Stephen Tavener has made a program called AiAi that plays some hundred abstract games, including the top-ten combinatorial ones at BGG from 2012 onwards.
It's a great tool to learn new games and the Ai opponent covers the whole range of levels, depending on the type of game (in the first place) and the setting of strength and thinking time.
A really important feature is that it allows human vs human play without the use of a browser. As I write I write, there 22 registered users and I expect that number to grow because hey, it's a great program and it's free!
Actually I don't know how strong the Havannah player is, but the program is generic and it's a connection game, and traditionally that combination is seldom very strong.
Rex, you can also play live with AiAi, just stay both at the keyboard. :)
One thing I can't figure out is how to review the moves of a completed game. Even though the "History" tab lists all the moves, there doesn't seem to be any way to actually play them out on the board again other than writing them down and redoing it manually. Am I missing something obvious or is this just a missing feature?
Anybody else on Windows struggling with "JNI" errors / Java exception when running AiAi? I muddled through the installation process for OpenJDK to try and use this, sigh...