While your question would be highly classified by both the U.S. and the Russians, I am just going to guess the Russians do not attempt to hunt for boomers. Boomers are the Navy’s ballistic missile submarines. They serve as an undetectable launch platform for submarine-launched ballistic missiles (SLBMs). These submarines are designed for stealth and the precise delivery of nuclear warheads. They rely on stealth to hide from rival boats, ships, and sub-hunting aircraft. The subs were designed to remain underwater for months at a time, using stealth so that potential enemies would never know where they were or where they could strike. Boomers are highly stealthy, and they are maneuvered and located in places where detection would be very difficult like under the polar icecaps. They will sit for months at a time under the ice where finding them would be beyond difficult.

On the other hand, America has ten aircraft carrier strike groups. Russian attack submarines follow each of those aircraft carrier strike groups. The Russian attack submarines are armed with nuclear torpedoes to take out the aircraft carrier groups. It is almost comical, there is an American attack submarine assigned to follow the Russian attack submarine. In case of an ultimate incident, the American attack submarine would hopefully take out the Russian attack submarine before it was able to launch its nuclear torpedoes.

“The United States Navy has a total of 64 submarines, which include 53 fast attack submarines, 14 ballistic missile submarines, and 4 guided-missile submarines. “

“ Russia has an estimated total of 64 submarines, which includes 16 nuclear-powered ballistic missile submarines, 14 nuclear-powered attack submarines, and various other types. “

128 submarines in total….
Do you know HOW BIG the oceans are????
Ballistic missile submarines, and guided-missile submarines are just floating around waiting for launch orders.
Fast attack submarines would be looking for surface ships.