Hello Jano, conceptually it is as you say, but the reality is a bit different:
1) For a cluster where each master has two replicas (just an example)
to be down, you don't need any three random nodes to be down, but they
must be the master and its replicas. The larger is N, the less likely
is that if three random nodes fail they are all related (master and
its slaves).
2) P, the probability of nodes failing, is small compared to the
greatest intended N for Redis Cluster, which is at max 1000.
3) Single node failures are (unlike partitions) unrelated events that
hardly happen at the same time. So even in a network with a very high
P (unreliable hardware), using the Redis Cluster feature know as
"replicas migration", multiple failures can occur one after the other
and the additional slaves will migrate to the orphaned masters, making
the real world availability much better than the theoretical one,
which is instead computed in terms of multiple simultaneous failures.
So about 3, if you have 100 nodes with 1 slave each, but then you
attach 10 additional slaves to a single random master, as failures
will continue to happen and masters non backed by slaves will be
created as a result, the additional slaves will migrate to the
unbacked masters in order to protect them.
Cheers,
Salvatore