east, so the emperor ordered the two armies to swap places. Huo Qubing met a Xiongnu force, led by the Xiongnu's Worthy Prince of the East. He quickly defeated it in a straightforward battle, suffering 30% losses, which were quickly replaced. Next he went on and chased the remaining enemies as far as Lake Baikal.
The tactically more interesting battle was fought on the western side, between Wei Qing and chanyu Yizhixie. The Xiongnu were waiting for the enemy and tried to ambush them. Wei Qing's troops were tired from the march, but he organized a defense by arranging his heavy chariots in a ring. From it, archers shot arrows and cavalry made sorties to drive off the nomads. The result was a stalemate. When dusk fell, a dust storm rose up. Instead of bunkering down, Wei Qing used the poor visibility to sneak out and attack the Xiongnu with a pincer movement. Tired and frightened by the surprise attack that seemed to come from all sides, the nomads quickly fled. Yizhixie himself only barely escaped. Wei Qing killed far less enemies than Huo Qubing, though probably also suffered less casualties on his own side. After the battle he too pushed on into central Mongolia, killing and displacing enemies. Yizhixie lost contact with the rest of his forces for so long that the Xiongnu thought that he was dead and installed a new chanyu.
The battle(s) of Mobei was/were not decisive and the campaigns cost the Han a lot of money, many men and even more horses. However the nomads were pushed back from fertile grasslands into the Gobi desert and suffered even more. It weakened their position and for a time gave the Han the advantage over them.