I'm not sure it would work. You'd have to set the chance of getting a "correct" number pretty high to get any bot to respond at all, but then you've also got a very good chance for multiple bots to respond.
It's the birthday paradox at work.
http://en.wikipedia.org/wiki/Birthday_paradox
I would be really annoyed if 2 or 3 bots replied with an answer every time a question was asked.
Just go with token ring. You're trying to do ethernet...
On the subject of auction bots: You don't need somebody to spend all day in the AH. (I'm sure there are those people though!) All you need is to tie a side-channel broadcast to the auction house events. As soon as you go to the AH, you notify all bots you're there.
You'd need to create an enhanced whisper function that takes "symbolic" player names. The bot could keep track of the symbol -> player mapping. Actually that would be kind of cool in general. It would be nice to have 1/2/3/4 for party members. "/w 1 ..." would whisper party1.