Cache stampede prevention: probabilistic vs mutex-based approaches

we've had a few incidents recently due to cache stampedes, where multiple processes try to regenerate a popular cache key simultaneously when it expires. we've discussed two main approaches: mutex-based locking, where only one thread/process is allowed to rebuild the cache, and probabilistic early expiration, where a small percentage of requests get a slightly stale cache entry and trigger an async refresh. mutex-based adds latency for the threads waiting for the lock. probabilistic doesn't fully eliminate the problem, just reduces its likelihood. another option is background cache warming for our most popular keys. what's your go-to strategy for cache stampede prevention in high-traffic scenarios? i'm looking for practical insights into which method works best under what conditions and their respective performance characteristics.