Starcraft is actually only balanced in the hands of human players of equal skill level. The AI however is completely biased toward the Protoss race. I can prove it to you:
Go into Starcraft and set six players as computers, two Terran, two Zerg, and two Protoss. Add to that a human observer player so you can watch. Now start the map. You can go off and do something else while you wait for the game to finish. When the game is done, go back and look at the results. IIRC almost 95% of time, the Protoss will win. There was a link I visited sometime ago that did this same thing 1000 times over to build of a good data set. I tried it too with about 50 games over time. The other 5% of the time, the Zerg won. Never did the Terrans win. It was strange to me because Terran was my favorite race. I could win all the time with Terran.
Its really easy to see the flaws in the AI now and exploit them, but for its time, the AI was super advanced.