There was no assumptions. It is definitionally what you said. There are only two cases to consider:
1) you reject any prior (i.e. you always say the outcome, whether hit or miss, "was not random"), in which case you are vacuously demonstrative of the fallacy or
2) your prior is the information I provided, which only points to the negative outcome, and so your conclusion, that "it was not random chance that he connected" rests exclusively on the information that he actually connected. Whereas if you actually did have information that lent credence to his ability, like seeing the "components of a swing of [his] bat" or something similar (like maybe he played behind two major leaguers in high school, and was a great hitter in middle school), then your conclusion might have been built on the prior information (and you might have been able to more correctly identify the skillful batter who missed from a non-skillful batter who connected, for example).
The fact that you need multiple trials to parse skill/competency from luck/randomness, whether it be in baseball, law, finance, or chess, means that luck is inherent in the activity. Nothing humans do is fully deterministic.
"There were no assumptions", I assume you meant .
You're looking at this bass ackwards. Being one iota deterministic is all that is required for something to be skill based. If you want to say that there is *luck* *in* a *game*, then that luck must be built into the game itself as a factor that exists regardless of the player involved and sans any application of skill by the players. When you buy Monopoly, the game comes with a pair of dice, and uses randomly shuffled cards. Those factors are what constitute luck in a game.
For chess, this only occurs in initial piece selection. If you develop a chess engine, you will use the random number generator to select white/black, and perhaps to create a fudge factor for the engine to make random mistakes, so that the engine can play at pseudo-beginner level. There's no other place for it.
There is no such thing as iota deterministic. Something is either deterministic or non-deterministic. In non-deterministic systems, luck is inherent within the system. If you cannot categorize, with a 0% false positive and 0% false negative, the relative competencies of players after a single trial, then there is definitionally luck within the act itself.
You are very close to gaining understanding with your monopoly example. In the same way that luck is built in to the roll of a dice, luck is built in to the game of chess by virtue of having to select a move. Just as how a person is not exhibiting skill when they roll a dice, a person is not necessarily exhibiting skill when they select a move. You have say a 1-in-50 chance of selecting the "correct" move in any random position. They could even choose their move by rolling a dice if that helps you imagine! Someone with no knowledge of the rules of chess could take a given position and select the correct move, whereas a GM might make an incorrect move in the same one.
By only looking at the outcome (good move vs. bad move, hit vs. miss, conviction vs. acquittal, etc.) as indicative of skill within the trial, you are being fallacious in your reasoning
There was no assumptions. It is definitionally what you said. There are only two cases to consider:
1) you reject any prior (i.e. you always say the outcome, whether hit or miss, "was not random"), in which case you are vacuously demonstrative of the fallacy or
2) your prior is the information I provided, which only points to the negative outcome, and so your conclusion, that "it was not random chance that he connected" rests exclusively on the information that he actually connected. Whereas if you actually did have information that lent credence to his ability, like seeing the "components of a swing of [his] bat" or something similar (like maybe he played behind two major leaguers in high school, and was a great hitter in middle school), then your conclusion might have been built on the prior information (and you might have been able to more correctly identify the skillful batter who missed from a non-skillful batter who connected, for example).
The fact that you need multiple trials to parse skill/competency from luck/randomness, whether it be in baseball, law, finance, or chess, means that luck is inherent in the activity. Nothing humans do is fully deterministic.
"There were no assumptions", I assume you meant
.
You're looking at this bass ackwards. Being one iota deterministic is all that is required for something to be skill based. Once a player makes any decision to make a move in the game of chess, their effort is skill based because there's no luck factor built into chess at the turn-based move level...good moves will show various skills and bad moves will show corresponding lack of skills.
If you want to say that there is *luck* *in* a *game*, then that luck must be built into the game itself as a factor that exists regardless of the player involved and sans any application of skill by the players. When you buy Monopoly, the game comes with a pair of dice, and uses randomly shuffled cards. Those factors are what constitute luck in a game.
For chess, this only occurs in initial piece selection. If you develop a chess engine, you will use the random number generator to select white/black, and perhaps to create a fudge factor for the engine to make random mistakes, so that the engine can play at pseudo-beginner level. There's no other place for it. There is no other luck in chess. A PGN encapsulates everything meaningful in a game of chess. Now show me the notation tags that denote "luck". Anything you cannot represent in a PGN is not part of the game of chess, it's just an environmental factor external to the game itself. What you ate that morning, the player that coughed at the wrong moment, the tournament pairings, your restroom break, the rollup vinyl board whose corners won't stay down...all external factors.
I'll go you one further. If 2 Super GMs exactly replay a game from 2 other GMs decades before, then that is not a new game. It's the same game. In the same way that no matter what orchestra performs Beethoven's Fifth, it's still Beethoven's Fifth.
You need to learn to see the game of chess for the logical construct that it is, and each played game as an instantiation of that construct, to understand why there's no luck in the game of chess beyond color selection.