Cache eviction: when are randomized algorithms better than LRU?

Once upon a time, my computer architecture professor mentioned that using a random eviction policy for caches really isn’t so bad. That random eviction isn’t bad can be surprising – if your cache fills up and you have to get rid of something, choosing the least recently used (LRU) is an obvious choice, since you’re more likely to use something if you’ve used it recently. If you have a tight loop, LRU is going to be perfect as long as the loop fits in cache, but it’s going to cause a miss every time if the loop doesn’t fit. A random eviction policy degrades gracefully as the loop gets too big.

In practice, on real workloads, random tends to do worse than other algorithms. But what if we take two random choices and just use LRU between those two choices?