Player Skill Relies on Probability

As for another "what is a game?" question, let's tackle the "what defines player skill?" question. To me, player skill needs probability. Without probability, the game is like chess, or scissors-paper-rock. Your skill at these games is your ability to memorize patterns, and choose the correct move based on the board layout. The old arcade game Pac Man became this, where certain patterns were used on certain board numbers. This really isn't player skill, it is memorization. You can be skilled at memorization, but not skilled at playing. Let me explain.

Take chess, and put a probability on capturing a piece. Let's say pawns capture at 50%, knights 75%, rooks 80%, and so on. Now what happens on a failed capture? You lose the attacking piece, and all of a sudden, what seemed like a certain thing is thrown into question. The player's skill is how well they can play odds, take risks, and react to unexpected losses. Skill becomes dealing with adversity, putting your pieces in a high probability situation of winning, and taking acceptable risks.

Risks. With a 100% capture chance, there is a skill in memorization and analyzing the board, but it is more of a view and memorize action that does not require a direct risk analysis. The risk analysis is "will the other player miss this pattern?" which is a memory versus memory contest, rather than "am I putting my pieces in the position of the best probability of winning?" The latter implies you are thinking tactically on the immediate moves, and strategically across many moves.

I admit, "player skill as probability reaction" is probably a controversial thing to say, especially to chess players. But we need to cut skill into these parts because it is too broadly defined in game theory. Skill at chess is reacting to situations with 100% certainty in their outcomes; skill at games with probabilities throws chaos, risk assessment, and reacting to unexpected situations into the mix. If everything says you should win this next fight, and you don't, how well do you recover? This is another measure of player skill that isn't taken into account with games where there is no random element.

So if we wanted to be fair, we could say chess relies more on "memory/analysis skill," and games with random elements may have some of the "memory/analysis" skill, but they also have a hefty amount of "risk management" skill. It's important to divide these skills in order to design a game, because you will need to ask yourself which skill do I want players to use to overcome this challenge? Is this a "power X always defeats power Y" memory challenge? Or is this a "I have a 65% chance of this working, is risking the potential loss worth it?" type question.

Know what type of player skill you are asking from your players before you design a game system or subsystem.