Knowing not so much about Tor but some about math: the number of nodes you need to compromise in order to de-anonymize a Tor user is exponential in the number of hops. Google says there are roughly 7000 Tor nodes, including 2000 guards (entry) and 1000 exit nodes. If you have a single hop, there's roughly a 1/1000 chance that you will connect to a single malicious node that can de-anonymize you, going up linearly with the number of nodes an attacker controls. If you have 3 hops, you have a 1 in 1000 * 7000 * 2000 = roughly 14 billion chance. 2 hops would give you 1 in 2 million, 4 hops would give you 1 in 1000 * 7000 * 7000 * 2000 = 98 trillion. In practical terms 1:14B is about the same as 1:98T (i.e. both are effectively zero), but 1:2M is a lot higher.

There are currently ~9000 relays if you look at https://metrics.torproject.org/networksize.html. The current problem is the fact that majority of relays are in Germany and if you rotate your circuits enough, you'll also notice the same path. German govt has been very hostile towards Tor for a long time, they were also behind KAX17. We need more relays obviously but also in different regions.

1 = no privacy from relay

2 = risk of collusion between relays

3 = goldilocks default

4 = ... actually, you have more attack surface and you are more susceptible to fingerprinting because everybody else is using 3, so you're timings etc help identify you

So the default is 3 and nobody ought change it! Use 3 like everybody else.

The exception is .onion sites. TOR actually deliberately defaults to 6 hops when accessing .oninon sites - 3 to protect you and 3 to project the site.

There's no exit nodes for onions because there's nothing to exit to. Nothing beats anonymity of onions and it's design is well created.

The right number for you to use is the default. But the right default is not necessarily 3.

That reminds me of the holy Handgranate of the Monty pythons

because then there is at least one node that knows neither the source nor the destination of a request

The law of diminishing returns