Solved Games and Luck

You may hear, or not, someone talking about a form of competition, primarily games, being “solved”. Examples are Tic-Tac-Toe, Connect 4, and Checkers. What does being “solved” mean. There are different kinds of solved games. Some like Tic-Tac-Toe, are easy to show an algorithm, or what response to every single move, a player should make to perform perfect play which will always force a win or draw (draw in the case of Tic-Tac-Toe). For easily solvable games like Tic-Tac-Toe, it makes game play very boring as anyone out of elementary school can pretty easily see the perfect drawing strategy. Connect 4, is also mathematically solved as a win for whoever goes first, but I’m not sure if many people know the whole algorithm in their head. However even without knowing the exact algorithm, many people will win every single time they go first, just with a general strategy and reacting on the whim to how their opponent plays. So even with people not knowing the algorithm, the game may still be unenjoyable due to inherently low skill cap of the game. Not many people know this but the game checkers is actually solved, it took something like 15+ years with 200 computers, so there’s no way no one out there actually knows perfect play and therefore the fact that it’s solved is not relevant to many.

What about games with luck? A game with luck can not be “solved” in a sense that a certain player can force a win or draw with perfect play. This is because even with perfect play, luck is outside of anyone’s control and cannot ensure anything. However, there is still the concept of “optimal play”. Games like Solitaire or King’s Corner are examples of easily found optimal play but luck involved. So solitaire has pretty easily discoverable best strategy, yet there is no way to guarantee a win due to randomness of starting position (there’s actually only one game that is un-winnable of the millions in Windows version of Solitaire now that I fact-checked it, not sure how it applies to real life solitaire though. Hope you still got the point though). This concept of losing despite perfect play may frustrate many and put people off from certain games. People will even insult a game for “having too much luck”. I believe this is a big indicator of what certain people want in a game: competition or fun. If someone is hyper-competitive (me), then they want to minimize the amount of luck so skill accordingly is increased. On the flip-side, many people just play games to have fun, and luck is a big factor of that. This is the reason gambling is such a profitable business (maybe I’ll touch on that and how it dances on the border of “competition” in another post). You see examples of this in video games where “party games” are very luck-oriented but when people turn the games competitive, such as Super Smash Bros. Melee for the Nintendo GameCube, they try to eliminate all types of luck throughout the game to maximize skill and competition.

The question of whether a game is solved or ever can be may seem trivial to you but many people are excited by this question for the games they love. A prime example is chess. As of right now computers, even on phones, can consistently beat the world’s greatest chess players. While we can make computers that are unbelievably talented at chess, humans are nowhere near close to mathematically solving the game and it’s a debate as to whether it will ever happen or not. I’ve heard that many chess grand masters believe the game will never be solved, but I think it’s just because they have so much pride in their own intellect they think no computer could fully handle it (/s). No one knows whether the solution would mean white (first player) wins every time, draw every time (most probable), or even black wins every time (that’d be crazy).

We only hear of "games" being solved, usually card or board games, but what about video games or sports* (*what is a sport anyway?)? The concept of "perfect play" and solutions being brought out of the theoretical algorithm-based mathematical world and into the physical world brings up way too many questions that I really don't want to answer. However that doesn't stop anyone from trying to achieve that perfect play and optimization.

Who knows though, maybe there will be a team of fast reacting and all physically capable robots that the Super Bowl winner will have to play against at the end of the season every year. Probably not but that'd be entertaining.