I've been playing a bit with creating a 3d tic-tac-toe game for the website. Turns out that it wasn't horrendously difficult to program, but I forgot how easy it is to win. There are a variety of popular handicaps. A popular one is to remove/disable the center square on the second level. This makes it marginally more difficult to win easily. Another popular tweak is to turn it into four-square (4X4X4) which also removes the center spot advantage. I haven't yet decided which tweak to go with, or figure out if I can balance the odds even further.
You can try it out at here, but be advised that I've still got a lot of work to do, and it still has some bugs.

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As of this morning you can still win without thinking too hard - but I just made it a bit more challenging. The computer player will now nab the center spot if it's available (though you still have the first move). There is also a 'handicap' mode that removes the center spot from the game.
The computer player is still pretty dumb. It's mostly playing a defensive game, and isn't really doing any strategic planning.
'The computer player is still pretty dumb. It's mostly playing a defensive game, and isn't really doing any strategic planning.'
...Yet. I've figured out some really killer 3d-t-t-t strategies. Now I just have to translate them into something that can be parsed by a machine.