I have three computers: MY box, FRIEND box and SERVER box. I know the following: MY ping to SERVER box. FRIEND ping to MY box. Is there a way to "guestimate" the ping from FRIEND to SERVER without directly pinging the two? I thought a ratio might work like so: MY pings 100 to SERVER. FRIEND pings 80 to ME. FRIEND will ping 90 to the SERVER. Is that a sufficient guess?

If we assume that your box doesn't route anything, then (from what you mention) we don't even know if FRIEND is connected to SERVER, let alone what manner of latency that connection may have.

It's reasonable to say that in all likelyhood, it's less than the sum of those two numbers.

Other than that, it's all guessing.

Not that it's likely very useful, but the results of a tracert may identify common routing nodes, which, if they exist, will allow you to reduce the likely upper bounding estimate. For example if your friend takes 1s to reach node X and 2s to reach you, and you take 2s to reach node X and 4s to reach the server, then your friend should ping <= 3s to the server (1s to X + 2s from X to server).

Tracert's are expensive though. Maybe there's a faster way to identify the route nodes?

I doubt very much, however, that you could obtain this estimated ping faster than you were able to obtain a real ping value directly from your friend to the server.