A December 1956 cover feature article in Radio-Electronics magazine describes "Relay Moe" which plays tic tac toe with adjustable levels of skill. It used 90 relays.
<https://www.vintagecomputer.net/cisc367/Radio%20Electronics%...>
Here is the full text, for discussing with agents:
https://archive.org/stream/RadioElectronics195701/Radio%20El...
This is a subject dear to my heart. I'm a mathematician who routinely uses symmetry in counting problems. As a kid I remember writing out a tic tac toe game tree in about ten pages. I must have used symmetry, and I must have only mapped a winning strategy, not all 765 game states up to symmetry.
So my first reaction to now reading that Bertie the Brain used "addition tubes" was "Really? Can't you do that with relays?" And the reality is that Bertie the Brain was a solution looking for a problem, a demo project for these tubes, not an attempt at the simplest way to implement such a machine.
Still, looking at the numbers, I'm impressed that Relay Moe managed multiple levels of game play using only 90 relays. The design exploited symmetry.