+ Show Spoiler [DISCLAIMER] +
Once again I am posting something that may result in some hate. If your first thought is some variation of "lol u dont no wat ur talking about", you're probably right and feel free to say so. But I love abstracting things and I wanted to share. <3
When I was in middle school, I prided myself in knowing that I would never lose a game of tic-tac-toe for the rest of my life. I could be playing the smartest person in the world, but guess what? I won't lose. Why? Because of this simple fact: if two people play perfect tic-tac-toe, the game will end in a draw. If you're organized and you have a free hour, it isn't too hard to prove this by playing out every possible game (up to rotations and reflections). If you do this, every time a friend asks you to play tic-tac-toe, you can say, "We might as well agree to a draw and save the time!" The game is all figured out.
A similar game is Connect Four. Though it would probably take more than an hour to prove it by hand, it turns out that the first player can always force a win with perfect play. No matter what moves the second player picks, the first can always find a response that leads to a win. So next time you play Connect Four and your opponent asks, "You want to go first?", you can say, "You could've just asked me, 'You want to win?'" The game is all figured out.
In July, 2007, the game of checkers was solved. More specifically, it was found that if two perfect players sat down for a game of checkers and played perfectly, then the game would result in a draw. Stated another way, a perfect checkers player cannot lose a game. Though you probably can't prove this in an hour either (PM me if you can, we'll write a paper), if your uncle asks if you want to play checkers, you can safely say, "We might as well play tic-tac-toe!" The game is all figured out.
Jonathan Schaeffer, wrote Chinook, the program that solved checkers
There are still other games like rock-paper-scissors, whose "perfect play" is simply to roll the dice. No matter how much your brother might insist that he has a perfect system for playing a rock-paper-scissors best-of-5, it is complete nonsense. In fact, for any strategy that does not rely on randomness, there exists another strategy that will beat it. Just last week my brother and I were fighting over who should bring out the trash, and he challenged me to a best of 7. (Really, 7.) I really did say, "We might as well toss a coin." The game is all figured out.
I'm a chess player myself: what am I to make of this game? At the time of this post, chess has not been solved in the same way as any of the above games. Chess computers have existed for decades, but it could be decades more until the technology exists to map out this game, if that ever happens. When I look at a chess set, I am afraid of the game. I am scared of the uncertainty of winning and losing. I am scared of being caught in a trap laid by a better player. I am scared of staring at an endgame, knowing that every possible move is a losing one. I am scared of the thought of driving home from a chess tournament, crying because I'm so pissed off at myself, after some cute high school freshman girl just so happens to be rated 200+ points more than me and knocks me out in the first round (hypothetically). If a chess grandmaster asked me to play a game of chess with him/her, anything could happen. Maybe I'll get some divine insight into a particular position that he/she never considered before and I'm able to take a game from him/her. After all, he/she can't play perfect in every position, or the game would be solved! But in the same way, if my little brother challenged me to a chess match (which unfortunately never happens), I can't be sure I'll win all the time, no matter how much better I think I am, for the same reasons. In both instances, I can only say, "Alright, let's play," and do my best. The game is not all figured out.
Kasparov vs. Deep Blue, the iconic man vs. machine chess match
I was looking at my Starcraft: Brood War battle chest box the other day, running through some thought experiments. What would happen if a "perfect" Protoss player played a "perfect" Zerg player on some theoretical, "perfect" PvZ map? Trusting in BW's balance and taking checkers as the model, I imagined some 5-hour long game: with the money long gone from the map and both armies having killed each other, the game resorts to probe vs drone micro, culminating in the P's last pylon and the Z's last extractor falling at the exact same time. Then the P and the Z would look up at each other, smile, and say "gg, re?". Taking this analogy a bit further, what would a game between a perfect P and an imperfect Z look like? Well, by definition, the Z would make a mistake somewhere. Maybe he missed his 184/184 overlord by 0.5 seconds. Maybe he mismicroed during a crucial battle and lost an extra zergling. Maybe the Z's building placement was wrong so the drones took a little too long to get to the mineral patches from the eggs. In any case, the result would be the P gaining some sort of advantage that compounded across the rest of the game, and, since P's play is perfect, Z could do nothing to come back due to that one mistake. Indeed, if the Z could make a mistake and still break even with the P, then a perfect Z who did not make this mistake would have to beat the P, or else it wouldn't be a mistake made by the imperfect Z, in which case the balance of PvZ is contradicted!
But maybe our faith in BW is in vain, and PvZ is, in fact, imbalanced: maybe perfect Protoss play can always adapt and beat any variation a Zerg might try, just like in Connect Four.
Or worse, is PvZ like rock-paper-scissors, where perfect play would simply be rolling the dice? After all, you can't guarantee perfect information in any matchup at all times, so perhaps a matchup between a perfect P and a perfect Z would just be both sides randomly choosing a percentage build? Is PvZ and BW in general just a glorified coin toss at the level of perfect play?
Personally, I hope BW is like chess, and will never be "solved" (at least not in the foreseeable future) in the same way that any of the other above games are, constantly evolving as new ideas are continually brought to progamer matches (and elsewhere!). Chess has been around for centuries, and yet the game is still alive: books are still being written about various openings and systems, tournaments are still being held all around the world, and I still get a copy of Chess Life every month. Perhaps it is because chess is so resistant to our attempts to figure it out that it remains so interesting even now. Young child prodigies, senior citizens, nerdy college BW players, pretty high school girls... no one is immune to the calling of this mysterious mental challenge. But what happens should a breakthrough in computing allow technology to beat chess? Presumably interest would decrease as the curtains open and the lights shine on what was once a seductive enigma shadowed in uncertainty. Is it too much of a stretch to compare this with BW? I, at least, have maintained interest in such a (relatively) old game only because it feels like there is always something more to be understood about the game, even for those progamers that spend hours daily learning about it. Perhaps the game has survived this long only because of this apparent lack of a limit to what can be achieved by playing it.
I sincerely hope that, when I'm old and wrinkled, chatcrafting in the Bnet 2.0 op irc chat channel, if someone asks me, "hey FiBsTeR want to 1:1 in bw?", I'll have no choice but to respond, "gogo!".
+ Show Spoiler [Addendum] +
After talking about "solved games" and "perfect play", I feel obliged to post some game theory related problems. If anyone else has any good ones, please post them!
 Consider a game called "double chess" in which the rules are all the same except each player is allowed two moves per turn. Prove that the second player cannot force a win.
 There is a circular table and a large pile of quarters. You and a friend take turns placing quarters on the table, such that no two quarters overlap. A player loses if he/she cannot place another quarter on the table. Do you want to move first or second?