IIRC the rules have a second solo variant as well, where you line up the cubes so that you know what is coming. Haven't tried that one yet though. In the basic solo rules you're drawing 3 cubes and keeping 2 each round. You lose the cube stacking/choosing aspect of multiplayer, but it's still thinky and very fun.
The cube lineup one is a pain, but a wonderful puzzle. I love this game solo, I've been tempted to draft the lineup of cubes, try to plan my order out to see if it makes a difference at all.