The Standoff
After the battle, Akhmat then retreated to the town of Vorotynsk, where he decided to wait for Casimir's army. Ivan III moved his army to Kremenets and started to negotiate with the khan, in an attempt to buy some time to restore his relations with his rebellious brothers (hence, the Great standing on the Ugra river). It took Ivan III four days (from September, 30 to October, 3) to reconcile with his brothers and another 17 days (until 20 October) for his brothers' armies to arrive at Kremenets. Unlike Dmitry Donskoy in a similar situation one hundred years before, Ivan decided not to cross the river, but to keep on his shore and bide his time.
Watching the increasing Russian army and receiving no word from the Polish king, Akhmat chose not to attack the Russians. In the meantime, Casimir IV was dealing with his own country's internal affairs and fighting with the Crimean Khanate. The Mongols waited for reinforcements until November 11 and then, lacking supplies and suffering from epidemics and freezing weather, turned south. English sources say that Akhmat was waiting for the river to freeze so that it could be crossed, and for the arrival of Lithuanian forces. These did not arrive because of Crimean raids and internal troubles in Lithuania. He turned south due to the onset of winter and the possible threat of Crimean, Nogai or other attacks on his unprotected home base, a common problem in nomadic warfare.
Tatar retreat was seen as victory in Muscovy. Ivan and his armies returned to Moscow to celebrate. As Nikolai Karamzin wrote in his "History of Russian State": "It should be an odd image: two armies ran away from each other, not pursued by anyone".
Read more about this topic: Great Stand On The Ugra River