Why knowing that a solution exists is not the same as knowing what to do
When we say that a game is “solved,” we often use the term loosely. Sometimes we mean that the outcome is already determined. Sometimes we mean that an optimal strategy exists. Sometimes we simply mean that an experienced player has seen the same situation so many times that the correct move feels obvious. Those are very different conditions, and the distinction matters because a game can have a solution without that solution destroying the experience.
The important question is not simply whether a game can, in principle, be solved. Almost every game asks players to move through a space of possible situations, and some of those spaces are small enough to analyze completely while others are far beyond what a human player can calculate. What matters to the experience is the relationship between that solution and the person sitting at the table: whether they can find it, understand it, remember it, and apply it while the game is actually happening.
That is where solvability and mastery begin to separate. A player can become much better at solving the situations a game presents without ever reducing the entire game to a known sequence of correct moves. In fact, many of the games with the greatest room for mastery are interesting precisely because players keep learning to solve more of the game without ever feeling that they have solved all of it.
A predetermined outcome is not the same as a solved decision
Consider the card game War. If the deck is dealt once and the cards are never reshuffled, the sequence of future cards determines the outcome from the beginning. The players do not know that outcome, but they also do not make meaningful decisions that can change it. They reveal a result that is already embedded in the deck. Calling this a solved game would miss the point, because there is no strategic problem for the player to solve in the first place.
Tic-Tac-Toe is different. It contains genuine choices, but its decision space is small enough that optimal play can be described completely. Once both players know what to do in every relevant position, neither can force a win against the other. The game has not become predetermined in the same sense as War; the players are still choosing moves. What has changed is that the strategic question can be answered in advance.
We can see the distinction even more clearly if we modify Snakes and Ladders. Imagine that instead of rolling a die, a player may choose any number from one to six on every turn. Suddenly there are decisions. From each space, the player must decide which destination is best. But because the board is finite and the consequences of each move are known, it is possible in principle to calculate the optimal choice from every position and construct an algorithm that tells the player what to do. Even if nobody at the table has performed that calculation, the structure of the game makes such a solution possible.
This gives us a useful distinction between a game that has been solved and a game that is solvable. The first describes the state of our knowledge: someone has actually found a solution. The second describes the structure of the problem: a solution can exist and be found, even if we have not found it yet.
The size of the solution matters
The fact that a game has been solved tells us surprisingly little about what playing it feels like. Tic-Tac-Toe and Checkers can both be described as solved games, but the scale of the achievement is completely different. The solution to Tic-Tac-Toe is small enough for an ordinary player to learn and apply. Checkers required enormous computational work to establish the result under perfect play, and knowing that result does not suddenly give a human player the ability to play every position perfectly.
This exposes an important gap between a theoretical solution and a usable one. A decision tree may exist, but that does not mean I can hold it in my head. A computer may be able to search millions of possibilities that I cannot meaningfully evaluate. Even when the relevant pattern is learnable, recognizing it under time pressure and applying it correctly can require substantial skill.
Chess makes the spectrum especially visible. Chess as a whole has not been solved, but individual positions often can be. A player may recognize a forced checkmate several moves ahead, and at that moment a small part of the game has effectively collapsed from an open decision into a known sequence. That does not make the game less interesting. On the contrary, spotting the sequence is part of the satisfaction of becoming better at chess. The next game will produce different positions, and the player will have to recognize different patterns and solve different local problems.
So the meaningful design question is not whether a solution exists somewhere in the abstract. It is how much of that solution is accessible to the player, and how quickly repeated play turns uncertain decisions into familiar ones.
Mastery is learning to solve more of the game
A Rubik’s Cube is a useful example because the puzzle is thoroughly understood and reliable solution methods can be learned, yet people continue to practice it for years. Once someone knows an algorithm that can return the cube to its solved state, the challenge does not necessarily disappear. They can become faster, recognize states more efficiently, reduce unnecessary moves, improve execution, and learn more advanced methods. The existence of a solution creates a path toward mastery rather than automatically ending it.
The same principle appears in competitive games. A stronger player has effectively solved more situations than a weaker one. They recognize patterns sooner, understand which options are irrelevant, anticipate consequences farther ahead, and know which apparent opportunities are traps. If I played against a world-class chess player, the game might be painfully one-sided, but not because chess itself has been solved. The gap would come from the fact that my opponent has internalized solutions to far more of the positions and patterns that arise during play.
This is one reason the number of rules is a poor measure of how difficult a game is to master. A game can have very few rules and still create an enormous space of meaningful choices. Once the rules are understood, the real learning begins: which possibilities deserve attention, which patterns repeat, which risks are acceptable, and which move is best in this particular situation. Mastery is not simply remembering more rules. It is becoming better at navigating the decision space those rules create.
The problem begins when the solution replaces the decision
There is a point, however, at which learning a game can make it less interesting. That point is not reached merely because the player becomes skilled. It is reached when the relevant solution becomes so accessible and so universal that it replaces the act of deciding.
In Tic-Tac-Toe, once I know the small set of patterns that govern optimal play, many positions no longer ask me a meaningful question. I recognize the situation and execute the answer. If both players have reached that point, the game still functions mechanically, but much of its decision-making has disappeared. The player is no longer exploring the system; they are running a known procedure.
This distinction matters because recognizing a solution can itself be pleasurable. Finding a checkmate in chess, completing a difficult combination in a card game, or noticing the efficient sequence that makes an engine work can all feel excellent. A game does not need to prevent players from finding answers. It needs to keep generating new questions. Local solutions can reward learning while the larger system remains open enough to continue demanding judgment.
A dominant strategy creates the opposite problem. If one approach is reliably superior across a wide range of situations, players do not need to read the changing state of the game very carefully. They can repeat the same answer. What disappears is not uncertainty for its own sake, but responsiveness: the need to ask what is correct now rather than what is always correct.
Randomness can preserve uncertainty without eliminating skill
Randomness changes this relationship because it allows a player to improve their decisions without gaining control over the outcome. In Pandemic or Ticket to Ride, an experienced player can understand the system extremely well, calculate probabilities, recognize dangerous situations and identify choices that are more likely to succeed. They can get closer to a probabilistic solution while still being surprised by what happens next.
Suppose one action succeeds 75 percent of the time and every available alternative is worse. Choosing it may be the correct decision, and it may still fail. The failure does not prove that the decision was wrong, just as success does not prove that a bad decision was good. The player is learning to solve the decision under uncertainty rather than learning to predict the exact outcome.
This is one reason randomness can support mastery rather than oppose it. A beginner may experience the game as a series of unpredictable events, while an expert sees distributions, likely consequences and acceptable risks. Both players face uncertainty, but they do not understand it at the same resolution. The expert has solved more of the decision without solving the future.
Randomness is not the only way to achieve this. Hidden information, simultaneous decisions and human opponents can all keep a system responsive. The common feature is that the player cannot reduce every future situation to a fixed script before it occurs. New information continues to arrive, and good play depends on interpreting it.
A game can teach answers without running out of questions
From a design perspective, this suggests a useful way to think about depth. A deep game does not need every decision to remain mysterious forever. Players should learn. Patterns should become recognizable. Situations that once required intense thought should sometimes become almost automatic, because that feeling of increased competence is one of the rewards of repeated play.
The danger appears when learning one answer removes too large a portion of the remaining decision space. If mastering a single opening, combination or strategy allows a player to stop responding to the game, then improvement begins to collapse the experience instead of enriching it. If learning that same pattern merely gives the player another tool to apply when circumstances make it appropriate, mastery expands what they can see without making the system disappear.
This also means that replayability is not only a matter of adding more cards, scenarios or random setup. A game can vary enormously and still feel solved if the same strategic answer dominates every variation. Conversely, a game with a relatively stable set of components can remain compelling when small changes in position, timing, information or opponent behavior continually alter which answer is appropriate.
The goal is not to make a game impossible to understand. A system that never becomes clearer may simply feel arbitrary. The more interesting target is a game that rewards understanding while continuing to produce situations in which that understanding has to be interpreted rather than merely executed.
The question is not whether the game has a solution
When players say that they have “figured out” a game, they are rarely making a mathematical claim. Usually they mean that the game has stopped asking them questions they find difficult. They have found a strategy that works often enough, learned the important patterns, or reached a level at which the remaining decisions no longer feel meaningfully different from decisions they have already made.
That is why solvability alone is not a useful measure of whether a game will remain interesting. A solution can exist far beyond human reach. It can exist but require years of practice to apply. Players can solve individual situations while the overall game remains open. They can even know the statistically correct choice and still face an uncertain result.
For a designer, the more useful question is what happens as the player gets better. Does knowledge allow them to see richer decisions, or does it gradually eliminate the need to decide? Does recognizing a pattern open a new layer of play, or simply tell them which move to make from now on? Can they learn reliable principles while still needing to respond to the particular situation in front of them?
Mastery works when learning the game gives the player more understanding without giving them a script for everything that follows. A good game does not have to hide its answers forever. It has to keep giving us new problems worth solving.