Actually, in first Chechen war during the assault of Groznyj, Russia suffered quite a defeat at first phase - they had sent tanks without any cover and without re-active armour. Lots of those were destroyed by RPG fire.
However, when there was more order and apropriate tactics and technology was used, the city was taken with not so high losses.
They also started sending in mobile AA with the tanks and APCs. The tanks main gun didnt have enough elevation to hit the chechens that were two, three, four floors up because of the confined spaces of the streets. They chechens would fire at the russians from a side street off the wide main roads to get the russians to chase after them. After they drew the column into street they would use multiple teams of 3 of a sniper, machine gunner, and rpg gunner to attack the formation. One of the best books on chechen and russian tactics without any bias is "Russia's Chechen Wars 1994-2000 Lessons from Urban Combat" by Olga Oliker. It was written for the US Military. I found my copy on Amazon.com for $10.
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